# data[].attributes.attachment_link.title
How ancient Egypt shaped our idea of beauty

# data[].attributes.attachment_link.description
Pop culture is steeped in images of smoky-eyed pharaohs and their queens. Were the ancient Egyptians insufferably vain – or are we simply projecting our own values onto them?

# data[].attributes.body
D'arah

# data[].attributes.attachment_link.readable_text
Ancient Egypt was a civilization that lasted from 3300 to 525 B.C.E. This is probably where the concept of health started. Some of the earliest records of medical care come from ancient Egypt.

The ancient Egyptians believed in prayer as a solution to health problems, but they also had natural, or practical, remedies, such as herbs.

It was a structured society with tools such as written language and mathematics, which enabled them to record and develop ideas, and it meant that others could learn from them.

Share on Pinterest
The ancient Egyptians had basic medical equipment, and they also believed that the gods controlled life and health. This picture shows Isis on a birthing stool,

The ancient Egyptians thought that gods, demons, and spirits played a key role in causing diseases.

Doctors believed that spirits blocked channels in the body and that this affected the way the body worked. They looked for ways to unblock these channels. They used a combination of prayer and natural - or non-spiritual - remedies.

Most healers were also priests, but, in time, the profession of a "doctor of medicine" emerged.

The fact that ancient Egyptians had systems of letters and numbers meant they were able to record and develop ideas and make calculations. Documented ancient Egyptian medical literature is among the oldest in existence today.

The ancient Egyptians had an organized economy and system of government, a settled population, social conventions, and properly enforced laws. Before this, the local people mainly lived a nomadic life.

This stability allowed medical research to develop.

In addition, there were also relatively wealthy individuals in ancient Egyptian society. They could afford some health care and also had time to ponder and study.

The ancient Egyptians were also traders. They traveled long distances, coming back with herbs and spices from faraway lands.

Research and learning

The ancient Egyptians' practice of preserving deceased people as mummies meant that they learned something about how the human body works.

In one process, the priest-doctor inserted a long, hooked implement through the nostril and broke the thin bone of the brain case to remove the brain.

Kings and queens from faraway lands sought Egyptian doctors because of their reputation for excellence.

Archaeologists have found a number of written records that describe ancient Egyptian medical practice, including the Ebers papyrus.

Share on Pinterest
The ancient Egyptians probably learned something about the human body through mummification.

This document contains over 700 remedies and magical formulas and scores of incantations aimed at repelling demons that cause disease.

The authors probably wrote them around 1500 B.C.E., but the document may contain copies of material dating back to 3400 B.C.E. They are among the oldest preserved medical documents in existence.

The scroll provides evidence of some sound scientific procedures.

Doctors appear to have had fairly good knowledge about bone structure and some awareness of how the brain and liver worked.

The heart: According to the Ebers Papyrus, the center of the body's blood supply is the heart, and every corner of the body is attached to vessels. The heart was the meeting point for vessels that carried tears, urine, semen, and blood. Researchers writing in 2014 described ancient Egyptian understanding of the cardiovascular system as "surprisingly sophisticated, if not accurate.

Mental illness: The document describes in detail the characteristics, causes, and treatment for mental disorders such as dementia and depression. The ancient Egyptians appear to have seen mental diseases as a combination of blocked channels and the influence of evil spirits and angry Gods.

Family planning: The scroll contains a section on birth control, how to tell if a person is pregnant, and some other gynecological issues.

There is also advice about:

skin problems

dental problems

diseases related to the eyes

intestinal disease

parasites

how to surgically treat an abscess or a tumor

In addition, there is evidence that doctors knew how to set broken bones and treat burns.

Medical advice

Some recommendations that physicians made then seem fairly sound to us now.

They advised people to wash and shave their bodies to prevent infections, to eat carefully, and to avoid unclean animals and raw fish.

Some, however, are less familiar. Putting a plug of crocodile dung into the entrance of the vagina, for example, was a method of birth control. People also used dung to disperse evil spirits.

Dentistry

The Egyptians also practiced dentistry. Caries and tooth decay appear to have been common.

Remedies included:

cumin, incense, and onion to treat swollen gums

opium, possibly, to treat pain pain

drilling holes into the jaw to drain an abscess

However, they do not seem to have extracted teeth.

Everyday life in Egypt involved beliefs and fear of magic, gods, demons, evils spirits, and so on. They believed that the gods created and controlled life.

Heka was the goddess of magic and medicine, while Bes, another god, protected women during pregnancy. People called upon Serket if they had a scorpion bite.

Angry gods or evil forces caused bad luck and disaster, so people used magic and religion to deal with these forces and to treat people.

Priests and doctors were often one and the same. Many healers were priests of Sekhmet, an Egyptian warrior goddess and the goddess of healing, curses, and threats.

As well as science, treatment involved the use of magic, incantations, amulets, aromas, offerings, tattoos, and statues.

The religious and magic rituals and procedures probably had a powerful placebo effect, so they may have resulted in healing.

The "channel theory" came from observing farmers who dug out irrigations channels for their crops. It allowed medicine to move from entirely spiritual cures towards practical, natural ones.

The doctors believed that, as in irrigation, channels provide the body with routes for good health. If blockages occurred, they used laxatives to unblock them.

The heart was the center of 46 channels, seen as types of tubes.

It is true that human veins, arteries, and intestines are types of tubes. However, the Egyptians did not understand that these channels had different functions.

Blockages in the human channels were thought to result from the doings of Wekhedu, an evil spirit. When Wekhedu came to the surface of the body, it showed as pus.

This idea that bodily function played a role in health was a breakthrough in the history of medicine.

Channels and the heart

The ancient Egyptians believed that the body consisted of a system of channels, or "Metu."

One researcher notes that they believed that bodily fluids could enter this system, including feces. This would have a negative effect, and enemas became an important method of treatment for many conditions, including malaria and smallpox.

The Ebers Papyrus notes that vessels run from the heart to all four limbs and every part of the body.

When a doctor, Sekmet priest, or exorcist places their hands on any part of the body, they are examining the heart, because all vessels come from the heart.

Channel theory holds that:

The heart is the source. It speaks out to each part of the body.

When people breathe in through the nose, the air enters their heart, lungs, and then the belly.

The nostrils have four vessels, two of which provide mucus and two provide blood.

The human body has four vessels, which lead to two ears. The "breath of life" enters the right ear and "breath of death" enters the left ear.

Four vessels that lead to the head cause baldness.

All eye diseases come from four vessels in the forehead, which supply blood to the eyes.

Two vessels enter the testicles and provide semen.

Two vessels in the buttocks supply them with vital nutrients.

Six vessels reach the soles of the feet and six lead down the arms to the fingers.

Two vessels supply the bladder with urine.

Four vessels supply the liver with liquid and air. When they overfill the liver with blood, they cause diseases.

Four vessels also supply the lungs and spleen with liquid and air.

The liquid and air that come out of the anus come from four vessels.

The anus is also exposed to all the vessels in the arms and legs when they overflow with waste.

Egyptian physicians underwent training and could successfully fix broken bones and dislocated joints.

Basic surgery - meaning procedures close to the surface of the skin or on the skin - was a common skill, and doctors knew how to stitch wounds effectively.

They used bandages and would bind certain plant products, such as willow leaves, into the bandages to treat inflammation.

However, they did not perform surgery deep inside the body, probably because there were no anesthetics or antiseptics.

Circumcision of baby boys was common practice. It is hard to tell whether female circumcision existed. There is one mention, but this may be a mistranslation.

Surgeons had an array of instruments, such as pincers, forceps, spoons, saws, containers with burning incense, hooks, and knives.

Prosthetics existed, but they were probably not very practical. People may have used them to make deceased people look more presentable during funerals or simply for decorative purposes.

Egyptian doctors said there were three types of injuries:

Treatable injuries: They dealt with these immediately.

Contestable injuries: The doctor believed these were not life-threatening and that the person could survive without intervention. The doctor would observe the patient. If they survived, the doctor would decide in time whether to intervene.

Untreatable ailments: The doctor would not intervene.

Common complaints included:

A remedy for headaches, mentioned in the Ebers Papyrus, appears to advise the following:

Mash together flour, incense, wood of wa, waneb plant, mint, a horn of a stag, sycamore seeds, mason's plaster, seeds of zart, water. Apply to the head.

People used aloe vera in ancient Egyptian times to heal burns and skin diseases.

Another remedy is to use poppy seeds or aloe.

Asthma: Honey and milk, sesame, frankincense

Burns and skin disease: Aloe

Pain: Thyme

Digestive problems: Juniper, mint, garlic, and sandalwood

Bad breath: Mint, caraway

Epilepsy: Camphor

Vomiting: Mint to stop it and mustard seeds to cause it

Other conditions and treatments include:

The cure for a cold was an incantation.

Early concepts of homeopathy

Some treatments used products or herbs or plants that looked similar to the illness they were treating, a practice known as simila similibus, or similar with similar.

Today, homeopathy follows a similar principle.

In Egyptian times, people used ostrich eggs to treat a fractured skull.

Cleanliness was an important part of Egyptian life, and homes had rudimentary baths and toilets. Appearance and the use of make-up were important.

The main aim was to meet social and religious requirements, although many people wore make-up around their eyes to protect them from disease.

People used mosquito nets during the hot months, whether to protect against malaria and other diseases or to avoid bites. Malaria was a common problem.

Priests washed themselves, their clothing, and their eating utensils regularly. This helped to protect their health, although they did it for religious reasons.

There was no public health infrastructure as we know of today. There were no sewage systems, systematic medical care, or public hygiene.

The ancient Egyptians were probably the first people to have professional doctors, and it was a respected occupation.

According to the Ancient History Encyclopedia, they had to be literate and clean in body and spirit. There were doctors all over Egypt.

The earliest ever record of a male physician was Hesy-Ra in 2700 B.C.E. He was was "Chief of Dentists and Doctors" to King Dioser.

The first record of a female doctor was probably Peseshet in 2400 B.C.E., the supervisor of all female doctors, but there may have been female doctors as early as 3000 B.C.E.

The top doctors worked in the royal court. Below them, inspectors would supervise the work of other doctors. There were specialists, such as dentists, proctologists, gastroenterologists, and ophthalmologists.

A proctologist - or possibly the giver of enemas - was called "nery phuyt," which translates as the "shepherd of the anus," according to an article published in the Journal of Vascular Surgery.

The ancient Egyptians had sophisticated methods of practicing medicine that combined the supernatural with the natural, such as herbal remedies and surgery.

Their written records have allowed their knowledge to pass down through the ages. While not always accurate, some of their theories and practices were not very different from those in use today.

# data[].attributes.attachment_link.title
Ancient Egyptian medicine: Influences, practice, magic, and religion

# data[].attributes.attachment_link.description
Ancient Egyptian documents are probably the earliest records of healthcare practice. The ancient Egyptians knew something about the human body and they sought healing through both herbal medicine and incantations. They also practiced basic surgery. Both male and female doctors were important. Find out more.

# data[].attributes.attachment_link.readable_text
Ancient civilizations have always held a special fascination for people, with their rich history and enthralling mysteries that transport us back in time, and they've all had their contribution at shaping the world as we know it today. But out of all ancient civilizations known to humankind, the ancient Egyptians are probably the ones that capture our imagination the most.

However, there's more to ancient Egypt than the amazing stories we hear about the pharaohs and the dynasties that have ruled the land of sand and pyramids for thousands of years. Egyptians left us a valuable legacy through their inventions and discoveries that changed the course of history and led to the development of the modern world. So, let's take a trip through Egypt's history and explore the most notable creations that ancient Egyptians gave us.
Medical science
Ancient Egyptians were quite knowledgeable when it came to understanding different ailments and they were quite skilled at treating them as well. Several medical texts have been discovered, describing medical procedures and recipes in great detail. They used herbs and animal parts to cure wounds and other health issues, so they didn't rely on magical powers or unearthly forces to ensure their good health and wellbeing. But what's even more impressive is that they also performed surgeries. The bronze surgical tools and the papyrus logs that have been discovered stand proof of their advanced medical skills, so Egyptians can be considered the precursors to modern medicine.
Mathematics
Egyptians were also great mathematicians, knowing how to perform calculations such as additions, subtractions, multiplications and divisions in effective ways, and there's evidence proving they were the first to come up with the concept of basic fractions. They also had knowledge in geometry and they made use of these skills to help them take accurate measurements and build their impressive monuments. Just think about the Great Pyramids and the level of mathematical and geometrical knowledge this civilization had to possess in order to build such massive structures.
Written language
Although the Egyptian alphabet is no longer in use today, they were the first civilization to use symbols to represent individual sounds, thus developing written language. Egyptians initially used hieroglyphs to express their ideas in written form, but over the course of time they invented 24 alphabets. They also took one step further by leaving behind the common practice of carving these symbols into stone and started using papyrus for their writings, crafted from the plant with the same name that grew on the banks of Nile. This inspired other civilizations to develop similar materials such as parchments and then the Chinese finally invented the paper in 100 BC.
Art and architecture
It's quite obvious that ancient Egyptians excelled in both art and architecture. Numerous structures and art pieces have stood the test of time and still amaze us today with their beauty and intricacy. It remains a mystery how such an ancient civilization could create these mesmerizing monuments. Archaeologists have discovered countless art pieces from different dynasties which make the object of fasciation to this day. So much so that people even try to replicate the style and artistry of ancient Egyptians, searching for Egyptian antiquities for sale to decorate their homes and bring an unique accent to their space.
Makeup and wigs
In ancient Egypt, both men and women were equally interested in makeup and enhancing their physical appearance. For them, beauty was related to sacredness, and people from all classes indulged in the art of makeup. We all know the stories about queen Cleopatra's ravishing beauty, so for Egyptians outward appearance was a matter of no small importance. Women from upper classes would use creams and powders to make their skin look lighter, but the most popular beauty trend was of course the use of heavy eye makeup. Egyptians would use either grepond eye-paint or black kohl to contour their eyes. Another widespread beauty trend in ancient Egypt was wearing wigs. It was a sign of nobility as most nobles would shave their heads and cover their heads with wigs made from natural hair.
The calendar
The Egyptian calendar is amongst the first dating systems known to mankind. The Egyptians who were skilled astronomers discovered the lunar year and created a calendar based on the phases of the moon, but they later introduced a civil calendar that very much resembles the one we use today. According to the Egyptian civil calendar, the year had 365 days and consisted of three seasons of 120 days each. The seasons would have four months of 30 days and at the end of each year there would be 5 epagomenal days added. So, we can all thank ancient Egyptians for forming the basis of the modern-day calendar.
Keep up with the top stories from Reader's Digest by subscribing to our weekly newsletter.

# data[].attributes.attachment_link.title
How ancient Egyptian civilization influenced the modern world - Reader's Digest

# data[].attributes.attachment_link.description
Ancient civilizations have always held a special fascination for people, with their rich history and enthralling mysteries that transport us back in time, and they’ve all had their contribution at shaping the world as we know it today. But out of all ancient civilizations known to humankind, the ancient Egyptians are probably the ones that capture our imagination the most.

# data[].attributes.attachment_link.readable_text
Medical practice in ancient Egypt was so advanced that many of their observations, policies, and commonplace procedures would not be surpassed in the west for centuries after the fall of Rome and their practices would inform both Greek and Roman medicine. They understood that disease could be treated by pharmaceuticals, recognized the healing potential in massage and aromas, had male and female doctors who specialized in certain specific areas, and understood the importance of cleanliness in treating patients.

In the modern day it is recognized that disease and infection can be caused by germs and one might think people have always believed so but this is a relatively late innovation in human understanding. It was not until the 19th century CE that the germ theory of disease was confirmed by Louis Pasteur and proven by the work of British surgeon Joseph Lister.

Before either of them, the Hungarian physician Ignaz Semmelweis (1818-1865 CE) offered the then outlandish proposal to the medical community that they could cut mortality rates in their practices simply by washing their hands. He was mocked by doctors, who saw no reason to wash their hands before even the most invasive surgical procedures, and grew increasingly frustrated and bitter. Semmelweis was committed to a mental institution in 1865 CE where he died, after being severely beaten by guards, for suggesting a practice recognized as common sense today.

The mortality rate following medical procedures in ancient Egypt was probably less than that of any European hospital in the Christian era until the mid-20th century CE.

The ancient Egyptians would have accepted Semmelweis' proposal without hesitation; not because they understood the concept of germs, but because they valued cleanliness. The mortality rate following medical procedures in ancient Egypt was probably less than that of any European hospital in the Christian era until the mid-20th century CE when personal cleanliness and the sterilization of instruments became common practice.

Egyptologist Barbara Watterson notes that " medicine in ancient Egypt was relatively advanced and Egyptian doctors, who were all, with one or two exceptions, male, were skilled (46). Even so, for a civilization which regularly dissected the dead for embalming, doctors had little understanding of how most of the internal organs worked and blamed disease on supernatural forces.

Injury & Disease

Injuries were easy to understand in ancient Egypt; disease was a bit more difficult. When someone was injured there was a plain cause and an effect which could then be treated; when a person was sick, however, the cause was less clear and so diagnosis more problematic.

Sign up for our free weekly email newsletter!

The cause of disease was usually understood as the consequence of sin and, when that seemed not the case, that the patient was under a demonic attack, was being plagued by an angry ghost, or that some god felt they needed to learn a lesson. Disease, therefore, was commonly treated through recitation by a doctor of magical spells. Watterson notes, "the earliest 'doctor' was a magician, for the Egyptians believed that disease and sickness were caused by an evil force entering the body" (65).

The types of diseases Egyptians suffered from were as numerous and varied as they are in the present day and included bilharsiasis (a disease contracted and spread through contaminated water); trachoma (an infection of the eye); malaria; dysentery; smallpox; pneumonia; cancer; heart disease; dementia; typhoid; arthritis; high blood pressure; bronchitis; tuberculosis; appendicitis; kidney stones; liver disease; curvature of the spine; the common cold, and ovarian cysts.

Besides magical spells, ancient Egyptians used incantations, amulets, offerings, aromas, tattoos, and statuary to either drive away the ghost or demon, placate the god or gods who had sent the illness, or invoke protection from a higher power as a preventative. The spells and incantations were written down on papyrus scrolls which became the medical texts of the day.

The Medical Texts

Although there were no doubt many more texts available in ancient Egypt, only a few have survived to the present. These few, however, provide a wealth of information on how the Egyptians saw disease and what they believed would alleviate a patient's symptoms or lead to a cure. They are named for the individual who owned them or the institution which houses them. All of them, to greater or lesser degrees, rely on sympathetic magic as well as practical technique.

The Chester Beatty Medical Papyrus, dated c. 1200 BCE, prescribes treatment for anorectal disease (problems associated with the anus and rectum) and prescribes cannabis for cancer patients (pre-dating the mention of cannabis in Herodotus, long thought to be the earliest mention of the drug). The Berlin Medical Papyrus (also known as the Brugsch Papyrus, dated to the New Kingdom, c. 1570 - c. 1069 BCE) deals with contraception, fertility, and includes the earliest known pregnancy tests. The Ebers Papyrus (c. 1550 BCE) treats cancer (for which, it says, there is no treatment), heart disease, diabetes, birth control, and depression. The Edwin Smith Papyrus (c. 1600 BCE) is the oldest work on surgical techniques. The Demotic Magical Papyrus of London and Leiden (c. 3rd century CE) is devoted entirely to magical spells and divination. The Hearst Medical Papyrus (dated to the New Kingdom) treats urinary tract infections and digestive problems. The Kahun Gynaecological Papyrus (c. 1800 BCE) deals with conception and pregnancy issues as well as contraception. The London Medical Papyrus (c. 1782-1570 BCE) offers prescriptions for issues related to the eyes, skin, burns, and pregnancy. These are only the papyrii recognized as focusing entirely on medicine. There are many more which touch on the subject but are not generally accepted as medical texts.

All of these works, at one time or another, were consulted by practicing doctors who routinely made house calls. The Egyptians called the science of medicine the "necessary art" for obvious reasons. Doctors were considered priests of the , the House of Life, a kind of library/school attached to a temple, but the concept of the 'house of life' was also considered the healing knowledge of the individual doctors.

Doctors, Midwives, Nurses, & Dentists

Physicians in ancient Egypt could be male or female. The "first physician", later deified as a god of medicine and healing, was the architect Imhotep (c. 2667-2600 BCE) best known for designing the Step Pyramid of Djoser at Saqqara. Imhotep is also remembered for initiating "secular medicine" through his treatises arguing that disease occurred naturally and was not a punishment from the gods. Women in the medical profession in Egypt go back to the Early Dynastic Period when Merit-Ptah was the royal court's chief physician c. 2700 BCE. Merit-Ptah is the first female doctor known by name in world history but evidence suggests a medical school at the Temple of Neith in Sais in Lower Egypt run by a woman whose name is unknown c. 3000 BCE.

Pesehet (c. 2500 BCE), another female physician often cited as the first, was the "Lady Overseer of Female Physicians", possibly associated with the school at Sais, attesting to the presence of women in medical practice at this time. The famous legend of Agnodice of Athens (c. 4th century BCE) relates how, denied entrance to the medical profession because she was a woman, she went to Egypt where women were respected in the field. How and where doctors received their training is not known although it has been established there was an important school in Alexandria as well as the one at Sais.

A doctor not only needed to be literate but also pure in body and spirit. Doctors were referred to as wabau, ritually pure, and were expected to bathe as frequently and carefully as a high priest. Each doctor had his or her speciality but there were also swnw, general practitioners, and sau, whose speciality was in the use of magic. Midwives, masseurs, nurses, attendants, and seers also assisted the doctor. Doctors are not thought to have had anything to do with births, however, which were handled entirely by midwives and the women of the house. Egyptologist Carolyn Graves-Brown writes:

Midwifery appears to have been a solely female profession in ancient Egypt. That this was so is suggested by medical texts, which include gynaecological information, but do not discuss obstetrics. Additionally, men are never shown in birthing scenes, and in the Papyrus Westcar, the mother is assisted in birth by four goddesses. (82)

There is no evidence for medical training of midwives. In the Old Kingdom the word for 'midwife' is associated with the word for 'nurse', one who assisted a doctor, but this association ends after that period. Midwives could be female relatives, friends, or neighbors and do not seem to have been regarded as medical professionals.

The nurse could be female or male and was a highly respected medical professional although, as with midwives, there is no evidence of a school or professional training. The most essential kind of nurse was the wet nurse. Graves-Brown notes, "with the probable likelihood of high mortality of mothers, wet nurses would have been particularly important" (83). Women regularly died in childbirth and legal documents show agreements between wet nurses and families to care for the newborn in the event of the mother's death. The dry nurse, who would assist in procedures, was accorded such respect that he or she was represented during the time of the New Kingdom as linked with the divine. The association of the nurse with the doctor seems well established but not so much their link with the dentist.

Dentistry grew out of the established medical profession but never developed as widely. The ancient Egyptians suffered from dental problems throughout the entire history of the civilization so why dentists were not more plentiful, or better documented, is unclear. Doctors also practiced dentistry but there were dentists as far back as the Early Dynastic Period. The first dentist known by name in the world, in fact, is Hesyre (c. 2600 BCE), Chief of Dentists and Physician to the King under the reign of Djoser (c. 2700 BCE). Dental problems were especially prevalent owing to the Egyptian diet of coarse bread and their inability to keep sand out of their food. Egyptologist and historian Margaret Bunson writes:

Egyptians of all eras had terrible teeth and peridontal problems. By the New Kingdom, however, dental decay was critical. Physicians packed some teeth with honey and herbs, perhaps to stem infection or to ease pain. Some mummies were also provided with bridges and gold teeth. It is not known if these dental materials were used by the wearer while alive or inserted in the embalming process. (158)

Queen Hatshepsut (1479-1458 BCE) of the New Kingdom died from an abscessed tooth as did many others. Toothaches and dental problems were thought to be caused by a tooth-worm which needed to be driven out by magical spells and incantations. This belief no doubt originated in Mesopotamia, specifically Sumer, where incantations against the tooth-worm have been found in ancient cuneiform inscriptions.

Healing Gods, Medicines, & Implements

As with doctors, dentists used magical incantations to drive the tooth-worm from the patient and then applied what medicines they had to ease the pain. Doctors and dentists frequently used herbs and spices medicinally. A cure for chronic bad breath, for example, was chewing a gum ball of honey, cinnamon, myrrh, frankincense, and pignon. There is evidence of tooth extraction and false teeth with opium used as an anaesthetic. The importance of diet was recognized and changes in one's diet for improved health were suggested. Practical, hands-on, remedies were always applied first in cases of obvious physical injury but with toothaches or gum disease, as with any disease, a supernatural cause was assumed.

A belief in magic was deeply ingrained in the Egyptian culture and was considered as natural and normal as any other aspect of existence. The god of magic was also a god of medicine, Heka, who carried a staff entwined with two serpents. This symbol was passed on to the Greeks who associated it with their god of healing, Asclepius, and which is recognizable today as the caduceus of the medical profession. Although the caduceus no doubt traveled from Egypt to Greece it originated in Sumer as the staff of Ninazu, son of the Sumerian goddess of healing Gula.

Besides Heka, there were a number of other important healing deities such as Sekhmet, Serket (also known as Selket), Sobek, and Nefertum. The priests of Serket were all doctors, though not every doctor was a member of her cult. Serket and Sekhmet were regularly invoked in magical spells and incantations along with Heka and, in certain cases, other deities such as Bes or Tawawret (usually dealing with fertility/children's diseases). Sobek, the crocodile god, seems to have been largely invoked for surgeries and invasive procedures. Nefertum, the god of perfumes associated with the lotus and healing, was invoked in procedures which today would be recognized as aromatherapy. In the Kahun Papyrus a course regularly prescribed for women is to fumigate them with incense to drive out an evil spirit and Nefertum would have been called upon in these instances.

Along with spells and incantations, the Egyptian doctors used naturally occurring herbs and spices as well as their own creations. Bunson writes:

The pharmaceuticals of the ancient Egyptian priest-physicians included antacids, copper salts, turpentine, alum, astringents, alkaline laxatives, diuretics, sedatives, antispasmodics, calcium carbonates, and magnesia. They also employed many exotic herbs. All dispensing of medicines carefully stipulated in the medical papyri, with explicit instructions as to the exact dosage, the manner in which the medicine was to be taken internally (as with wine or food), and external applications. (158)

Surgical procedures were common and many instruments have been identified which are still in use today. The Egyptians had a flint and a metal scalpel, dental pliers, a bone saw, probes, the catheter, clamps for stopping blood flow, specula, forceps, lancets for opening veins, sponges, scissors, phials, bandages of linen, and scales for weighing the proper amount of raw materials to mix for medicines. Surgeries were frequently successful as evidenced by mummies and other remains found who survived amputations and even brain surgery for years. Prosthetic limbs, made usually of wood, have also been found.

Conclusion

Not all of the medical practices in Egypt were so successful, however. Circumcision was a religious ritual performed on boys between the ages of 10 and 14 marking the transition from adolescence to manhood. It was performed by a doctor who also served as a temple priest, using a flint blade and reciting incantations, but in spite of their precautions this procedure still sometimes resulted in infection. Since the nature of the infection was unknown to them, it was considered the result of a supernatural influence and dealt with through magic spells; this most likely resulted in the deaths of many young men.

Because of their belief in the womb as connected to all parts of a woman's body, fumigation of the womb was a common prescription, accompanied by incantations, which would miss the actual cause of the problem. Eye problems were treated with a dose of bat's blood because it was thought the night-vision of the bat would be transferred to the patient; no evidence suggests this was effective.

Although the embalmers of Egypt no doubt came to understand how the organs they removed from the body worked with each other, this knowledge was never shared with doctors. These two professions moved in completely different spheres and what each did within their own job description was not considered relevant to the other. It is for this reason that, even though the Egyptians had the means of exploring internal medicine, they never did.

The heart, though recognized as a pump, was also thought to be the center of emotion, personality, and intellect; the heart was preserved in the deceased while the brain was scraped out and discarded as worthless. Although they recognized liver disease they had no understanding of the function of the liver and while regularly dealing with miscarriages and infertility, had no understanding of obstetrics. The culture's reliance on supernatural assistance from the gods prevented them from exploring more immediate and practical solutions to the medical problems they encountered daily.

Still, the Egyptian physician was widely respected for their skill and knowledge and was called upon by the kings and nobility of other nations. The Greeks especially admired the Egyptian medical profession and adopted a number of their beliefs and techniques. Later famous physicians of Rome and Greece - like Galen and Hippocrates ("father of modern medicine") - studied the Egyptian texts and symbols and so passed down the traditions to the present day.

# data[].attributes.attachment_link.description
Medical practice in ancient Egypt was so advanced that many of their observations, policies, and commonplace procedures would not be surpassed in the west for centuries after the fall of Rome and their practices would inform both Greek and Roman medicine.

# data[].attributes.attachment_link.title
How Ancient Egypt Shaped the Modern World [Infographic]

# data[].attributes.attachment_link.description
The knowledge of ancient Egyptian civilization not only had a powerful impact on other early civilizations but also helped on shaping our modern world.

# data[].attributes.attachment_link.readable_text
Tombs

The first royal tombs, called mastabas, were built at Abydos during the first and second dynasties. They were marked with a stele inscribed with the kings' names. The burial chambers were cut into the rock, lined with sun-baked bricks and faced with wooden boards that have long since disappeared. Beside the chambers were rooms containing jars, small objects, and offerings of food and drink. The tombs were surrounded by a large number of graves of women and dwarves. These people may have been servants of the kings who were sacrificed to serve them in their afterlife.

Pyramids were built as royal burials until 1640 B.C. The most famous is the Great Pyramid at Giza. To prevent robbery, the kings, queens and nobles of the New Kingdom built their tombs in a remote valley west of the Theban capital known as the Valley of the Kings. The tombs of Egypt are one of the greatest tourist attractions in the world. They are indeed a world treasure!

main menu | civilization | architecture

# data[].attributes.attachment_link.title
Egyptian civilization - Architecture - Tombs

# data[].attributes.attachment_link.description
Tombs The first royal tombs, called mastabas, were built at Abydos during the first and second dynasties. They were marked with a stele inscribed with the kings' names. The burial chambers were cut into the rock, lined with sun-baked bricks and faced with wooden boards that have long since disappeared.

# data[].attributes.attachment_link.readable_text
They made great contributions to modern mathematics. They discovered decimals, fractions, the number zero, negative numbers and even the value of Pi. They had an understanding of solid geometry and used it in their construction.

The ancient Egyptian number system was composed of 7 symbols - a single stroke, a heel bone (upside-down smile), a coil of rope, a lotus plant, a finger, a frog, and a kneeling god.

With these 7 symbols, the clever Egyptians could add, subtract, multiple, and divide and count into the many millions! They even created a system of algebra, which helped them build the pyramids.

Take a look! Click on the links below to try your hand at math the ancient Egyptian way.
Math Cats - The ancient Egyptian way to write fractions Ancient Egyptian Math

# data[].attributes.attachment_link.title
Ancient Egypt for Kids - Ancient Math - Ancient Egypt for Kids

# data[].attributes.attachment_link.description
They made great contributions to modern mathematics. They discovered decimals, fractions, the number zero, negative numbers and even the value of Pi. They had an understanding of solid geometry and used it in their construction.

# data[].attributes.body
Mitch

# data[].attributes.attachment_link.readable_text
Ancient Egypt was a civilization that lasted from 3300 to 525 B.C.E. This is probably where the concept of health started. Some of the earliest records of medical care come from ancient Egypt.

The ancient Egyptians believed in prayer as a solution to health problems, but they also had natural, or practical, remedies, such as herbs.

It was a structured society with tools such as written language and mathematics, which enabled them to record and develop ideas, and it meant that others could learn from them.

Share on Pinterest
The ancient Egyptians had basic medical equipment, and they also believed that the gods controlled life and health. This picture shows Isis on a birthing stool,

The ancient Egyptians thought that gods, demons, and spirits played a key role in causing diseases.

Doctors believed that spirits blocked channels in the body and that this affected the way the body worked. They looked for ways to unblock these channels. They used a combination of prayer and natural - or non-spiritual - remedies.

Most healers were also priests, but, in time, the profession of a "doctor of medicine" emerged.

The fact that ancient Egyptians had systems of letters and numbers meant they were able to record and develop ideas and make calculations. Documented ancient Egyptian medical literature is among the oldest in existence today.

The ancient Egyptians had an organized economy and system of government, a settled population, social conventions, and properly enforced laws. Before this, the local people mainly lived a nomadic life.

This stability allowed medical research to develop.

In addition, there were also relatively wealthy individuals in ancient Egyptian society. They could afford some health care and also had time to ponder and study.

The ancient Egyptians were also traders. They traveled long distances, coming back with herbs and spices from faraway lands.

Research and learning

The ancient Egyptians' practice of preserving deceased people as mummies meant that they learned something about how the human body works.

In one process, the priest-doctor inserted a long, hooked implement through the nostril and broke the thin bone of the brain case to remove the brain.

Kings and queens from faraway lands sought Egyptian doctors because of their reputation for excellence.

Archaeologists have found a number of written records that describe ancient Egyptian medical practice, including the Ebers papyrus.

Share on Pinterest
The ancient Egyptians probably learned something about the human body through mummification.

This document contains over 700 remedies and magical formulas and scores of incantations aimed at repelling demons that cause disease.

The authors probably wrote them around 1500 B.C.E., but the document may contain copies of material dating back to 3400 B.C.E. They are among the oldest preserved medical documents in existence.

The scroll provides evidence of some sound scientific procedures.

Doctors appear to have had fairly good knowledge about bone structure and some awareness of how the brain and liver worked.

The heart: According to the Ebers Papyrus, the center of the body's blood supply is the heart, and every corner of the body is attached to vessels. The heart was the meeting point for vessels that carried tears, urine, semen, and blood. Researchers writing in 2014 described ancient Egyptian understanding of the cardiovascular system as "surprisingly sophisticated, if not accurate.

Mental illness: The document describes in detail the characteristics, causes, and treatment for mental disorders such as dementia and depression. The ancient Egyptians appear to have seen mental diseases as a combination of blocked channels and the influence of evil spirits and angry Gods.

Family planning: The scroll contains a section on birth control, how to tell if a person is pregnant, and some other gynecological issues.

There is also advice about:

skin problems

dental problems

diseases related to the eyes

intestinal disease

parasites

how to surgically treat an abscess or a tumor

In addition, there is evidence that doctors knew how to set broken bones and treat burns.

Medical advice

Some recommendations that physicians made then seem fairly sound to us now.

They advised people to wash and shave their bodies to prevent infections, to eat carefully, and to avoid unclean animals and raw fish.

Some, however, are less familiar. Putting a plug of crocodile dung into the entrance of the vagina, for example, was a method of birth control. People also used dung to disperse evil spirits.

Dentistry

The Egyptians also practiced dentistry. Caries and tooth decay appear to have been common.

Remedies included:

cumin, incense, and onion to treat swollen gums

opium, possibly, to treat pain pain

drilling holes into the jaw to drain an abscess

However, they do not seem to have extracted teeth.

Everyday life in Egypt involved beliefs and fear of magic, gods, demons, evils spirits, and so on. They believed that the gods created and controlled life.

Heka was the goddess of magic and medicine, while Bes, another god, protected women during pregnancy. People called upon Serket if they had a scorpion bite.

Angry gods or evil forces caused bad luck and disaster, so people used magic and religion to deal with these forces and to treat people.

Priests and doctors were often one and the same. Many healers were priests of Sekhmet, an Egyptian warrior goddess and the goddess of healing, curses, and threats.

As well as science, treatment involved the use of magic, incantations, amulets, aromas, offerings, tattoos, and statues.

The religious and magic rituals and procedures probably had a powerful placebo effect, so they may have resulted in healing.

The "channel theory" came from observing farmers who dug out irrigations channels for their crops. It allowed medicine to move from entirely spiritual cures towards practical, natural ones.

The doctors believed that, as in irrigation, channels provide the body with routes for good health. If blockages occurred, they used laxatives to unblock them.

The heart was the center of 46 channels, seen as types of tubes.

It is true that human veins, arteries, and intestines are types of tubes. However, the Egyptians did not understand that these channels had different functions.

Blockages in the human channels were thought to result from the doings of Wekhedu, an evil spirit. When Wekhedu came to the surface of the body, it showed as pus.

This idea that bodily function played a role in health was a breakthrough in the history of medicine.

Channels and the heart

The ancient Egyptians believed that the body consisted of a system of channels, or "Metu."

One researcher notes that they believed that bodily fluids could enter this system, including feces. This would have a negative effect, and enemas became an important method of treatment for many conditions, including malaria and smallpox.

The Ebers Papyrus notes that vessels run from the heart to all four limbs and every part of the body.

When a doctor, Sekmet priest, or exorcist places their hands on any part of the body, they are examining the heart, because all vessels come from the heart.

Channel theory holds that:

The heart is the source. It speaks out to each part of the body.

When people breathe in through the nose, the air enters their heart, lungs, and then the belly.

The nostrils have four vessels, two of which provide mucus and two provide blood.

The human body has four vessels, which lead to two ears. The "breath of life" enters the right ear and "breath of death" enters the left ear.

Four vessels that lead to the head cause baldness.

All eye diseases come from four vessels in the forehead, which supply blood to the eyes.

Two vessels enter the testicles and provide semen.

Two vessels in the buttocks supply them with vital nutrients.

Six vessels reach the soles of the feet and six lead down the arms to the fingers.

Two vessels supply the bladder with urine.

Four vessels supply the liver with liquid and air. When they overfill the liver with blood, they cause diseases.

Four vessels also supply the lungs and spleen with liquid and air.

The liquid and air that come out of the anus come from four vessels.

The anus is also exposed to all the vessels in the arms and legs when they overflow with waste.

Egyptian physicians underwent training and could successfully fix broken bones and dislocated joints.

Basic surgery - meaning procedures close to the surface of the skin or on the skin - was a common skill, and doctors knew how to stitch wounds effectively.

They used bandages and would bind certain plant products, such as willow leaves, into the bandages to treat inflammation.

However, they did not perform surgery deep inside the body, probably because there were no anesthetics or antiseptics.

Circumcision of baby boys was common practice. It is hard to tell whether female circumcision existed. There is one mention, but this may be a mistranslation.

Surgeons had an array of instruments, such as pincers, forceps, spoons, saws, containers with burning incense, hooks, and knives.

Prosthetics existed, but they were probably not very practical. People may have used them to make deceased people look more presentable during funerals or simply for decorative purposes.

Egyptian doctors said there were three types of injuries:

Treatable injuries: They dealt with these immediately.

Contestable injuries: The doctor believed these were not life-threatening and that the person could survive without intervention. The doctor would observe the patient. If they survived, the doctor would decide in time whether to intervene.

Untreatable ailments: The doctor would not intervene.

Common complaints included:

A remedy for headaches, mentioned in the Ebers Papyrus, appears to advise the following:

Mash together flour, incense, wood of wa, waneb plant, mint, a horn of a stag, sycamore seeds, mason's plaster, seeds of zart, water. Apply to the head.

People used aloe vera in ancient Egyptian times to heal burns and skin diseases.

Another remedy is to use poppy seeds or aloe.

Asthma: Honey and milk, sesame, frankincense

Burns and skin disease: Aloe

Pain: Thyme

Digestive problems: Juniper, mint, garlic, and sandalwood

Bad breath: Mint, caraway

Epilepsy: Camphor

Vomiting: Mint to stop it and mustard seeds to cause it

Other conditions and treatments include:

The cure for a cold was an incantation.

Early concepts of homeopathy

Some treatments used products or herbs or plants that looked similar to the illness they were treating, a practice known as simila similibus, or similar with similar.

Today, homeopathy follows a similar principle.

In Egyptian times, people used ostrich eggs to treat a fractured skull.

Cleanliness was an important part of Egyptian life, and homes had rudimentary baths and toilets. Appearance and the use of make-up were important.

The main aim was to meet social and religious requirements, although many people wore make-up around their eyes to protect them from disease.

People used mosquito nets during the hot months, whether to protect against malaria and other diseases or to avoid bites. Malaria was a common problem.

Priests washed themselves, their clothing, and their eating utensils regularly. This helped to protect their health, although they did it for religious reasons.

There was no public health infrastructure as we know of today. There were no sewage systems, systematic medical care, or public hygiene.

The ancient Egyptians were probably the first people to have professional doctors, and it was a respected occupation.

According to the Ancient History Encyclopedia, they had to be literate and clean in body and spirit. There were doctors all over Egypt.

The earliest ever record of a male physician was Hesy-Ra in 2700 B.C.E. He was was "Chief of Dentists and Doctors" to King Dioser.

The first record of a female doctor was probably Peseshet in 2400 B.C.E., the supervisor of all female doctors, but there may have been female doctors as early as 3000 B.C.E.

The top doctors worked in the royal court. Below them, inspectors would supervise the work of other doctors. There were specialists, such as dentists, proctologists, gastroenterologists, and ophthalmologists.

A proctologist - or possibly the giver of enemas - was called "nery phuyt," which translates as the "shepherd of the anus," according to an article published in the Journal of Vascular Surgery.

The ancient Egyptians had sophisticated methods of practicing medicine that combined the supernatural with the natural, such as herbal remedies and surgery.

Their written records have allowed their knowledge to pass down through the ages. While not always accurate, some of their theories and practices were not very different from those in use today.

# data[].attributes.attachment_link.title
Ancient Egyptian medicine: Influences, practice, magic, and religion

# data[].attributes.attachment_link.description
Ancient Egyptian documents are probably the earliest records of healthcare practice. The ancient Egyptians knew something about the human body and they sought healing through both herbal medicine and incantations. They also practiced basic surgery. Both male and female doctors were important. Find out more.

# data[].attributes.attachment_link.readable_text
THE FRACTION TWO-THIRDS TABLES FOR THE ADDITION OF UNIT FRACTIONS, AND THE G RULE AN INTERESTING OSTRACON THE SCRIBAL RULE FOR RECIPROCALS DEMOTIC MATHEMATICAL PAPYRI AN INTERPRETATION OF RMP 79 PESU PROBLEMS EGYPTIAN MEASURES BIBILOGRAPHY ADDITIONAL BIBLIOGRAPHICAL NOTES R. J. Gillings
When one refers to mathematics in the time of the pharaohs, the significance of the word "mathematics" inevitably comes into consideration. In the long period of ancient Egypt, some three millennia, mathematics meant first arithmetic, then some elementary geometry, then varied problems that by modern standards had an algebraic flavor. The historian would be wise not to judge too hastily the very few genuinely mathematical papyri and ostraca that have come down to us, by making critical comparisons with the more numerous and detailed works of the Greeks, which have been known and studied for over two thousand years. Pharaonic mathematics has been available to the student and the historian for barely a century, although it originated nearly four thousand years ago. One had to wait for a Champollion and a Rosetta Stone before interpretation of hieroglyphs, and the cursive hieratic writing and numbers, became possible. When it appeared that Egyptian arithmetic was based solely upon a complete knowledge of the "two-times" table and an ability to find two-thirds of any number, integral or fractional; that their geometry dealt almost wholly with areas and volumes; and that problems were solved by a kind of literal algebraic reasoning, the question arose whether this can be called mathematics.

It is a matter of semantics; and to help resolve it, one should note what Ernst Mach wrote in 1898: "There is no problem in all mathematics that cannot be solved by direct counting, but with present implements, many operations can be performed in a few minutes, which without mathematical methods, would take a lifetime." And Comte wrote: "There is no inquiry which is not finally reducible to a question of numbers." Acceptance of these statements would perhaps justify saying that Egyptians at the time of the pharaohs did have mathematics, in their own particular way.

Of all the ancient papyri and ostraca that have been recovered from ancient Egypt and are preserved in universities, museums, and other institutions, relatively few are of a mathematical nature. About a dozen of these, often referred to in a study of the history of mathematics, are briefly listed below, not in order of their importance but alphabetically, with their abbreviations that will be used throughout the essay. More detail regarding these papyri will be found following the bibliographical notes.
THE FOUR OPERATIONS
Addition . Modern arithmetic books give special techniques for addition, subtraction, multiplication, and division. Combinations like 3 + 5 = 8 and 2 + 7 = 9 are taught first by simple counting, and then they are memorized; at the same time the

subtractive operations of 8 - 5 = 3 and 9 - 7 = 2, being related, are also learned. Subtraction of large numbers is taught in several different ways, however, such as the "borrow and pay back" method or the "equal additions" method. For multiplication and division, the present technique is that all multiplication tables must be learned by heart up to that for twelve -a time-consuming operation for students, many of whom never really learn them.

We are to examine the probable techniques of the Egyptian scribes for the four operations with their hieratic notation, which, although it was based on a decimal system, is still unlike our modern Hindu-Arabic form. Many historians have glossed over considerations of how the ancient scribes performed any of the four operations, with statements like the following: "Addition is simple counting. Subtraction is merely counting backwards. Multiplication is a special form of counting, and division is the reverse of multiplication." How easy it all sounds! "People who could count beyond a million had no difficulty about the addition and subtraction of whole numbers." But they did, and we still do, which explains the invention of the abacus and desk computers. "For ordinary additions and subtractions, nothing needs be said." Oh, but it does!

The proper alignment of digits in their correct columns was not so necessary to the Egyptian scribes as it is to us, because the hieratic sign for (say) three units was , for three tens it was , and for three hundreds it was -symbols that are quite different. The scribe would therefore know at once not to add units to hundreds merely because they appeared to be in the same column. Nevertheless, all these additions need careful attention, especially the last; and to say that "there are no difficulties about addition and subtraction,"and leave it at that, is clearly evading the issue.

Many tables for the addition of fractions have come down to us, notably the EMLR. These will be considered in a separate section.

Subtraction . Tables for the addition of integers at least up to 10, and possibly further, prepared by simple counting, were most surely available, although none has come down to us in the papyri. Such tables would be equally useful for subtraction, for the scribe did not say "Subtract 5 from 8"or "Subtract 7 from 9,"but "5, how many to make

8 "and" 7, how many to make 9 "Thus we find in MMP9," Complete thou the excess of these 10 over these 4. Result 6."And in KP LV, 4. "Make thou the excess of 100 over 45. The result thereof is 55."

Subtraction of unit fractions was done in the same way; and in this case tables of the addition of fractions have certainly come down to us, the best example of which is the EMLR. Examples of such subtractions, taken from the Recto of the RMP, are given below.

Consider the subtrahend of the last subtraction. To it add

In the RMP Recto there are more than twenty such subtractions, some much more complicated than those shown here; but in no case is the working shown. Only the answer is written, and there are no errors.

Multiplication . This process was done by repeated multiplications of 2, and a thorough knowledge of the "two-times"table was all that the scribal arithmetician required. Preferred or favored multipliers were 3, 7, 15, 31, 63,· · ·. Thus, to multiply 29 by 7, the scribe proceeded as shown below.

The sums of terms of the series 1, 2, 4, 8, 16, · · · produce, in order, the totals 3, 7, 15, 31, 63, · · ·, which, if they are used as multipliers, means that every number in the second column is included in the final addition. The scribes early found, however, that any multiplier at all could be expressed uniquely as the sum of certain terms of this geometrical progression, a minor difficulty being to locate which terms these were. Thus, suppose that the multiplier of 29 was 21 instead of 7.

The scribe located the numbers in the first column that totaled 21 in one way only - 1 + 4 + 16 = 21-and placed a check mark alongside them, indicating that the product was the sum of the corresponding numbers in the second column: 29 + 116 + 464 = 609. This particular property of the progression 1, 2, 4, 8, 16, ... is nowhere referred to in any Egyptian papyri known to me; but there are various other properties of both arithmetical and geometrical progressions that arise in certain problems and will be considered later.

Sometimes other multipliers were used, such as 10. which meant that the hieratic digits of the multiplicand were merely rewritten, the units as tens. the tens as hundreds, and so on, since the notation is of course a decimal one. The multiplier 1/10 was used in a similar manner. The fraction two-thirds (written γ, but here ) was frequently used, and tables giving of numbers were available. The scribal rule for expressing of any fraction, in unit fractions, is given in RMP 61 B. Two-thirds of quite large numbers occurs often. For example, in RMP 33 we find of 5,432 written as 3,621 . The rule given for of the odd fraction was to add the double of the number to six times the number, giving (. and similarly for all odd fractions. The rule holds equally for even fractions, so that of would be : it was seldom used, however, because the value was simpler, from the addition to 6 of its half 3. That the reciprocal of 1 was was well-known to the scribes; indeed, the hieroglyph for was originally , one vertical line being half the length of the other. Or, again, would be written as , as indicated by line 3 of the EM LR, , which becomes on multiplication of the numbers by 3.

For the ordinary multiplication of integers the work was simple enough; but with fractions in the multiplicand, it sometimes became difficult just to multiply by 2. For example, the double of was , and the double of was ; but the double of or any other odd unit fraction was quite another matter. The doubling of the fifty "odd"unit fractions , is performed by the scribe in the first portion of the RMP, called the Recto; and it takes up almost one-third of the eighteen feet of the papyrus.

Division . Little further needs to be said about division, because the method of dividing was the same as that of multiplying. To calculate 297 divided by 11, the scribe thought of it as "By what must I multiply 11 to give me 297?"Thus 11 became the multiplicand, and he kept on doubling it until 297 was reached, just like a multiplication sum.

A further doubling would give 352, which is beyond 297. The problem is now to determine which numbers of the second column will add to 297, or come close to it -a task not always easy. In this case the numbers are 11 + 22 + 88 + 176 = 297, indicated by check marks, so that the required quotient is the sum of the corresponding numbers in the first column: 1 + 2 + 8 + 16 = 27. When the divisor contained one or more odd unit fractions, then trouble brewed, just as it did when the division of two integers did not produce an integral quotient, as 297÷11 does. To illustrate this, divide 297 by 12.

A study of the right-hand column shows that 192 + 96 = 288 is the closest sum to 297; and these, and/ or 16 and 8, are ticked. Also, 288 + 9 = 297. Then of 12 = 6, and of 12 = 3, so that we now have
The Rmp Recto
The Recto of the RMP gives the ancient Egyptian values chosen and accepted by the scribes for the expression of 2÷(2 n - 1) as the sum of not more than four unit fractions, where n had the fifty values, 2, 3, 4, 5, ..., 51. Since the latter part of the nineteenth century, historians of mathematics have discussed and debated how and why the scribes determined the values given in this table, and still no general agreement has been reached. In 1967, with the purpose of examining more closely the various equalities possible, I was able to enlist the services of Prof. C. L. Hamblin of the University of New South Wales to program the computer KDF-9 at Sydney University to produce all the possible answers for these equivalents. The restrictions were such that not more than four unit fractions should be included in any one equality, and that none of the denominators should exceed 1,000.

On this basis KDF-9 produced the grand total of 22,295 equivalents. But for the purpose of proper comparison of these values with the specific value given in each case by A'hmosé, the scribe of the RMP , 22,295 must be reduced by the number of redundancies properly included by KDF - 9, according to its instructions, such as

and

because ancient Egyptian scribes would never accept two equal fractions in any stated number. Therefore the total of 22,295 must be reduced by 2,024. Further, the program for KDF - 9 stated. "No fraction less than 1/1,000 should be included,"when it should have been instructed to "include only fractions greater than 1/1,000."This is a fine distinction, but it means that the nine values in which the unit fraction 1/1,000 occurs should be subtracted, so that the total for comparison purposes is reduced to 20,262.

The purpose of this table, giving the numbers of the possible decompositions of the RMP Recto fractions, is to make clear the nature of the problems historians have puzzled over for some years. Some general agreement appears to have been reached that the scribal values for 2 divided by the odd numbers are the very best available, although in some cases there are differences of opinion. On what are these differences based? Some critics appear not to be clear on the purpose of the table, which is primarily to simplify ordinary multiplication and division, and not just an interesting operation in the theory of numbers. Attempts to explain how the scribe arrived at his values have varied considerably; indeed, there is little agreement over what precepts guided the scribe in choosing his specific

values, although some are of course obvious.

The scribe first states what solution he has selected and then, by ordinary multiplication, proves that the equality is correct. In these proofs there are no scribal errors. Nowhere in any papyrus known to me is there any indication of the scribal technique used by the scribe. Some theories regarding this technique seem to be based on modern mathematics; and attempts to reproduce the scribal values, following these theories but using only the techniques of which the scribe was capable, often are not possible. J. J. Sylvester's treatment is a classic example. I suggest the following as the precepts that guided the scribe in his choice of equalities; and to assist in understanding their significance. I precede them with some of the Recto equalities for reference (bars over the numbers of the unit fractions have been omitted).

Canon for the RMP Recto .

Precept No. 1: Of the possible equalities, those with the smaller numbers are preferred, but none as large as 1,000.

Precept No. 2: An equality of two terms is preferred to one of three terms, and one of three terms to one of four terms; but an equality of more than four terms is never to be used.

Precept No. 3: The unit fractions are set down in descending order of magnitude -that is, smaller numbers come first -but never the same number twice.

Precept No. 4: The smallness of the first number is the main consideration, but the scribe will accept a slightly larger first number if it will greatly reduce the last number.

Precept No. 5: Even numbers are preferred to odd numbers, even though they might be larger, and even though the number of terms might thereby be increased. (There are more than one hundred even numbers used in the table, but only twenty-four odd numbers.)

There can be no doubt about the general acceptance among authorities of the first three precepts, and I am sure that competent critics will agree with the last two. It is of course possible that they might wish to add further precepts.

Historians' Views on the Recto Equalities .

The following statements represent a cross section of opinions:

O. Becker and Hofmann - "The principle of calculation does not seem to be uniform."

L. Hogben -"They went to extraordinary pains to split up fractions like 2/43 into a sum of unit fractions, a procedure that was as useless as it was ambiguous. The Greeks and Alexandrians continued this extraordinary performance."

A. B. Chace -"Of the discussions which I have seen, the clearest is that by Loria, but no formula or rule has been discovered that will give all the results of the table."

F. O. Hultsch - "Attempts to explain it have hitherto not succeeded."

P. Mansion -"The decompositions are always, from one point of view or another, simpler than any other decompositions."

J. J. Sylvester (1882) -"The very beautiful ancient Egyptian method of expressing all fractions under the form of a sum of the reciprocals of continually increasing integers."

In hieratic papyri all fractions had only unity as numerator, although the unit 1 was not written. A number became its own reciprocal by putting the sign ( r, an open mouth), above it in the hieroglyphs, or a large dot in the cursive hieratic. The solitary exception to this notation was their largest fraction, 2/3, written as a hieroglyph but γ in hieratic; and it was used whenever possible, (There is evidence that a hieroglyph for 3/4 was used.) Tables for finding two-thirds (here written ) of both integers and fractions were available to the scribes, and in RMP 61 there is such a table giving of seventeen different fractions. As late as the seventh century of the Christian era, the Greek AMP had an extensive table giving of integers up to ten thousand, shortened and condensed in some obvious ways. There are similar tables in Coptic of an even later date (see Crum's Catalogue). In the RMP alone there are more than seventy occasions on which the scribe writes of both integers and fractions, including seventeen where is written with the intermediary value omitted for brevity.

In RMP 61 B , the scribe A'mosé states the rule for odd unit fractions. Chace translates it as follows: "The making of two-thirds of a fraction uneven. If it is said to thee. What is two-thirds of , make thou times of it 2, and times of it 6, two-thirds of it this is. Behold does one according to the like, for fraction every uneven, which may occur."Although the rule applies equally well to even unit fractions, it was seldom used for them, because the scribe knew that was the reciprocal of 1 (see the hieroglyph for ). and it was easier and simpler merely to increase the even number by its half, like of is .

Examples of the two-thirds rule are shown below.

RMP 32;

RMP 33;
RMP42;
Because of its brittle condition, the leather roll remained unopened for sixty years. When A. Scott and H. R. Hall finally succeeded, it was found to contain a table of twenty-six unit-fraction equalities, in duplicate. The disappointment of archaeologists over the contents was not shared by historians of mathematics, who have found it of great interest. In common with other scribal tables, no methods of calculation are shown, nor is there even a heading or title that might indicate the use to which the entries could be put. The following selection of entries from the EMLR will interest historians.

A close study of these equalities shows that the scribe clearly knew that any equality-forexample, 9 18 = 6 - can be multiplied by 2 or 3 or 4, and so on, to produce other equalities, such as 18 36 = 12; therefore division would do the same, but only if the denominators of the fractions had a common factor, so that division by 3 would produce 3 6 = 2. Other possibilities at once suggest themselves, such as combining 4 12 = 3 and 5 20 = 4, to produce, by simple substitution, 5 12 20 = 3 -and so on indefinitely, as Sylvester's treatment suggests. This short table shows how the scribe of the EMLR utilized the two most elementary of his unit fraction equalities, 3 6 = 2 and 2 3 6 = 1, to produce seven of the thirteen equalities shown.

A study of the papyri, particularly the RMP and the MMP , will show how frequently the use of these equalities was necessary. To illustrate this, I choose a rather extreme example from RMP 70, which, on the evidence, the scribe did in his head.

Summation of Sixteen Unir Fractions From KMP 70

There are seven groups of unit fractions within parentheses in this summation. Their respective sums, shown above, are derived from scribal tables like the EMLR and are listed below.

In the above expressions the occurrence of the same fraction twice is an accident of the detail of the calculations involved. Duplication would never occur in a scribal answer to the problem.

An ingenious and competent scribe might conceivably devise a more expeditious method of deriving the answer, unity. Or he could use the "red auxiliaries,"When using the red auxiliaries, the scribes invariably chose the largest number of the set of fractions for use as their "common denominator."Each number was then divided into this largest number, and the sum of all the quotients was found as shown below.

Quite by chance, 1,008 is here what we call the least common multiple; but usually in such summations this does not happen, and there may be several unit fractions occurring in the quotients. The division of the quotients' total by the "common denominator"chosen is seldom as simple as 1,008 divided by 1,008. Furthermore, the scribes seldom show the actual divisions (sixteen of them in RMP 70), which probably were performed on an odd piece of scribbling papyrus or ostracon; this work might well have been quite voluminous, compared with the apparent brevity and conciseness of the table above.

The detail shown above has been included because this summation is a very small portion of RMP 70, so small that the scribe merely writes the total as I, with no further comment. But he could never have done this mentally. He is concerned to find the amount of meal in each of 100 loaves made from 7 hekats of meal, as well as their pesu - and this is quite a calculation. Just how the scribe performed the summation of these sixteen fractions, the historian can never truly know.

Of the twenty-six equalities in the EMLR table, ten are examples of, and are derivable from, the simplest of all the additions of unit fractions known to the scribes - -which fundamental dual sum I have designated as having the generator (1,2) - that is, the second term is double the first. A scribe preparing a table of such equalities would naturally begin with it and, by simple multiplication or simple addition, produce the following, which could be extended indefinitely.

The equality of EMLR line 3 is , which I refer to as of generator (1, 3); and it produces the table below, again by either multiplication or addition, which also could be extended indefinitely.

The third table would of course be that resulting from the generator (1, 4), as on lines 2 and 1 of the EMLR.

The G Rule . An observant scribe looking at the equalities of generator (1, 2) could well have summed up the situation briefly in some such manner as "For adding two fractions, if one is double the other, divide it by three."A little further observation would enable him to change the word "double"to "three times,""four times,"and so on, and to divide by four, five, and so on for the generators (1, 3), (1, 4), and so on. This is in essence what I have called the G rule: but using modern terms and introducing some further detail, I express it as follows:" If of two unit fractions, one is K times the other, then their sum is found by dividing the larger number by ( K + 1) if, and only if, the quotient is an integer. If it is not an integer, then a unit-fraction sum is not possible."So far as the scribe was concerned, his rule, if he used it as suggested, did not apply to equalities from generators such as (2, 3), (2, 5),· · ·, (3, 4), (3, 5), · · ·, (4, 5), (4, 7), · · ·. Mathematically the G rule still held, although with his notation he could not apply it. It would have been clear to him, however, that pairs of unit fractions like , which evolve from the generator (1, 2), cannot add up to another unit fraction,

Let us look at line 1 of the EMLR, which is . It is related to line 2, which is . while line 4 is .

Now the only other dual equalities with as the first term are and . The first of these clearly follows the G rule but is not among the twenty-six equalities of the EMLR, although it might well have been. The student of ancient Egyptian mathematics may now ask, "If the scribe knew that , how did he find it?"

Three-Term Equalities . The simplest three-term equalities of unit fractions have the generators (1, 2, 4), (1, 3, 6), (2, 3, 6), which produce the following equalities:

Eight of these are included in the EMLR table, five of them from the generator (2, 3, 6) forming lines 14- 18;

Line 12 of the EMLR is , one of the more interesting of all the equalities, which could have been derived in many ways. We look here at one method. The Egyptian table of length was simple enough:

4 digits = 1 palm
7 palms = 1 cubit.

Therefore,

And by addition,

Thus

Four-Term Equalities . Only two four-term equalities occur in the EMLR:

One finds it hard to understand why these two particular examples should have been chosen, when so many simpler and more useful ones might have been included:

which have generators (1, 2, 3, 6), (1, 3, 4, 6), (2, 3, 4, 6), and (2, 3, 5, 6), compared with generator (5, 3, 15, 40). An explanation why the first two terms are out of normal order would make very interesting reading for the reflective scholar.

Ostracon 153, dating from the early New Kingdom and thus somewhat later than the RMP, contains abbreviated divisions of 2 by 7 and 4 by 7, as in the RMP Recto, but uses the red auxiliaries and a reference number. What the scribe in fact does is to consider the divisions of 6 by 21 and 12 by 42; 6 is partitioned as , written in red. When divided by 21, these auxiliaries produce the answer . which is not as simple or convenient as the Recto value of . The scribe proceeded by partitioning 12 as . again in red; when divided by 42, these auxiliaries produce the answer .

Of the fifty divisions of 2 by the odd numbers in the Recto, only one, that of 2 ÷ 35, discloses anything of the scribe's methods-and it happens to be the same as that of the scribe of Ostracon 153. Thus A'hmosé considers 2 ÷ 35 as 12 ÷ 210, and then partitions 12 as (7 5), which auxiliaries, on division by 210, produce the answer . The only other pair of red auxiliaries he could have chosen is (10 2), which would have given -not so acceptable as the first answer.

The following examples show that the scribes were familiar with the operation that in modern notation may be written as "If a × K = b, then 1/ b × K = 1/ a."In RMP 33 it is clearly shown that the reciprocal of is 1 .

RMP 34. "A quantity, its half, and its quarter, added together, become 10. What is this quantity?"Multiply 1 so as to obtain 10.

Line 3 states that , and therefore line 4 drives that of . Line 5 is line 4 multiplied through by 2, so that from the Recto the scribe finds that 2×7, which is 2 / 7, is . Again, multiplying by 2, line 6 shows that of 1 = 1. The answer is 5 .

RMP 70.

The scribe finds that

He then writes that of

RMP 32.

The scribe finds that

He then writes that .

RMP 38.

The scribe finds that .

He then writes that .

RMP 33.

The scribe finds that of 42 = 28.

He then writes that of .

For the translations of the DMP that follow, I am indebted to R. A. Parker of Brown University. (See the bibliography and "Mathematical Papyri and Ostraca.")

Cairo Papyrus (JE 89127) , Discovered at Tuna el-Gebel in 1938 and first examined by Parker in 1962, this papyrus contains forty problems of a mathematical nature. Of these, eight are obscure or fragmentary, and fourteen have counterparts in the much earlier hieratic papyri. The Cairo papyrus dates from 300 B.C. or possibly earlier, and it is interesting to examine what advances or developments are to be found in its mathematical techniques.

First we note that there are nine problems dealing solely with Pythagoras' theorem -for instance, "A ladder of ten cubits has its foot six cubits from a wall; to what height will it reach?"With one exception, the numbers used are those of the triads (3, 4, 5), (5, 12, 13), and (20, 21, 29); and no such problems have been noted in the earlier papyri. The one exception requires the calculation of an approximate square root.

Two problems deal with rectangles having areas of sixty square cubits and diagonals of thirteen and fifteen cubits, respectively. It is required to find the sides. The directions for their solution are identical with the steps of the following algebra, but of course they are entirely descriptive.

The second problem is the same except for the numbers, and so the square roots of 345 and 105 are to be found. The formula used is the approximation usually attributed to Archimedes or Hero, . Thus we find the square roots to be and from

correct to .05 percent correct to .03 percent

There are two problems on the areas of circles in which the equivalent of ダ is 3, the Old Testament value, as compared with the RMP value of more than a millennium earlier, 256/81, or 3.16. The problems are to find the diameters of circles with areas of 100 square cubits and 10 square cubits. The answers given are 11 and , as further approximations from the formula of Hero given above.

Finally, there are three problems concerning the areas of circles that circumscribe two equilateral triangles and a square. Rather surprisingly, the scribe finds the areas of the triangles and the square separately, and then the areas of the segments of the circles. The arithmetic for the areas of the segments is equivalent to using the formula A = ½ s( s+ c), where s, where s is the height ( sagitta) and c is the chord length of the segment. This is unexpected, and the earliest reference I can find to it is the Chui-chang suan-shu from China ( ca. 300 B.C.).

In the Cairo papyri the old notation for unit fractions is clearly retained, but there are signs of slight changes developing. In the forty problems there are demotic signs for 5/6 and 2/3. In addition, the fractions 6/47, 39/47, 17/53, 35/53, and at least a dozen others are used, written with both numerator and denominator on the same line, but the numerator underlined to distinguish it. These are the first nonunit fractions.

P. Dem. Heidelberg 663 . Parker's translation of the fragmentary demotic papyrus P. Dem. Heidelberg 663 ( Journal of Egyptian Archaeology, 61 [1975], 189-196) deals with four problems concerning the dimensions of isosceles trapezoidal fields. Of great interest is the division of one such field into two equal areas, by a straight line parallel to the top and bottom sides, and the determination of its length. Parker remarks that the details of the papyrus are "so scanty that it is rarely possible to do more than suggest a connected translation, but with the help of the four figures, it is possible to reconstruct the aim of each problem."He then offers a careful translation of the papyrus, which dates from the Ptolemaic period of the first or second century B.C.

The second problem deals with the length of the parallel line x that divides the field into two equal areas.

The detail of this calculation is not clear in the papyrus, but Parker suggests that the formula or its equivalent in demotic terms could have been used and that the square root, if not integral, could be found from Hero's approximation,

For problem 2 the formula gives

Because 164 is not a perfect square, its square root from Heron's formula would be approx. Because of the demotic units of measure, the value of x had to be expressed 12 ½ ¼ 1/6, a reasonably close approximation. One naturally wonders whether the dimensions of the trapezoid could have been chosen so that the bisector x would turn out to be a whole number, and it so happens that this can be done.

Yule Babylonian Collection clay tablet 4675, dating some centuries earlier than Heidelberg 663, contains a similar problem in which the parallel sides of the trapezoid are 7 and 17. From Mathematical Cuneiform Texts, American Oriental Society, 1975, by Neugebauer and Sachs, The translation of this tablet indicates in the cuneiform sexagesimal number system that the method for calculating x using only

the values of a and b would have followed in modern terms the steps indicated by the formula

in which there is no reference to perpendicular heights or to sides or areas. With the sides a and b given as 17 and 7, we have

We ask ourselves if the Babylonian scribes had some method of their own in this type of problem for avoiding awkward square roots, even though they may have had some sort of a square root rule like Hero's many centuries before he had made it known. Indeed, we find another related problem in the clay tablet VAT 7535 ³ at the Berlin Muséum, dating from ancient Babylonia.

Using the same formula we have

so that

There are many ways of finding the length of the area-bisecting parallel of a trapezoid, isosceles or otherwise; and methods or formulas may be devised to include sides, perpendicular heights, and areas. The simplest formula in modern terms is

The apparently simple problem suggested by the ancients is thus conveniently shown in Figure 5, in which it is required to devise integral values of a, b, and x, so that A ₁ = A ₂

A solution of the problem treated purely as theory of numbers was given by A. Guibert in 1862; reference to it is made in L. E. Dickson's History of the Theory of Numbers. There the general solution in positive relatively prime integers of a ² + c ² = 2 b ² is staled to be

where p and q are relatively prime and one even.

We note that the scribe of VAT 7535 utilized the first trio (1, 5, 7) multiplied through by 15, while the scribe of YBC 4675 used the second trio (7, 13, 17). It would be of great interest to the historian of mathematics if it were ever determined exactly how these values were determined.

British Muséum Papyrus (10399, 10520) . These papyri date from the period of the Ptolemies and the early Romans, say 300 B.C. They contain twenty-seven problems, of which about half are similar to those found in the hieratic papyri. Thus, six deal with the four operations, mostly operations with unit fractions: two with the areas of rectangles; three are multiplication tables -64 times the numbers 1 to 16, times the numbers 1 to 10, and times the numbers 1 to 10; and two are not sufficiently preserved to be translated. But the other half are of interest to the historian.

There are four similar problems on frustums of cones and the calculations of their volumes. This is done by averaging the top and bottom diameters; finding the area of the circle with this diameter, using the formula A = 3/4 d ²; and then multiplying by the height. This is a better approximation than that of averaging the areas of the top and bottom circles. Then there are six consecutive very closely allied problems, the first of which is worded "The fraction is added to 1. Determine what fraction of 1 must be subtracted from it to give 1 again."The succeeding questions are similarly worded, with the fractions to be added to unity changed to , and 5/6. The answers given are , and 5/11. There are two questions requiring the square roots of 10 and . The controversial (only regarding its origin) formula used is and is found as but requires preliminary treatment. The scribe replaces by 18/36 and thus finds . The division of 2 by 35. almost exactly as A'hmosé indicated it should be done in RMP Recto, is calculated to be , as in the Recto. Parker, like Peet, expected to find ⁹

The last remaining problem is of particular interest. It deals with the sum of a number of terms of certain progressions, the first of which is the arithmetical progression formed by the natural numbers. In order to understand clearly what series the scribe is summing to ten terms, I write them first, because the scribe did not so write them but merely described them in his own way. He plans to find the sum of the first ten terms of the following series, but actually does so for only the first two, which are 1 "filled once up"to 10, and 1 "filled twice up"to 10. The third (and fourth, and so on), which would have been 1 "filled thrice (and so on) up"to 10, are not included,

The scribe writes:

You shall say, 1 up to 10 amounts to 55.

You shall reckon 10, 10 times.

Result 100.

You shall add 10 to 100.

Result 110.

You shall take the half.

Result 55.

You shall say, 1 up to 10 amounts to 55.

You shall add 2 to 10.

Result 12.

You shall take the third of 12.

Result 4.

You shall reckon 4, 55 times.

Result 220.

You shall say, 1 is "filled twice up"to 10.

Result 220.

The scribe's directions hold, of course, for any number in the natural number series, merely by replacing the 10 that he chose for his example. Let us first rewrite the above as follows.

First,

1 is "filled once up"to 10 1/2; (10 ² + 10)= 55

Then,

10 + 2 = 12

⅓(10+2) = 4

1 is "filled twice up"to 10 4×55 = 220

Now we replace the 10 by n, representing any term of the natural number series.

1 is "filled twice up"to n, Sn = 1/3 (n+2) ½ (n²+n)

And if he proceeded to the next series, he would have written

I is "filled thrice up"to, n, Sn =

We may now say that in our modern notation, we have the formulas for the sum to n terms of the series, as follows.

Series(A)

for instance,

Series (B)

for instance,

RMP 79 consists of a house inventory.

In the second column the scribe starts with 7, multiplies it by 7, then multiplies this product by 7, repeats these multiplications by 7 a certain number of times, then adds all the products for a grand total. This operation is self-explanatory. In order to explain the multiplication of 2,801 by 7 (1 use the index notation for brevity), we take the foregoing step by step.

1 term No 7=7 =7 =7
additions

2 terms 7+7 ² = 7[1+ (7)] =7(1 + 7) =56
One addition

If the scribe wished to go one step further, he would need only to add unity to the total 19,607, and then multiply by 7. In the scribe's setting for RMP 79, the shorter method was shown first -that of multiplying 2.801 by 7 - and then its correctness proved by the longer, detailed calculation. It would appear that in this problem, the scribe is concerned only with a property of certain geometrical progressions, an exercise in the field of numbers. The title "A House Inventory"(or "The Contents of a House"; there is some doubt in the translation) and the names given to the successive totals -Houses, Cats (in the houses). Mice (that the cats would destroy), Spelt (ears of grain the mice would eat). and Hekats (the number of particles of grain that would be saved) - are all put in to give the problem an air of verisimilitude. But if this was the scribe's plan, it failed, because the grand total he is seeking cannot have any sensible meaning in regard to the contents of a house.

If, as is elsewhere claimed, this problem is the origin of the Mother Goose nursery rhyme "As I was going to St. Ives, I met a man with seven wives ... how many were coming from St. Ives?"(not "going to St. Ives."which is the storyteller's trick), then the change to seven wives, seven sacks, seven cats, seven kits removes this disability and makes the problem sensible. Not only that, the multiplications are reduced and the problem slightly simplified to the multiplication of 400 by 7.

Pesu is a number indicating the strength of bread or of beer made from grain. If one hekat (about 1/8 bushel) of grain were used to produce one loaf of bread or one des jug of beer, then its pesu was one. If one hekat of grain produced two loaves or two jugs of beer, their pesu was two, and so on, so that the higher the pesu number, the weaker the bread or beer. The relation was expressed as

There are twenty problems concerning pesus in the RMP and MMP. Generally speaking, their arithmetic is simple, as the examples below indicate.

Two problems. RMP 74 and 76, merit closer attention than the others, even though at first glance they appear simple enough and, indeed, very similar.

RMP 74. 1,000 loaves of pesu 5 are exchanged, half of them for loaves of pesu 20 and half for loaves of pesu 10. How many of each will there be?

RMP 76. 1,000 loaves of pesu 10 are exchanged for a number of loaves of pesu 20 and the same number of loaves of pesu 30. How many of each will there be?

The scribe's solutions are shown below.

RMP 76. For loaves of pesu 20, hekat produces one loaf. For loaves of pesu 30, hekat produces one loaf. Then, hekat produces two loaves, one of each kind. The number of hekats in 1,000 loaves of pesu 10 is 100. Multiply 100 by 12; the result is 1,200, the number of loaves of each kind for the exchange.

We now restate the scribe's processes for these two problems in modern terms, for our own information.

RMP 74. 1,000 loaves of pesu 5 required 200 hekats of grain. The arithmetic mean of"the two new pesus is ½ (20 + 10) = 15. Then the number of loaves received in exchange is greater, in the ratio of 15 to 5 -that is, 3 to 1. Therefore the number of loaves received is 1,000 × 3, or 3,000 total. The new pesus are in the ratio of 20 to 10, or 2 to 1. Hence there must be 2,000 loaves of pesu 20 and 1,000 loaves of pesu 10.

Now consider the problems RMP 73 and 72, in that order.

RMP 72 Solution. Instead of a simple solution like the above, of 10 × 45 = 450 loaves, the scribe has the following:

The excess of 45 over 10 is 35

Divide this 35 by 10; it makes 3

45 - 10 = 35 Q - P

Divide this 35 by 10; it makes 3

35 ÷ 10 = 3½

Multiply 3 by 100; it makes 350

3½ × 100 = 350

Add 100 to 350; it makes 450

350+100 = 450

and since the number of hekats is constant, he would have

Therefore,

or (alternando),

and (dividendo),

so that

Hence,

and, finally, adding L to both sides, which is the formula of the method the scribe adopted for RMP 73 and all the other pesu problems of a like nature. The incidence of the step that we today term "dividendo"is unavoidable, because of the instruction to find the excess of the final pesu of 45 over the original pesu of 10.

Although the pesu problems of the RMP and the MMP are in general similar, there are one or two (as we have seen) that call for special mention. The scribe of the MMP was not as careful, nor as good a writer of hieratic as was A'hmosé; and MMP 21 is one such problem, which may resemble RMP 76. It is included here for interest and inquiry.

MMP 21. This problem involves the method of calculating the mixing of sacrificial bread.

If one names 20 measured as of a hekat.
And 40 measured as of a hekat.
Compute of 20. Result 2 .
Compute of 40. Result 2 .
The total of both these halves is 5.
Compute the sum of both halves. Result 60.
Divide thou 5 by 60.
Result . Lo! The mixture is .
You have correctly found it.

Listed below are some of the Egyptian measures.

Arura

A unit of area equal to that of a square with a side of 100 royal cubits, thus a square hayt or khet.

Cubit

A royal cubit was 20.6 inches and a short cubit 17.7 inches; hence the phrase "a cubit and a hand's breadth."

Deben

A weight of about 3.2 ounces or 90 grams, used for metals.

Des Jug

A unit of volume used generally for beer, approximately half a liter or 7/8 of a pint.

Digit

Or finger. A quarter of a palm, and thus 1/28 cubit.

Double Remen

The length of the diagonal of a square with a side of one cubit, thus 29.13 inches.

Finger

The same as the digit.

Hayt

100 royal cubits in length. The same as a khet.

hekat
A dry measure for barley, flour, spelt, corn, and grain in general; about 1/8 of a bushel.

Hinu

A smaller unit for grain, 1/10 of a hekat.

Khar

Two-thirds of a cubic cubit, a measure more commonly used for the contents of granaries.

Palm

Or hand's breadth, 1/7 of a cubit.

Pesu

A number giving the relation between the number of loaves of bread (or des jugs of beer) and the number of hekats of grain required to produce them.

Remen

The half of adoubleremen, 14.56 inches; that is, half the diagonal of a square with a side of one cubit.

Ro

The smallest named unit for grain, 1/320 part of a hekat.

Seked

The inclination of the face of a right pyramid, measured as so many horizontal palms or cubits per vertical palm or cubit.

Setat

One square khet, or 10,000 square cubits.

Areas and Volumes . The areas of triangles and rectangles were found in the usual way, half the base times the height, and length times breadth: but the areas of circles were something quite different. RMP 50 states the rule as "Take away one-ninth of the diameter, and square the remainder,"In modern terms we would express this as

We may therefore say that the ancient Egyptian equivalent of π was 256/81 or 3.1605, an unexpectedly close value, in excess of the true value by 0.6 percent.

Those problems concerned with finding the contents of cylindrical granaries, expressed in khars, where 1.5 khars equals a cubic cubit, were solved by multiplying the area of the circular base by the height in cubits, and then multiplying by 1.5. The area of the circular base was found by the formula above.

There are two problems, KP IV, 3 and RMP 43, where this calculation was done differently. The directions read: "Add to the diameter its one-third part, square the total, and then multiply by two-thirds of the height. This is the contents in khar."How the scribes thought out this variation is not explained in the papyri; but it worked correctly, as we can check by setting down both methods in modern form.

METHOD I

METHOD 2

A challenge remains for the historian of mathematics: to explain the scribal thought process of transforming the first method into the second, without using any symbolic algebra.

Pyramids . The problems that concern pyramids show that the scribes were able to calculate the slope or inclination of the sides of a pyramid, the volume of a pyramid, and, perhaps surprisingly, the volume of a truncated pyramid or the frustum of a pyramid. The slope or seked of the side of a pyramid was stated as the relation between the vertical height and half the base, and was given as so many palms horizontally for each cubit measured vertically-usually 5 palms, or 5 palms, 1 finger, or 5 palms, possibly because of the seked of Cheops was 5 palms.

Struve's translation of MMP 14 is as follows:

Method of calculating a truncated pyramid.

If it is said to thee, a truncated pyramid of 6 cubits in height,

Of 4 cubits of the base by 2 cubits of the top,

Reckon thou with this 4, its square is 16.

Multiply this 4 by 2, Result 8.

Reckon thou with this 2, its square is 4.

Add together this 16, with this 8, and with this 4, Result 28.

Calculate thou 3̄ of 6. Result 2.

Calculate thou with 28 twice. Result 56.

Lo! It is 56! You have correctly found it.

If we replace the base of 4 cubits by a, the top of 2 cubits by b, and the height of 6 cubits by h, we find that the scribe has calculated the volume of the frustum, according to the modern formula V = 1/3 h ( a ² + ab + b ²). It is generally accepted that the Egyptians knew that the volume of a right square pyramid was one-third that of a right square prism of equal base and height, although this is nowhere specifically attested (to my knowledge) and although there are several simple ways in which the scribes may have found the equivalent of the modern formula V = 1/3 a ² h. Even with the powerful help of such a formula or its equivalent, however, it is still not easy to establish just how the scribes arrived at this relatively erudite method for finding the frustum of a pyramid, an achievement that, in the words of B. G. Gunn and T. E. Peet, "has not been improved upon in 4,000 years."

Area of the Surface of a Hemisphere . Struve's translation of MMP 10 is as follows.

Method of calculating a basket.

If it is said to thee, a basket with an opening,

Of 4 in its containing, Oh!

Let me know its surface.

Calculate thou of 9, because the basket

Is the half of an egg. There results 1.

Calculate thou the remainder as 8.

Calculate thou of 8.

There results .

Calculate thou the remainder of these 8 left

After taking away these . There results 7 .

Reckon thou with 7 , 4 times.

There results 32. Lo! This is its area.

You have correctly found it.

In modern terms, we would express the operations above in the form , which is the equivalent of A = 2π r ².

W. W. Struve ( d. 1965), the original translator of the MMP, was thoroughly convinced that the above is the correct interpretation of MMP 10, T. E. Peet ( d, 1934) thought that a semicylinder may have been concerned, but had to introduce two new terms, "diameter and heights,"into the translation. B. L. van der Waerden and R. J. Gillings agree with Struve: and T. G. H. James, while acknowledging the translation difficulties raised by Peet. inclines to concur with Struve's conclusion. O. Neugebauer still has some doubts that the paleography is definite enough to convince him beyond question."Thus far, no authorities have expressed any views or opinions, in scientific or historical journals, contrary to those expressed here; and MMP 10 and MMP 14 remain the outstanding mathematical achievements of the ancient Egyptians, A detailed discussion of the views of the above-mentioned writers is given by Gillings.

In this section we consider problems requiring for their solution what we might call algebraic reasoning, but which are treated by the scribes quite literally and perhaps termed "rhetorical algebra."For clarity and brevity, I will not give complete translations from the hieratic writing of the papyri: and so that we may examine the thought processes involved, I use the standard x, y, z for unknowns, and a, b, c for knowns. For obvious reasons, however, I retain the standard notation for the ancient Egyptian unit fractions. Thus, in a limited space we may cover a considerable field of study of the mathematical techniques of the scribes.

First-Degree Equations, One Unknown . Below are several first-degree equations, with one unknown.

These are straightforward enough, largely arithmetical operations with unit fractions. In each case the scribe gives the proof that his answer is correct.

This second group of equations represents a slight advance on the first four, each of which was solved by a method that today is called "false position"or "false assumption."Methods for the second four vary.

Answers

If the scribe A'hmosé faltered, he did so here. His method of solution was that of division: and if he was teaching a technique, his choice of fractions and of integers, or both, was unfortunate, for the answers, all of which are correct, show that the problems were not of a practical nature. So here he was, lost in a maze of four-digit unit fractions, in one instance (RMP 33) finding it necessary to add sixteen unit fractions, the last twelve of which have the denominators

which he found by using red auxiliaries. This could all have been neatly avoided had he chosen 97 instead of 37, and his answer would have been 42. And in RMP 31, had he written instead of . he would have simplified it so greatly that the answer would have been . Finally, the answer to RMP 32 could have been simplified from to in the scribal working, as the G rule shows, since

Second-Degree Equations, Two Unknowns . In the discussion of the demotic papyri, the solution of simultaneous second-degree equations is shown, so they are not repeated here. DMP 34 and 35 were

xy = 60,

xy = 60.

DMP 34, in exactly the form shown above and with the same numbers, occurs in W. E. Paterson's School Algebra ([London, 1916], 250), where the textual work on solutions is the same as that of the scribe. Two problems from BP 6619, restored and translated by H. Schack-Schackenburg, are

F. L. Griffith, in his translation of a problem in KP IV, 4 (1897), was notable to understand certain incomplete lines, which have since been restored with reasonable surety and produce another problem of simultaneous equations, details of which may be studied in Mathematics in the Time of the Pharaohs (162 - 165):

xy = 12

Progressions. RMP 40 speaks of an arithmetic progression of five terms, in which the sum of the three largest terms is seven times the sum of the two smallest terms. Chace's translation reads:"100 loaves for 5 men, one-seventh of the total of the largest 3 shares shall equal the total of the smallest 2 shares. What is the common difference of the shares?"

KP IV, 3, is solely a column of eleven decreasing numbers, and next to it is a short multiplication. There are no words! I have judged the calculations shown to be an answer to the problem "The sum of 12 terms of an arithmetic progression is 110, and the common difference is 5/6. What is this series?"

RMP 64 gives the sum of ten terms of an arithmetic progression as 10, and the common difference as one-eighth. What are the terms of this series? Since the scribal statement of the problem speaks of dividing ten hekats of barley among ten men, the fractions used are all Horus-eye fractions, which were used for grain: , of a heket, written in a special way. The scribe's method of solving RMP 64 is quite unexpected; and if one follows each step of the solution, and replaces each word and number with the modern notation used in algebra texts-such as S for the sum, d for the difference, a and l for the first and last terms, n for the number of terms -one has, at the conclusion,

The problem stated in RMP 79 has been treated elsewhere in some detail. Here we can state it as "Find the sum of five terms of a geometrical progression of which the first term is 7, and of which the common ratio is also 7."

Think of a Number . RMP 28 reads in Chace's translation:

Two-thirds is to be added, then one-third is to be subtracted.

[The foregoing is in red, all else is in black.]

There remains 10.

Make one-tenth of this, there becomes 1. The remainder is 9.

Two-thirds of it, namely 6, is to be added. The total is 15.

One-third of this is 5. Lo! 5 is that which goes out, and the remainder is 10.

Chace concludes, "The solution does not seem to be complete. The words ' The doing as it occurs,' are usually put at the beginning, and in no other problem are they at the end. Peet has suggested that in copying, the scribe let his eye pass to the same words in the next question."There are no such words in the next question!

I draw attention to the title page of the RMP, where the first sentence (again in red) is "Accurate reckoning of entering into the knowledge of all existing things, and all mysteries and secrets."RMP 28 is the first problem in which the scribe discloses one of his secrets and shows how his magic works. Having done this, he writes, " The doing this it occurs."it is in its proper place. I restate the problem in modern terms. "Think of a number. Add to it its two-thirds part. From this number take away its third part. What is your answer? Suppose you are told the answer is 10. Then you (mentally) subtract its tenth part, and say that the number first thought of was nine! That is how you do it. That is your magic!"

RMP 29 is a second example of "think of a number"problems given by A'hmosé, and they are probably the earliest in recorded history: "Think of a number. Add to it its two-thirds part. To this number add its third part. Find one-third of this number. What is your answer? Suppose you are told the answer is 10. Then you (mentally) add a quarter and a tenth part to this 10, and say that the number you first thought of was 13½ That is how you do it. That is your magic!"

In the section on DMP, the summation of the terms of the natural number series is treated, as are certain other series derived therefrom.

J. J. Sylvester's Formula . This formula is quoted in the additional bibliographical notes. From his formula the mathematician can derive unit fraction equalities very similar to those found in the EMLR, when it was successfully unrolled. I have found the following:

Other sets are possible. A careful scrutiny will show that they are interrelated.

Two-Term, Three-Term, and Four-Term Equalities for Unit Fractions . Note that the overbars have been omitted.

Hekat Measures for Grain . One hekat of grain was approximately one-eighth of a bushel. For stating the contents of larger containers, the unit used was sometimes a double hekat, or even a quadruple

hekat. For granaries, an even larger unit was used, "100 quadruple hekats."A cubic cubit of grain was equal to thirty hekats. For smaller quantities, fractions of a hekat were used-but only 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, which were called Horus-eye fractions. They were not written like ordinary unit fractions, but as portions of the eye of the god Horus, which he lost in battle. The very smallest measure used was the ro, which was 1/320 of a hekat-about a tablespoonful. Some other non-Horus-eye units were also sometimes used: the hinu. which was one-tenth of a hekat, and the khar. which was twenty hekats.

The RMP Recto . In the section dealing with the RMP Recto, the views of some historians are given on how they thought the scribes calculated the fifty values of 2 ÷ (2 n- 1), expressed in unit fractions. My own theory has been published in Archive for the History of Exact Sciences.

I do not consider it proper, however, to discuss that article in detail until it has been read and studied or reviewed by competent judges, and its merits evaluated. It is therefore sufficient to state that I considered the one equality of the Recto that was entirely unique in its context (as verified by the computer KDF-9): the very last, 2 ÷ 101 = , which is the only possible four-term unit fraction value for this division. From this equality, expressed generally . I derive every other equality of the Recto, using those methods and techniques accepted as being attributable to the scribes. I direct the attention of those interested in the problem to my article.

1. R. W. Sloley, "Science,"166.

2. E. T. Peel, "Mathematics in Ancient Kgypt,"412.

3. O. Neugcbauer, The Exact Sciences in Antiquity, 73.

4. In the papyrus KP IV, 2, a portion of the Recto is included: 2 divided by 3, 5, 7, · · ·, 21. Proofs are identical bill briefer.

6. See, for example, R.J. trillings, "The Addition of Egyptian Unit Fractions."in Journal of Egyptian Archaeology, 51 1956), 95.

7. See W. C. Hayes, Ostraca From the Tomb of Sen-Mut.

8. Further references are in Heronis Alexundrini Opera quae supersunt omnia, 5 vols. (Leipzig, 1899-1914), III, 73; IV, 357; V, 187.

9. Compare the Canon for the RMP Recto. See R. J. G tilings, Mathematics in the Time of the Pharaohs, 99.

10. Ibid., ch. 17, "Pyramids and Truncated Pyramids,"185-193.

11. B. L. van der Waerden, letter (1967); R. J. Gillings, "The Area of the Curved Surface of a Hemisphere in Ancient Egypt,"in Australian Journal of Science, 30, no, 4 (1967), 113-116; T. G. H. James, letter (1970).

12. O, Neugebauer, letter (1967).

13. Gillings, Mathematics in the Time of the Pharaohs, ch, 18.

14. A. B. Chace, L. Bull, H. P. Manning, and R. C. Archibald, The Rhine Mathematical Papyrus. II (Oberlin, Ohio, 1929), prob. 40, pl, 62.

15. Gillings, Mathematics in the Time of the Pharaohs, 176-180.

16. Ibid., 173-175.

17. A. B. Chace el al., The Rhind Mathematical Papyrus. II, pl. 51.

This bibliography, which should not be regarded as complete, may suggest further sources of information to students of the history of ancient Egyptian mathematics.

R. C. Archibald, Bibliography of Egyptian Mathematics, I and supp. (Oberlin, Ohio. 1927- 1929).

O. Becker and J. E. Hofmann, Geschichte der Mathematik (Bonn, 1951).

V. V. Bobynin. Bibliotheca mathematics, 2nd ser., 3 (1889). 104- 108; 4 (1890), 109- 112; 8 (1894), 55-60; 10(1896), 97-101.

L. Borchardt, Gegen die Zahienmystik an der grossen Pyramide bei Gise (Berlin. 1922).

C. B. Boyer, A History of Mathematics ( New York, 1968).

J. H. Breasted, A History of Egypt (London, 1946).

E. M, Bruins, "Ancient Egyptian Arithmetic: 2/N,"in Indagationes mathematicae, 14 (1952), 81-91.

E. A. W. Budge, The Rosetta Stone (London, 1922; rev. eds., 1950, 1957).

E. A. W. Budge, "The Rosetta Stone,"ch. 3, pt. 3,of M. Wheeler, A Second Book of Archaeology (London, 1959).

A. B. Chace, L. S. Bull, H. P. Manning, and R. C. Archibald. The Rhind Mathematical Papyrus, 2 vols. (Oberlin, Ohio, 1927-1929).

J. F, Champollion, Précis du Système hiéroglyphique (Paris, 1824).

L. Cottrell, Life Under the Pharaohs (London, 1957).

W. E. Crum. Coptic Ostraca From the Collations of the Egypt Exploration Fund, Cario Muséum (London, 1905).

W. E. Crum, Catalogue of Coptic Manuscripts in the British Muséum (London, 1905).

G. Daressy, "Calculs égyptiens du moyen-empire."in Recueil de travaux relatifs è l'archéologie (Paris, 1906).

D. Davidson and H. Aldersmith, The Great Pyramid, Its Divine Message (London. 1924).

L. E. Dickson, History of the Theory of Numbers, 3 vols. (Washington, D.C., 1919-1923; repr. New York, 1934), 437-438.

J. Edgar and M. Edgar, The Great Pyramid Passages and Chambers (London, 1923).

I. E. S. Edwards. The Pyramids of Egypt (London, 1952; rev. ed., 1961).

A. Eisenlohr, Ein mathematisches Handbuch der alten Ägypter. RMP (Leipzig. 1877).

R. Engelbach. "The Volume of a Truncated Pyramid,"in Journal of Egyptian Archaeology, 14 (1927).

H. Eves, An Introduction to the History of Mathematics (New York, 1964).

A. H. Gardiner, Egyptian Grammar, 3rd ed., rev. (London, 1969).

O. Gillain. La science égyptienne, L'arithmethpie an moyen empire (Paris, 1927).

R. J. Gillings, Mathematics in the Time of the Pharaohs (Cambridge. Mass., 1972).

R.J. Gillings, "The Recto of the Rhind Mathematical Papyrus. How Did the Ancient Egyptian Scribe Prepare It?"in Archive for the History of Exact Sciences, 12, no. 4(1974), 291-298.

R. J. Gillings, "What Is the Relation Between the EMLR and the RMP Recto?" ibid., 14, no. 3 (1975), 159-167.

S. R. K. Glanville, "The Mathematical Leather Roll in the British Muséum,"in Journal of Egyptian Archaeology. 13(1927), 232-239.

S. R. K. Glanville. ed., The Legacy of Egypt (Oxford, 1942; repr., 1963; 2nd ed., 1971).

F. L. Griffith, Hieratic Papyri From Kahun und Gurob (London, 1898).

W. C. Hayes, Ostracon 153. Osttaca and Name Stones From the Tomb of Sen-Mat at Thebes, Metropolitan Muséum of Fine Art Publication 15 (New York, 1942).

L. Hogben, Mathematics for the Million (London, 1945), 261, 297, 555.

F, Hultsch, Die Elemente der ägyptischen Theilungs-rechuung (Leipzig, 1895).

P. E. B. Jourdain. "The Nature of Mathematics,"1 ch. 1, of J. R. Newman, ed., The World of Mathematics (New York, 1956).

L. C. Karpinski, "Algebraical Developments Among the Egyptians and the Babylonians,"in American Mathematical Monthly, 24 (1917), 257-265.

M. Kline, Mathematics, a Cultural Approach (Reading, Mass., 1962).

G. Loria, "Studi intorno alla logística grecoegiziana."in Giornale di matematiche di Battaglini, 32 (1894), 28-57, decompositions of 2/(2 n-1).

P. Luckey, "Anschauliche Summierung der Quadrat-zahlen und Berechnung des Pyramideninhalts."in Zeitschrift für mathematischen und naturwissenschaftlichen Unterricht, 61 (1930), 145-158.

P. Mansion. "Sur une table du papyrus Rhind,"in Annales de ia Société scientifique de Bruxelles, 12 (1888), 44-46.

E. K. Milliken, Cradles of Western Civilisation (London, 1955), 86-98.

O. NeÜbert, The Valley of the Kings (London, 1957).

O. Neugebauer, The Exact Sciences in Antiquity (Copenhagen, 1951; New York. 1962), 91-96.

J. R. Newman. "The Rhind Papyrus,"1, ch. 2, of J. R. Newman, ed., The World of Mathematics (New York, 1956).

C. F. Nims. "The Bread and Beer Problems of the Moscow Mathematical Papyrus,"in Journal of Egyptian Archaeology, 44 (1958), 56-65.

R. A. Parker, "A Demotic Mathematical Papyrus Fragment,"in Journal of Near Eastern Studies, 18, no. 4 (1959), 275-279.

R. A, Parker, Demotic Mathematical Papyri (Providence, R.I.-London. 1972), prob. 56 (pl, 20; C8-16), pp. 65-66.

T. E. Peet, The Rhind Mathematical Papyrus (London, 1923).

T. E. Peet, "Mathematics in Ancient Egypt," in Bulletin of the John Rylands Library, 15, no. 2 (1931), 409-441, esp. 412.

W. M. F. Petrie, The Pyramids and Temples of Gizeh (London, 1883).

G. Posener, Dictionary of Egyptian Civilization (New York, 1959).

V. Sanford, A Short History of Mathematics (London, 1930), 225.

G. Sarton, The Study of the History of Mathematics (Cambridge, Mass., 1936; New York. 1957).

H. Schack-Schackenhurg. "Der Berliner Papyrus 6619,"in Zeitschrift für ägyptische Sprache, 38 (1900), 135-140.

A. Scott and H. R. Hall, "Egyptian Leather Roll of the 17th Century B.C.,"in British Muséum Quarterly, 2 (1927), 56-57.

K. H. Sethe. "Von Zahlen und Zahlworten bei den alten Ägyptern,"in Schriften der Wissenschaftlichen Gesellschaft in Strassburg, no. 25 (1916), 85- 119.

J. W. S. Sewell, "The Calendars and Chronology."ch. I of S. R. K. Glanville, ed., The Legacy of Egypt (London, 1942; repr. 1963; 2nd ed., 1971).

W, K. Simpson, The Papyrus Reisner, 3 vols. (Boston, 1963-1969).

R. W. Sloley, "Science."ch. 6 of S. R. K. Glanville, ed., The Legacy of Egypt (London, 1942; repr, 1963; 2nd ed., 1971).

Piazzi Smyth, Our inheritance in the Great Pyramid (London, 1864 and repr. eds.)

D. J. Struik, A Concise History of Mathematics (New York, 1948), 19-23.

W. W. Struve, Mathematischer Papyrus des Staatlichen Muséums der schönen Künste in Moskau, which is Quellen und Studien zur Geschichte der Mathematik, Abt. A, I (Berlin, 1930), esp. 98 ff.

D. P. Tsinzerling, "Geometria v drevnikh egiptyan"("Geometry in Ancient Egypt"), in Izvestiya Rossyskoy Akademii nauk SSSR, 6th ser., 19 (1925), 541-568.

B. A. Turaev, "The Volume of the Truncated Pyramid in Egyptian Mathematics,"in Ancient Egypt (1917), 100-102.

B. L. van der Waerden, Science A wakening, translated by Arnold Dresden (Groningen, 1954), 15-36.

K. Vogel, "Erweitert die Lederolle unsere Kenntniss ägyptischer Mathematik?"in Archiv für Geschichte der Mathematik (1929), 386 ff.

K. Vogel, "The Truncated Pyramid in Egyptian Mathematics,"in Journal of Egyptian Archaeology. 16 (1930), 242-249.

K. Vogel, Vorgriechische Mathematik, I, Vorgeschichte und Ägypten (Hanover, 1958).

N. F. Wheeler, "Pyramids and Their Purpose,"in Antiquity. 9 (1935), 5-21.

J. A. Wilson, Signs and Wonders Upon Pharaoh. A History of American Egyptology (Chicago, 1964).

Names included here may be referred to in general reading on the history of ancient Egypt. Such references may concern articles on specific topics, notes on archaeological work or Egyptology generally, or a published text from which lines may have been quoted. However brief the notes, the names included are of interest to the historian.

Abd el-Rasoul. Dealer in Egyptian antiquities who sold a papyrus to Golenischev in 1893, "pour une somme assez modique."that was early referred to as the Golenischev Papyrus.

J. Baitlet, The Akhmim Papyrus (Paris, 1892). A Greek mathematical papyrus of a.d. 750, that still used Egyptian unit fractions, as in RMP Recto.

G. B. Belzoni. A six-foot, six-inch strong man who discovered the tomb of Seti I at Thebes and the entrance to the Cephren pyramid at Giza in 1818.

L. Borchardt. Archaeologist who excavated in Egypt. Found the now famous head of Queen Nefertiti at Tellel-Amarna in 1907.

J. H. Breasted. First professor of Egyptology in the United States, 1895. Author of many books. Original director of the Oriental Institute at the University of Chicago, 1919. Died 1935.

H. K. Brugsch. Wrote a dictionary of demotic, 7 vols., and Aegyptische Studien (Leipzig, 1855). Articles on RMP. Professor of Egyptology, Göttingen, 1868. Died 1894.

L. S. Bull. One of the authors of vol. II of RMP: photographs, transcriptions, transliterations, and literal translations of the papyrus.

H. Carter. Associated with Lord George Carnarvon from 1907 in Egyptian excavations. Responsible for the discovery and clearance of the tomb of Tutankhamen, Valley of the Kings, in 1922. Died 1939.

J. Cerny. Wrote on the religion of the ancient Egyptians in Annales du Service des antiquités de l'Égypte, 43 (1943), 179 ff.

E. Collignon. Discussed the decomposition of fractions, of the form 2 /(2 n - 1), as in the RMP. Recto (Paris, 1881).

W. R. Dawson. Who Was Who in Egyptology (London. 1951).

G. M, Ebers. Professor of Egyptology, Leipzig. Obtained a medical papyrus at Luxor (1872) that bears his name. Died 1898.

J. P. A. Erman. Professor of Egyptology at Berlin. Produced Egyptian dictionary (1926). A major figure. Died 1937.

M. Eyth. A pyramid mystic. Wrote Der Kampf um die Cheops Pyramide, 2 vols. (Heidelberg, 1902). Quotes value of ダ to forty decimal places.

A. Fakhry. Details the history of Cheops in The Pyramids (Chicago. 1961).

A. Favaro. An early disputant on Eisenlohr's translation of the RMP Recto and unit fraction values of 2/(2 n -1). See "Sulla interpretazione matemática del papiro Rhind pubblicato ed illustrato dal Prof. Augusto Eisenlohr,"in Memorie della R. Accademia di scienze, lettere ed arti in Modena, 2nd ser., 19 (1879), 89-143.

V. S. Golenischev, Member of the tsarist nobility who became professor of Egyptology at Cairo University. His collection of antiquities, loaned to the Moscow Museum in 1912 "contre une rente viagère,"included the famous Golenischev Papyrus. After the 1917 Revolution, payments ceased; the collection became government property; and the roll became known as the Moscow Mathematical Papyrus. Died 1947.

H. Grapow. Edited an Egyptian dictionary in association with Erman.

B. G. Gunn. Worked for the Service of Antiquities and for the Cairo Muséum. Professor of Egyptology at Oxford in 1934. Wrote article on finger numbering for Zeitschrift far ägyptische Spruche. 57 (1922). 71-72, dealing with Horus-eye fractions. Died 1950.

H. R. Hall. Keeper of Egyptian antiquities in the British Muséum. 1924. Hin Ancient History of the Near East (London, 1913) went through many editions. With Dr. A, Scott he unrolled the Egyptian Mathematical Leather Roll, which had remained rolled in the museum for sixty years, owing to its brittle condition. The EMLR came to the trustees, with the RMP, from A, H. Rhind in 1864.

E. Iversen. In his book The Myth of Egypt and Its Hieroglyphs in European Tradition (Copenhagen, 1961), Iversen discusses some of the misconceptions regarding the deciphering of the hieroglyphic writings.

T. G. H. James. Editor of Journal of Egyptian Archaeology, published annually by the Egypt Exploration Society, Manchester Square, London.

A. Jarolimek, Die Rätsel der Cheops Pyramide (Berlin, 1910). supports the pyramid mysticism of Taylor and Smyth, particularly with regard to π and the golden section, and surveys the works of other mystics: Neikes, and Eyth.

K. R. Lepsius. Curator of Egyptian antiquities at Berlin, 1865. Produced Denkmäler aus Aegypten und Aethiopien. 12 vols, (plus) (Berlin. 1859). An authority on the Egyptian language and monuments. Died 1884.

A. F. F. Mariette. A famous Egyptologist. Wrote Les papyrus egyptiens du Musée de Boalag (Paris, 1872), Discoverer of the Scrapeum at Sakkarah. Became curator of Egyptian monuments at Cairo. Died 1881.

G. Möller. In "Die Zeichen für die Bruchteile des Hohlmasses und das Uzatauge,"in Zeitschrift für ägyptische Sprache, 48(1911). 99- 106, Möller discusses the unit fractions used as portions of the hekat, the measure of capacity, referred to as Horus-eye fractions.

G. A. Reisner. Professor of Egyptology at Harvard, 1914. Excavator of renown who died at Giza in 1942. Many publications, including History of the Giza Necropolis, 2vols. (Cambridge, Mass., 1942).

A. H. Rhind. A Scotsman who went to Thebes for health reasons and became interested in excavating. In 1858 he purchased the RMP and the EMLR, which after his death (1863) came to the British Muséum. He wrote Thebes, its Tombs and Their Tenants (London, 1862).

M. Simon. Wrote at least four articles on the mathematics of the RMP-1904, 1905, 1907, 1909-dealing with π and with the unit fractions of the Recto.

E. Smith. A dealer in Egyptian antiquities and hieratic papyri, including the Ebers Papyrus and the Edwin Smith Papyrus. Died 1906.

J.J. Sylvester, Considered the 2 ÷(2 n - 1) of the RMP Recto as a problem in number theory, to which he gave the name "fractional sorites."In "On the Theory of Vulgar Fractions,"in American Journal of Mathematics, 3(1880), 332-385. 388-389; and Educational Times, 37(1882), 42-43, 80; he wrote: "It was their [the ancient Egyptians] curious custom to resolve every fraction into a sum of unit fractions according to a certain traditional method."

J. Taylor. One of the earliest pyramid mystics, perhaps the first. His théories were expressed in The Great Pyramid, Why It Was Built, and Who Built It? (London, 1859; 2nd ed., 1864). They were supported and fürther developed by the astronomer royal for Scotland, Piazzi Smyth (see Bibliography).

H. W. Turnbull. In The Great Mathematicians (London, 1951), 2-5, Turnbull refers to the geometry of the Great Pyramid, to the golden section, and to some of the théories of the pyramid mystics.

Q. Vetter. Discussed the methods of Egyptian division, especially with regard to 2-(2 n -1) of the RMP Recto, in Egypliské deleni (Prague, 1921).

H. E. Winlock. One of the more successful excavators in Egypt. Discovered statues and relics of Queen Hat-shepsut at Deir-el-Bahri in 1927. Became director of the New York Metropolitan Muséum of Art in 1932. Highly regarded in the field of Oriental scholarship. Died 1950.

T. Young. British physicist, originator of the wave theory of light. An early decipherer of certain hieroglyphs. in 1814 he recognized that the cartouches contained the names of pharaohs and queens, but did not pursue these studies. Died 1829.

Mathematical Papyri and Ostraca: Abbreviations Used, Approximate Dates, Other Details

DMP

Demotic Mathematical Papyrus (Cairo Mus.)

30(1 B.C.

CAIRO Cat. no. 89127 - 89137. Discovered 1938 at Tuna el-Gebel.

Demotic. Contains 40 problems on equations, series, volumes of pyramids, Pythagorean theorem. Uses fractions like 5/6 and 6/47.

Mich P

Michigan Papyrus

a.d. 350

ANN ARBOR University of Michigan. From the Fayum, Egypt. Cat. no. 621, also 145.

Greek. Contains several multiplication tables, all in unit fractions, and some problems. Since 6.000 drachmas made a talent, many fractions of 6,000 for tax offices.

MMP

Moscow Mathematical Papyrus

1850 B.C.

MOSCOW Bought by Golenischev in 1893, loaned to Moscow Museum in 1912. Cat. No. 4576, Pushkin Muséum of Fine Arts.

Hieratic. Contains 25 problems. 11 on pesus of beer and bread, 6 on triangle areas, one on volume of truncated pyramid, one on area of hemisphere. See Abd el-Rasoul and Golenischev in additional bibliographical notes.

RP

Reisner Papyrus

1880 B.C.

BOSTON Museum of Fine Arts. Found by Dr. G. Reisner at Giza in 1904

Hieratic. Concerns calculations of blocks of stone, and payment of workmen, for building a temple in the reign of Sesostris I.See W. K. Simpson in the bibliography.

RMP

Rhind Mathematical Papyrus

1650 B.C. Copy of a papyrus 200 years older

LONDON British Museum. Cat. no. 10,057-8. Bought with the EMLR by A. H, Rhind at Luxor, Egypt, in 1858.

Hieratic. The Recto contains divisions of 2 by the odd numbers 3 to 101 in unit fractions, and the numbers 1 to 9, by 10. The Verso has 87 problems on the 4 operations, solution of equations, progressions, volumes of granaries, sekeds of pyramids, pesus, the two-thirds rule, tables of Horus-eye fractions. See A. B. Chace, .1. R. Newman, E. T. Peet, A. H. Rhind in bibliography and additional bibliographical notes.

# data[].attributes.attachment_link.keywords[]
the mathematics of ancient egyptthe fraction two-thirdsthe emlrtables for the addition of unit fractions

# data[].attributes.attachment_link.keywords[]
and the g rulean interesting ostraconthe scribal rule for reciprocalsdemotic mathematical papyrian interpretation of rmp 79pesu problemsegyptian measuresequationsaddendanotes

# data[].attributes.attachment_link.description
THE MATHEMATICS OF ANCIENT EGYPTTHE FRACTION TWO-THIRDSTHE EMLRTABLES FOR THE ADDITION OF UNIT FRACTIONS, AND THE G RULEAN INTERESTING OSTRACONTHE SCRIBAL RULE FOR RECIPROCALSDEMOTIC MATHEMATICAL PAPYRIAN INTERPRETATION OF RMP 79PESU PROBLEMSEGYPTIAN MEASURESEQUATIONSADDENDANOTES Source for information on The Mathematics of Ancient Egypt: Complete Dictionary of Scientific Biography dictionary.

# data[].attributes.attachment_link.readable_text
The ancient Egyptians built their pyramids, tombs, temples and palaces out of stone, the most durable of all building materials. Although earthquakes, wars and the forces of nature have taken their toll, the remains of Egypt's monumental architectural achievements are visible across the land, a tribute to the greatness of this civilization. These building projects took a high degree of architectural and engineering skill, and the organization of a large workforce consisting of highly trained craftsmen and labourers.

Apart from the pyramids, Egyptian buildings were decorated with paintings, carved stone images, hieroglyphs and three-dimensional statues. The art tells the story of the pharaohs, the gods, the common people and the natural world of plants, birds and animals. The beauty and grandeur of these sites are beyond compare. How the ancient Egyptians were able to construct these massive structures using primitive tools is still a mystery.

main menu | civilization

# data[].attributes.attachment_link.description
The ancient Egyptians built their pyramids, tombs, temples and palaces out of stone, the most durable of all building materials. Although earthquakes, wars and the forces of nature have taken their toll, the remains of Egypt's monumental architectural achievements are visible across the land, a tribute to the greatness of this civilization.

# data[].attributes.attachment_link.description
Penn Medicine blogs provide information on a variety of health topics, from the latest news about Penn Medicine services and programs to details about upcoming events in your area.

# data[].attributes.attachment_link.title
How Did Writing Evolve in Ancient Egypt?

# data[].attributes.attachment_link.description
Ancient Egypt was one of the world's first two literate societies, having discovered the art/science of writing around the year 3,100 BC, not long after the first scripts were invented in Mesopotamia. But writing in Egypt developed very differently than in Mesopotamia.

# data[].attributes.attachment_link.readable_text
What would the beauty world be without the best beauty blogs? On the weekend (or whenever-who are we kidding?), we love nothing more than checking out what our favorite influencers are posting, from the products they're raving about or the makeup tutorials they're loving. While makeup and skincare blogs launch all the time, we continue to go back to certain experts over and over again, whether that's because they've been pillars of the beauty community for a long time or their expert knowledge is simply unrivaled. Because it's rude not to share, we thought we'd let you in on the Byrdie edit of the world's best beauty bloggers.

Katie Jane Hughes

Why follow: There are many things we love about Katie Jane Hughes's approach to beauty. Whether that's the most gorgeous eye makeup tutorials we've ever seen or a blow-by-blow account of getting microblading on her Insta Stories, we're hooked.

A Style Album

Why follow: Em and Lou of A Style Album know exactly what you need in your beauty wardrobe. Whether that's a great-smelling candle or your perfect signature lippie, these are the ladies who help us find true classics.

Why follow: If you want awesome beauty tips as well as a slice of life advice on the side, visit Tia Ward's blog.

Patricia Bright

Why follow: If it's super-glam beauty looks you're after, you'll find them at Patricia Bright's page. While you can watch her YouTube videos, we also love her detailed posts on how to get dolled up, complete with lists and ratings of the products she uses.

Shirley's Wardrobe

Why follow: London-based Shirley appears to be all about fashion, but she has some incredible beauty tricks and tips, too. From wedding-guest beauty ideas to the ideal nude face, she's got you covered.

Why follow: While we love checking out Bleach London's Insta feed for hair-color ideas, we also often turn to Zoe London, who changes hers up with bold and bright hues. And if you're worried about how much dye is affecting your strands, fear not- she even has a great tip for how to fix that.

Beauty Is Boring

Why follow: Despite this blog's moniker, its approach to beauty is anything but. Expect bold, bright and breathtaking images from this contemporary site. In other words, it's the ideal place to find inspiration when you're tired of your old makeup routine and looking to kick-start a transformation.

Sali Hughes Beauty

Why follow: You can't talk about beauty and not mention Sali Hughes. As well as being the resident beauty columnist for The Guardian and having written one of the most brilliant books on beauty we've ever read (Pretty Honest), she also runs the blog Sali Hughes Beauty. Expect to find tutorials, product reviews and videos of chats in her bathroom with fellow beauty people. Reviews are honest, upfront and always exactly what you need.

The Anna Edit

Why follow: Blogger Anna Gardner has been running Vivianna Does Makeup since about 2010. She currently has nearly 400,000 subscribers to her YouTube channel, and it's easy to see why. She is a true makeup and beauty addict and offers up fantastic details about the products she reviews. Not only does she look at the luxury market, but she's also up for hunting out a big bargain, something we always love finding out about too.

The Beauty of It Is

Why follow: Care about the environment and want to avoid toxic beauty products but can't seem to find decent products? Allow Katey Denno of The Beauty of It Is to be your guide. She often updates her Insta feed with great "green" product reviews. She's also an incredible makeup artist.

I Covet Thee

Why follow: We enjoy a fellow makeup addict, which is why I Covet Thee features in our best-bloggers list. As well as an array of pretty covetable products on her Instagram account (hence the name, we imagine), there's also a great range of tutorials on her YouTube account.

Why follow: In the world of beauty vloggers, sisters Samantha Chapman and Nicola Haste are true veterans. They launched their YouTube channel 11 years ago and now have over two million subscribers. Their tutorials are easy to follow and entertaining, and range from Gwen Stefani to Halloween costumes, as well as more basic how-tos such as light contouring.

A Model Recommends

Why follow: What we love about Ruth Crilly of A Model Recommends is her down-to-earth approach to skincare and makeup. The international model is one to follow for skincare advice that actually works-you need only read a couple of the comments on her blog to realize that she knows exactly what she's talking about and understands how to get results.

Where to follow: YouTube (@amodelrecommends), Instagram (@ruthcrilly), Twitter (@ModelRecommends), AModelRecommends.com

Estée Lalonde

Why follow: Formerly known as Essie Button, Estée Lalonde has been running her beauty and lifestyle blog for five years. As well as providing helpful beauty video tutorials on her YouTube channel, she shares a inside look at her life on Instagram, as well as her current favorite beauty buys. The gorgeous aesthetic that runs throughout her blog is total #goals.

Barefoot Blonde

Why follow: Amber Clark is a beauty blogger who hails from NYC but is currently in Hawaii. While there are lots of snaps on her Insta feed featuring her husband and kids, there's one reason why we keep coming back to her blog: her braids. A self-confessed plait-obsessive, she has given us serious hair envy.

The Sunday Girl

Why follow: If you know anything about British blog The Sunday Girl, you'll know that this is dedicated to review new products; there are no tutorials here. But that's just one of the reasons why this blog is so refreshing; it sticks to what it knows it does best. From perfumes to toothbrushes, as well as all the latest makeup launches, this has a lot to offer the makeup addict.

Doina Ciobanu

Where to follow: Instagram (@doina)

Claire Marshall

Why follow: We've been following makeup artist and blogger Claire Marshall for some time now, and we quite often like to see what she's up to on Snapchat. Not only because she gives us a sneak peek at her daily life but also because she does great beauty looks. Her hair always looks amazing, and we just love her tattoos as well.

Where to follow: Snapchat (@heyclaire), Instagram (@heyclaire)

Fresh Lengths

Why follow: If you're a fan of Byrdie, you'll have noticed that we've featured Lesley of Fresh Lengths a lot. And there's a good reason for that. She's an incredible blogger with new and exciting ideas for natural hair. And she's super gorgeous too. Need we say more?

Lisa Eldridge

Why follow: Want seriously easy yet incredible makeup tutorials? Head straight to makeup artist Lisa Eldridge's YouTube channel. From a daily beauty routine for work to giving you a step-by-step no-makeup look, pull out these videos when you want to nail a new style immediately. On Instagram, you'll get fun behind-the-scenes shots with many of her A-list clients.

Pretty Sickly

Why follow: Yanin Namasonthi is super cool. Not only is her style on point, she also gives us great behind-the-scenes looks at cool events and shopping experiences (like visiting a nail polish vending machine). We're incredibly jealous right now.

Where to follow: Instagram (@idressmyselff)

The Beauty Look Book

Why follow: Sometimes you just need a good swatch to see if you like a beauty product. Instead of tutorials, The Beauty Look Book focuses on high-end beauty products, which is great if you're a total skincare and makeup junkie.

Where to follow: TheBeautyLookBook.com

Cult of Pretty

Why follow: When you're tired of all the other beauty products, go to Cult of Pretty immediately. It's run by Ann Colville Somma, who has worked in the beauty industry for over a decade and works in product development and innovation, so she knows a thing or two about the hottest new beauty products.

Where to follow: CultofPretty.com

Lisa Potter-Dixon

Why follow: Fun is the word we'd use to describe head Benefit makeup artist Lisa Potter-Dixon. Because that's exactly what you get-beauty tutorials with a slice of excitement. From advice on how to do wedding makeup to the fake freckle trend, you'll enjoy watching her videos as much as you will learning from them.

Where to follow: YouTube (@lisapotterdixon)

# data[].attributes.attachment_link.title
26 of the Best Beauty Blogs You Should Be Following

# data[].attributes.attachment_link.description
What would the beauty world be without the best beauty blogs? On the weekend (or whenever-who are we kidding?), we love nothing more than checking out what our favorite influencers are posting, from the products they're raving about or the makeup tutorials they're loving.

# data[].attributes.attachment_link.readable_text
Ancient Egyptian Writing is known as hieroglyphics ('sacred carvings') and developed at some point prior to the Early Dynastic Period (c. 3150 -2613 BCE). According to some scholars, the concept of the written word was first developed in Mesopotamia and came to Egypt through trade. While there certainly was cross-cultural exchange between the two regions, Egyptian hieroglyphics are completely Egyptian in origin; there is no evidence of early writings which describe non-Egyptian concepts, places, or objects, and early Egyptian pictographs have no correlation to early Mesopotamian signs. The designation 'hieroglyphics' is a Greek word; the Egyptians referred to their writing as medu-netjer, 'the god's words,' as they believed writing had been given to them by the great god Thoth.

According to one ancient Egyptian tale, in the beginning of time Thoth created himself and, in the form of an ibis, lay the cosmic egg which held all of creation. In another story, Thoth emerged from the lips of the sun god Ra at the dawn of time, and in another, he was born of the contendings of the gods Horus and Set, representing the forces of order and chaos. In all of these, however, the constant is that Thoth was born with an immense breadth of knowledge and, among the most important, the knowledge of the power of words.

Thoth gave human beings this knowledge freely, but it was a responsibility he expected them to take seriously. Words could hurt, heal, elevate, destroy, condemn, and even raise someone from death to life. Egyptologist Rosalie David comments on this:

The main purpose of writing was not decorative, and it was not originally intended for literary or commercial use. Its most important function was to provide a means by which certain concepts or events could be brought into existence. The Egyptians believed that if something were committed to writing it could be repeatedly "made to happen" by means of magic. (199)

This concept is not as strange as it might first appear. Any writer knows that one often has no idea what one wants to say until the end of the first draft, and every avid reader understands the "magic" of discovering unknown worlds between the covers of a book and making that magic happen again each time the book is opened. David's reference to "concepts or events" coming into existence through writing is a common understanding among writers. American author William Faulkner stated in his Nobel Prize address that he wrote "to create out of the materials of the human spirit something which did not exist before" (1). This same motivation has been expressed in different words by many writers over the centuries, but before any of them even existed the ancient Egyptians understood this concept well. The great gift of Thoth was the ability not only to express one's self but to literally be able to change the world through the power of words. Before that could happen, however, before the gift could be put to its full use, it had to be understood.

The Creation of Writing

However much Thoth had to do with giving humans their system of writing (and, to the Egyptians, 'humanity' equaled 'Egyptian'), the ancient Egyptians had to work out for themselves what this gift was and how to use it. Sometime in the latter part of the Predynastic Period in Egypt (c. 6000 - c. 3150 BCE), they began to use symbols to represent simple concepts. Egyptologist Miriam Lichtheim writes how this early script "was limited to the briefest notations designed to identify a person or a place, an event or a possession" (3). Most likely the earliest purpose writing served was in trade, to convey information about goods, prices, purchases, between one point and another. The first actual extant evidence of Egyptian writing, however, comes from tombs in the form of Offering Lists in the Early Dynastic Period.

Death was not the end of life for the ancient Egyptians; it was only a transition from one state to another. The dead lived on in the afterlife and relied upon the living to remember them and present them with offerings of food and drink. An Offering List was an inventory of the gifts due to a particular person and inscribed on the wall of their tomb. Someone who had performed great deeds, held a high position of authority, or led troops to victory in battle were due greater offerings than another who had done relatively little with their lives. Along with the list was a brief epitaph stating who the person was, what they had done, and why they were due such offerings. These lists and epitaphs might sometimes be quite brief but most of the time were not and became longer as this practice continued. Lichtheim explains:

Sign up for our free weekly email newsletter!

The Offering List grew to enormous length till the day on which an inventive mind realized that a short Prayer for Offerings would be an effective substitute for the unwieldy list. Once the prayer, which may already have existed in spoken form, was put into writing, it became the basic element around which tomb-texts and representations were organized. Similarly, the ever lengthening lists of an official's ranks and titles were infused with life when the imagination began to flesh them out with narration, and the Autobiography was born. (3)

The autobiography and the prayer became the first forms of Egyptian literature and were created using the hieroglyphic script.

Development & Use of Hieroglyphic Script

Hieroglyphics developed out of the early pictographs. People used symbols, pictures to represent concepts such as a person or event. The problem with a pictogram, however, is that the information it contains is quite limited. One may draw a picture of a woman and a temple and a sheep but has no way of relaying their connection. Is the woman coming from or going to the temple? Is the sheep an offering she is leading to the priests or a gift to her from them? Is the woman even going to the temple at all or is she merely walking a sheep in the vicinity? Are the woman and sheep even related at all? The early pictographic writing lacked any ability to answer these questions.

The Egyptians developed the same system as the Sumerians but added logograms (symbols representing words) and ideograms to their script.

The Sumerians of ancient Mesopotamia had already come upon this problem in writing and created an advanced script c. 3200 BCE in the city of Uruk. The theory that Egyptian script developed from Mesopotamian writing is most sharply challenged by this development, in fact, because if the Egyptians had learned the art of writing from the Sumerians, they would have bypassed the stage of pictograms and begun with the Sumerian creation of phonograms - symbols which represent sound. The Sumerians learned to expand their written language through symbols directly representing that language so that if they wished to relay some specific information regarding a woman, a temple, and a sheep, they could write, "The woman took the sheep as an offering to the temple," and the message was clear.

The Egyptians developed this same system but added logograms (symbols representing words) and ideograms to their script. An ideogram is a 'sense sign' that conveys a certain message clearly through a recognizable symbol. The best example of an ideogram is probably a minus sign: one recognizes that it means subtraction. The emoji is a modern example familiar to anyone acquainted with texting; placing the image of a laughing face at the end of one's sentence lets a reader know that one is joking or finds the subject funny. The phonogram, logogram, and ideogram made up the basis for hieroglyphic script. Rosalie David explains:

There are three types of phonograms in hieroglypics: uniliteral or alphabetic signs, where one hieroglyph (picture) represents a single consonant or sound value; biliteral signs, where one hieroglyph represents two consonants; and triliteral signs where one hieroglyph represents three consonants. There are twenty-four hieroglyphic signs in the Egyptian alphabet and these are the phonograms most commonly used. But since there was never a purely alphabetic system, these signs were placed alongside other phonograms (biliterals and triliterals) and ideograms. Ideograms were often placed at the end of a word (spelled out in phonograms) to clarify the meaning of that word and, when used in this way, we refer to them as "determinatives." This assists in two ways: the addition of a determinative helps to clarify the meaning of a particular word, since some words look similar or identical to each other when spelled out and written down only in the phonograms; and beacuse determinatives stand at the end of the word they can indicate where one word ends and another begins. (193)

A modern-day example of how hieroglyphics were written would be a text message in which an emoji of an angry face is placed after an image of a school. Without having to use any words one could convey the concept of "I hate school" or "I am angry about school." If one wanted to make one's problem clearer, one could place an image of a teacher or fellow student before the angry-face-ideogram or a series of pictures telling a story of a problem one had with a teacher. Determinatives were important in the script, especially because hieroglyphics could be written left-to-right or right-to-left or down-to-up or up-to-down. Inscriptions over temple doors, palace gates, and tombs go in whatever direction was best served for that message. The beauty of the final work was the only consideration in which direction the script was to be read. Egyptologist Karl-Theodor Zauzich notes:

The placement of hieroglyphs in relation to one another was governed by aesthetic rules. The Egyptians always tried to group signs in balanced rectangles. For example, the word for "health" was written with the three consonants s-n-b. These would not be written [in a linear fashion] by an Egyptian because the group would look ugly, it would be considered "incorrect". The "correct" writing would be the grouping of the signs into a rectangle...The labor of construction was lightened somewhat by the fact that individual hieroglyphs could be enlarged or shrunk as the grouping required and that some signs could be placed either horizontally or vertically. Scribes would even reverse the order of signs if it seemed that a more balanced rectangle could be obtained by writing them in the wrong order. (4)

The script could easily be read by recognizing the direction the phonograms were facing. Images in any inscription always face the beginning of the line of text; if the text is to be read left-to-right then the faces of the people, birds, and animals will be looking to the left. These sentences were easy enough to read for those who knew the Egyptian language but not for others. Zauzich notes how "nowhere among all the hieroglyphs is there a single sign that represents the sound of a vowel" (6). Vowels were placed in a sentence by the reader who understood the spoken language. Zauzich writes:

This is less complicated than it sounds. For example, any of us can read an advertisement that consists almost entirely of consonants:

3rd flr apt in hse, 4 lg rms, exclnt loc nr cntr, prkg, w-b-frpl, hdwd flrs, skylts, ldry, $600 incl ht (6).

In this same way, the ancient Egyptians would be able to read hieroglyphic script by recognizing what 'letters' were missing in a sentence and applying them.

Other Scripts

Hieroglyphics were comprised of an 'alphabet' of 24 basic consonants which would convey meaning but over 800 different symbols to express that meaning precisely which all had to be memorized and used correctly. Zauzich answers the question which may immediately come to mind:

It may well be asked why the Egyptians developed a complicated writing system that used several hundred signs when they could have used their alphabet of some thirty signs and made their language much easier to read and write. This puzzling fact probably has a historical explanation: the one-consonant signs were not "discovered" until after the other signs were in use. Since by that time the entire writing system was established, it could not be discarded, for specific religious reasons. Hieroglyphics were regarded as a precious gift of Thoth, the god of wisdom. To stop using many of these signs and to change the entire system of writing would have been considered both a sacrilege and an immense loss, not to mention the fact that such a change would make all the older texts meaningless at a single blow. (11)

Even so, hieroglyphics were obviously quite labor-intensive for a scribe and so another faster script was developed shortly after known as hieratic ('sacred writing'). Hieratic script used characters which were simplified versions of hieroglyphic symbols. Hieratic appeared in the Early Dynastic Period in Egypt after hieroglyphic writing was already firmly developed.

Hieroglyphics continued to be used throughout Egypt's history in all forms of writing but came primarily to be the script of monuments and temples. Hieroglyphics, grouped in their beautifully formed rectangles, leant themselves to the grandeur of monumental inscriptions. Hieratic came to be used first in religious texts but then in other areas such as business administration, magical texts, personal and business letters, and legal documents such as wills and court records. Hieratic was written on papyrus or ostraca and practiced on stone and wood. It developed into a cursive script around 800 BCE (known as 'abnormal hieratic') and then was replaced c. 700 BCE by demotic script.

Demotic script ('popular writing') was used in every kind of writing while hieroglyphics continued to be the script of monumental inscriptions in stone. The Egyptians called demotic sekh-shat, 'writing for documents,' and it became the most popular for the next 1,000 years in all kinds of written works. Demotic script seems to have originated in the Delta region of Lower Egypt and spread south during the 26th Dynasty of the Third Intermediate Period (c. 1069-525 BCE). Demotic continued in use through the Late Period of Ancient Egypt (525-332 BCE) and the Ptolemaic Dynasty (332-30 BCE) into Roman Egypt when it was replaced by Coptic script.Coptic was the script of the Copts, Egyptian Christians, who spoke Egyptian dialects but wrote in the Greek alphabet with some additions from demotic script. Since the Greek language had vowels, the Copts incorporated them in their script to make the meaning clear to anyone reading it, no matter what their native language. Coptic script was used to copy and preserve a number of important documents, most notably the books of the Christian New Testament, and also served to provide the key to later generations for understanding hieroglyphics.

Loss & Discovery

It has been argued that the meaning of hieroglyphics was lost throughout the later periods of Egyptian history as people forgot how to read and write the symbols. Actually, hieroglyphics were still in use as late as the Ptolemaic Dynasty and only fell out of favor with the rise of the new religion of Christianity during the early Roman Period. There were lapses throughout the country's history in the use of hieroglyphics, but the art was not lost until the world the script represented changed. As Coptic script continued to be used in the new paradigm of Egyptian culture; hieroglyphic writing faded into memory. By the time of the Arab Invasion of the 7th century CE, no one living in Egypt knew what the hieroglyphic inscriptions meant.

When the European nations began exploring the country in the 17th century CE, they had no more of an idea that the hieroglyphics were a written language than the Muslims had. In the 17th century CE, hieroglyphics were firmly claimed to be magical symbols and this understanding was primarily encouraged through the work of the German scholar and polymath Athanasius Kircher (1620-1680 CE). Kircher followed the lead of ancient Greek writers who had also failed to understand the meaning of hieroglyphics and believed they were symbols. Taking their interpretation as fact instead of conjecture, Kircher insisted on an interpretation where each symbol represented a concept, much in the way the modern peace sign would be understood. His attempts to decipher Egyptian writing failed, therefore, because he was operating from a wrong model.

Many other scholars would attempt to decipher the meaning of the ancient Egyptian symbols without success between Kircher's work and the 19th century CE but had no basis for understanding what they were working with. Even when it seemed as though the symbols suggested a certain pattern such as one would find in a writing system, there was no way to recognize what those patterns translated to. In 1798 CE, however, when Napoleon's army invaded Egypt, the Rosetta Stone was discovered by one of his lieutenants, who recognized its potential importance and had it sent to Napoleon's institute for study in Cairo. The Rosetta Stone is a proclamation in Greek, hieroglyphics, and demotic from the reign of Ptolemy V (204-181 BCE). All three texts relay the same information in keeping with the Ptolemaic ideal of a multi-cultural society; whether one read Greek, hieroglyphic, or demotic, one would be able to understand the message on the stone.

Work on deciphering hieroglyphics with the help of the stone was delayed until the English defeated the French in the Napoleonic Wars and the stone was brought from Cairo to England. Once there, scholars set about trying to understand the ancient writing system but were still working from the earlier understanding Kircher had so convincingly advanced. The English polymath and scholar Thomas Young (1773-1829 CE) came to believe that the symbols represented words and that hieroglyphics were closely related to demotic and later Coptic scripts. His work was built upon by his sometimes-colleague-sometimes-rival, the philologist and scholar Jean-Francois Champollion (1790-1832 CE).

Champollion's name is forever linked with the Rosetta Stone and the decipherment of hieroglyphics because of the famous publication of his work in 1824 CE which conclusively showed that Egyptian hieroglyphics were a writing system composed of phonograms, logograms, and ideograms. Contention between Young and Champollion over who made the more significant discoveries and who deserves the greater credit is reflected in the same ongoing debate in the present day by scholars. It seems quite clear, however, that Young's work lay the foundation on which Champollion was able to build but it was Champollion's breakthrough which finally deciphered the ancient writing system and opened up Egyptian culture and history for the world.

# data[].attributes.attachment_link.description
Ancient Egyptian Writing is known as hieroglyphics ('sacred carvings') and developed at some point prior to the Early Dynastic Period (c. 3150 -2613 BCE). According to some scholars, the concept of the written word was first developed in Mesopotamia and came to Egypt through trade.

# data[].attributes.attachment_link.provider_name
archisoup | Architecture Guides & Resources

# data[].attributes.attachment_link.readable_text
Keeping up to date with what's occurring within the architectural and design world is an important part of our professional development, and so here we have a selection of our favourite (and best) most visited blogs and websites.

We're firm believers that these should at least be visited on a weekly basis, if not every day! ...so keep yourself up to date with this selection of the best Architecture and design blogs:

Archdaily delivers inspiration, tools and knowledge to millions architects and much like Dezeen is one of the biggest architecture blogs out there ...and so not to be missed

Divisare (meaning imagining, designing with the mind) originally called Europaconcorsi, has been an online architecture blog since 1998. Unlike other blogs, Divisare only publishes exemplar work by the best and up and coming architects which is further supported by a large data base of architecture typologies and elements

The "AJ" provides daily news and analysis into issues that are affecting our industry, comprehensive building studies with technical details and drawings, client profiles, competition updates as well as letting you know who's won what and why. ...so well worth regularly checking in

Architizer was founded in 2009, and aims to offer architects with information on how to build better buildings, they have a large amount of very useful information within their blog section, with lots tips, tricks and information for architecture students and young professionals.

Founded in 1999, design boom has established itself as one of the first online design and architecture magazines, publishing the latest news and key issues in all aspects of design, architecture and art. With their daily updates, it is well worth regular checking in.

The Architectural Review is a global architecture magazine offering critiques and the critical thinking behind the buildings shaping the architectural discourse. Its slightly more academic that the likes of Dezeen, Archdaily and Design Boom but well worth a look when you've got a bit more time on your hands.

BLDGBLOG ("building blog") was launched in 2004 by Geoff Managua, and offers an alternative to the "normal" architecture and design blog, by providing a series of narratives and investigations in his posts. It's a fantastic resource for developing your own design brief or looking for an area to research.

The architecture section of Reddit is one of the few active architecture forums on the internet and is bursting with useful information by its constant updates and vibrant user conversation. They also have a forum dedicated to students called young students.

This is a blog about architectureand what it's like to be an architect. Frequently the topics help explain what architect's do for a living

Founded in 2006 Architect Magazine The premier site of the American Institute of Architects, providing regular and up to date industry news & building resources for architects and architecture industry professionals

Sister site to the above mentioned Archinect, Bustler is a premier online publication that focuses on keeping the design community as a whole "busy and inspired", through tracking activity from around the globe with breaking stories on outstanding competitions and events

Founded in 1999 and run and operated by the Danish Architecture Centre, arcspace is an architecture webzine that features the most current and creative of todays projects from the worlds leading architects, as well as the most influential of the past.

World-Architects is a membership-based network of contemporary architects and building professionals, that advocate quality in architecture. Their selection of projects is carefully curated by a highly discerning group of critics from around the world ...Bringing daily news, building reviews, an international job board and events calendar, along with a multilingual weekly newsletter.

e-architect claims to be one of the world's largest architecture websites with its 22,000 pages of dedicated architectural information. unlike other online architecture journals, e-architect also provides a building database that can be searched by country, city, type or by architect.

"For example you could find information on Wembley Stadium via our England, London, Football Stadium or Foster + Partners pages."

Alongside this e-architect provides all the usual online features such as building news, events, competitions, photos, jobs, awards and products.

Founded in 1896 The Architectural Review is one of the oldest and widest read architectural magazines in the world.

This global architecture magazine, provides diverse and incisive coverage spanning all parts of the world. With a 120-year history as the world's favourite architecture publication, it is a leader of debates and a must-have for architecture and design communities around the world.

Founded in 1989, Architecture Today is an independently-published British architecture magazine. Largely comprising in-depth building studies, it is physically published ten times per annum and is available free-of-charge to Architects Registration Board-registered architects, however for those that are not registered, there is still a wealth of information available via the website.

The Architect's Newspaper serves up news and inside reports to a niche community of architects, designers, engineers and landscape architects to name a few. Delivering quality news and cultural reporting through print, web, and a newsletter.

More with less is a very modern and clean online design and architecture publication that showcases the best projects of architects and designers from all around the world so every creative mind can find inspiration.

Study Architecture is an online resource for undergraduate and graduate students who are interested in joining the Architecture profession. They bring together colleges and universities, students and working architecture professionals to create a forum for sharing information and ideas.

# data[].attributes.attachment_link.title
The Best Architecture and Design Blogs - archisoup | Architecture Guides & Resources

# data[].attributes.attachment_link.description
Keeping up to date with what's occurring within the architectural and design world is an important part of our professional development, and so here we have a selection of our favourite (and best) most visited blogs and websites. We're firm believers that these should at least be visited on a weekly basis, if not every day!

# data[].attributes.body
Mitch

# data[].attributes.attachment_link.title
How ancient Egypt shaped our idea of beauty

# data[].attributes.attachment_link.description
Pop culture is steeped in images of smoky-eyed pharaohs and their queens. Were the ancient Egyptians insufferably vain – or are we simply projecting our own values onto them?

# data[].attributes.attachment_link.readable_text
Ancient Egypt was a civilization that lasted from 3300 to 525 B.C.E. This is probably where the concept of health started. Some of the earliest records of medical care come from ancient Egypt.

The ancient Egyptians believed in prayer as a solution to health problems, but they also had natural, or practical, remedies, such as herbs.

It was a structured society with tools such as written language and mathematics, which enabled them to record and develop ideas, and it meant that others could learn from them.

Share on Pinterest
The ancient Egyptians had basic medical equipment, and they also believed that the gods controlled life and health. This picture shows Isis on a birthing stool,

The ancient Egyptians thought that gods, demons, and spirits played a key role in causing diseases.

Doctors believed that spirits blocked channels in the body and that this affected the way the body worked. They looked for ways to unblock these channels. They used a combination of prayer and natural - or non-spiritual - remedies.

Most healers were also priests, but, in time, the profession of a "doctor of medicine" emerged.

The fact that ancient Egyptians had systems of letters and numbers meant they were able to record and develop ideas and make calculations. Documented ancient Egyptian medical literature is among the oldest in existence today.

The ancient Egyptians had an organized economy and system of government, a settled population, social conventions, and properly enforced laws. Before this, the local people mainly lived a nomadic life.

This stability allowed medical research to develop.

In addition, there were also relatively wealthy individuals in ancient Egyptian society. They could afford some health care and also had time to ponder and study.

The ancient Egyptians were also traders. They traveled long distances, coming back with herbs and spices from faraway lands.

Research and learning

The ancient Egyptians' practice of preserving deceased people as mummies meant that they learned something about how the human body works.

In one process, the priest-doctor inserted a long, hooked implement through the nostril and broke the thin bone of the brain case to remove the brain.

Kings and queens from faraway lands sought Egyptian doctors because of their reputation for excellence.

Archaeologists have found a number of written records that describe ancient Egyptian medical practice, including the Ebers papyrus.

Share on Pinterest
The ancient Egyptians probably learned something about the human body through mummification.

This document contains over 700 remedies and magical formulas and scores of incantations aimed at repelling demons that cause disease.

The authors probably wrote them around 1500 B.C.E., but the document may contain copies of material dating back to 3400 B.C.E. They are among the oldest preserved medical documents in existence.

The scroll provides evidence of some sound scientific procedures.

Doctors appear to have had fairly good knowledge about bone structure and some awareness of how the brain and liver worked.

The heart: According to the Ebers Papyrus, the center of the body's blood supply is the heart, and every corner of the body is attached to vessels. The heart was the meeting point for vessels that carried tears, urine, semen, and blood. Researchers writing in 2014 described ancient Egyptian understanding of the cardiovascular system as "surprisingly sophisticated, if not accurate.

Mental illness: The document describes in detail the characteristics, causes, and treatment for mental disorders such as dementia and depression. The ancient Egyptians appear to have seen mental diseases as a combination of blocked channels and the influence of evil spirits and angry Gods.

Family planning: The scroll contains a section on birth control, how to tell if a person is pregnant, and some other gynecological issues.

There is also advice about:

skin problems

dental problems

diseases related to the eyes

intestinal disease

parasites

how to surgically treat an abscess or a tumor

In addition, there is evidence that doctors knew how to set broken bones and treat burns.

Medical advice

Some recommendations that physicians made then seem fairly sound to us now.

They advised people to wash and shave their bodies to prevent infections, to eat carefully, and to avoid unclean animals and raw fish.

Some, however, are less familiar. Putting a plug of crocodile dung into the entrance of the vagina, for example, was a method of birth control. People also used dung to disperse evil spirits.

Dentistry

The Egyptians also practiced dentistry. Caries and tooth decay appear to have been common.

Remedies included:

cumin, incense, and onion to treat swollen gums

opium, possibly, to treat pain pain

drilling holes into the jaw to drain an abscess

However, they do not seem to have extracted teeth.

Everyday life in Egypt involved beliefs and fear of magic, gods, demons, evils spirits, and so on. They believed that the gods created and controlled life.

Heka was the goddess of magic and medicine, while Bes, another god, protected women during pregnancy. People called upon Serket if they had a scorpion bite.

Angry gods or evil forces caused bad luck and disaster, so people used magic and religion to deal with these forces and to treat people.

Priests and doctors were often one and the same. Many healers were priests of Sekhmet, an Egyptian warrior goddess and the goddess of healing, curses, and threats.

As well as science, treatment involved the use of magic, incantations, amulets, aromas, offerings, tattoos, and statues.

The religious and magic rituals and procedures probably had a powerful placebo effect, so they may have resulted in healing.

The "channel theory" came from observing farmers who dug out irrigations channels for their crops. It allowed medicine to move from entirely spiritual cures towards practical, natural ones.

The doctors believed that, as in irrigation, channels provide the body with routes for good health. If blockages occurred, they used laxatives to unblock them.

The heart was the center of 46 channels, seen as types of tubes.

It is true that human veins, arteries, and intestines are types of tubes. However, the Egyptians did not understand that these channels had different functions.

Blockages in the human channels were thought to result from the doings of Wekhedu, an evil spirit. When Wekhedu came to the surface of the body, it showed as pus.

This idea that bodily function played a role in health was a breakthrough in the history of medicine.

Channels and the heart

The ancient Egyptians believed that the body consisted of a system of channels, or "Metu."

One researcher notes that they believed that bodily fluids could enter this system, including feces. This would have a negative effect, and enemas became an important method of treatment for many conditions, including malaria and smallpox.

The Ebers Papyrus notes that vessels run from the heart to all four limbs and every part of the body.

When a doctor, Sekmet priest, or exorcist places their hands on any part of the body, they are examining the heart, because all vessels come from the heart.

Channel theory holds that:

The heart is the source. It speaks out to each part of the body.

When people breathe in through the nose, the air enters their heart, lungs, and then the belly.

The nostrils have four vessels, two of which provide mucus and two provide blood.

The human body has four vessels, which lead to two ears. The "breath of life" enters the right ear and "breath of death" enters the left ear.

Four vessels that lead to the head cause baldness.

All eye diseases come from four vessels in the forehead, which supply blood to the eyes.

Two vessels enter the testicles and provide semen.

Two vessels in the buttocks supply them with vital nutrients.

Six vessels reach the soles of the feet and six lead down the arms to the fingers.

Two vessels supply the bladder with urine.

Four vessels supply the liver with liquid and air. When they overfill the liver with blood, they cause diseases.

Four vessels also supply the lungs and spleen with liquid and air.

The liquid and air that come out of the anus come from four vessels.

The anus is also exposed to all the vessels in the arms and legs when they overflow with waste.

Egyptian physicians underwent training and could successfully fix broken bones and dislocated joints.

Basic surgery - meaning procedures close to the surface of the skin or on the skin - was a common skill, and doctors knew how to stitch wounds effectively.

They used bandages and would bind certain plant products, such as willow leaves, into the bandages to treat inflammation.

However, they did not perform surgery deep inside the body, probably because there were no anesthetics or antiseptics.

Circumcision of baby boys was common practice. It is hard to tell whether female circumcision existed. There is one mention, but this may be a mistranslation.

Surgeons had an array of instruments, such as pincers, forceps, spoons, saws, containers with burning incense, hooks, and knives.

Prosthetics existed, but they were probably not very practical. People may have used them to make deceased people look more presentable during funerals or simply for decorative purposes.

Egyptian doctors said there were three types of injuries:

Treatable injuries: They dealt with these immediately.

Contestable injuries: The doctor believed these were not life-threatening and that the person could survive without intervention. The doctor would observe the patient. If they survived, the doctor would decide in time whether to intervene.

Untreatable ailments: The doctor would not intervene.

Common complaints included:

A remedy for headaches, mentioned in the Ebers Papyrus, appears to advise the following:

Mash together flour, incense, wood of wa, waneb plant, mint, a horn of a stag, sycamore seeds, mason's plaster, seeds of zart, water. Apply to the head.

People used aloe vera in ancient Egyptian times to heal burns and skin diseases.

Another remedy is to use poppy seeds or aloe.

Asthma: Honey and milk, sesame, frankincense

Burns and skin disease: Aloe

Pain: Thyme

Digestive problems: Juniper, mint, garlic, and sandalwood

Bad breath: Mint, caraway

Epilepsy: Camphor

Vomiting: Mint to stop it and mustard seeds to cause it

Other conditions and treatments include:

The cure for a cold was an incantation.

Early concepts of homeopathy

Some treatments used products or herbs or plants that looked similar to the illness they were treating, a practice known as simila similibus, or similar with similar.

Today, homeopathy follows a similar principle.

In Egyptian times, people used ostrich eggs to treat a fractured skull.

Cleanliness was an important part of Egyptian life, and homes had rudimentary baths and toilets. Appearance and the use of make-up were important.

The main aim was to meet social and religious requirements, although many people wore make-up around their eyes to protect them from disease.

People used mosquito nets during the hot months, whether to protect against malaria and other diseases or to avoid bites. Malaria was a common problem.

Priests washed themselves, their clothing, and their eating utensils regularly. This helped to protect their health, although they did it for religious reasons.

There was no public health infrastructure as we know of today. There were no sewage systems, systematic medical care, or public hygiene.

The ancient Egyptians were probably the first people to have professional doctors, and it was a respected occupation.

According to the Ancient History Encyclopedia, they had to be literate and clean in body and spirit. There were doctors all over Egypt.

The earliest ever record of a male physician was Hesy-Ra in 2700 B.C.E. He was was "Chief of Dentists and Doctors" to King Dioser.

The first record of a female doctor was probably Peseshet in 2400 B.C.E., the supervisor of all female doctors, but there may have been female doctors as early as 3000 B.C.E.

The top doctors worked in the royal court. Below them, inspectors would supervise the work of other doctors. There were specialists, such as dentists, proctologists, gastroenterologists, and ophthalmologists.

A proctologist - or possibly the giver of enemas - was called "nery phuyt," which translates as the "shepherd of the anus," according to an article published in the Journal of Vascular Surgery.

The ancient Egyptians had sophisticated methods of practicing medicine that combined the supernatural with the natural, such as herbal remedies and surgery.

Their written records have allowed their knowledge to pass down through the ages. While not always accurate, some of their theories and practices were not very different from those in use today.

# data[].attributes.attachment_link.title
Ancient Egyptian medicine: Influences, practice, magic, and religion

# data[].attributes.attachment_link.description
Ancient Egyptian documents are probably the earliest records of healthcare practice. The ancient Egyptians knew something about the human body and they sought healing through both herbal medicine and incantations. They also practiced basic surgery. Both male and female doctors were important. Find out more.

# data[].attributes.attachment_link.readable_text
You are here

Press enter to open the dropdown list, then press tab and enter to choose the language.

produced by Michael Guillen, 1959- , in Where Did it Come From? (New York, NY: A&E Television Networks, 2011) , 54 mins

Cite Email Playlist Embed/Link Select item

Your browser does not support video tag.

This is a sample. For full access:

Please choose from the following options to gain full access to this content

Log in via your academic institution

Purchase via Single Title Sales

Choose one of the terms below and share access with the rest of your institution.

Streaming Access

1 year

$149

Add to Cart

3 years

$299

Add to Cart

This is a sample. For full access:

Please choose from the following options to gain full access to this content

Log in via your academic institution

Purchase via Single Title Sales

Choose one of the terms below and share access with the rest of your institution.

Streaming Access

1 year

$149

Add to Cart

3 years

$299

Add to Cart

# data[].attributes.attachment_link.title
Where Did it Come From?, Ancient Egypt: Modern Medicine | Alexander Street, a ProQuest Company

# data[].attributes.attachment_link.description
You are here Press enter to open the dropdown list, then press tab and enter to choose the language. produced by Michael Guillen, 1959- , in Where Did it Come From? (New York, NY: A&E Television Networks, 2011) , 54 mins Cite Email Playlist Embed/Link Select item Your browser does not support video tag.

# data[].attributes.body
Mitch

# data[].attributes.attachment_link.readable_text
Ancient Egypt was one of the world's first two literate societies, having discovered the art/science of writing around the year 3,100 BC, not long after the first scripts were invented in Mesopotamia. But writing in Egypt developed very differently than in Mesopotamia. The initial development of writing in Mesopotamia can be followed along a very gradual yet definite path, while in Egypt, the appearance of the first written texts was somewhat sudden.

The Egyptians quickly mastered writing, and before too long, they used it in several different literary genres. During the period known as the Old Kingdom, Egyptians used writing to convey their ideas about the afterlife in tombs and on monumental inscriptions, and they first began to experiment with what would be known as "literature" in the modern sense. It was during the Middle Kingdom, though, when the Egyptian written language flourished the most, and literary works were written that were dutifully copied for centuries by countless scribes.

By the time of the New Kingdom, the Egyptian written language had evolved to the point where written texts were quite ubiquitous, and alternate forms of writing became common. In addition to the hieroglyphic script, the Egyptians developed cursive scripts known as hieratic and demotic, which were shorthand versions of the hieroglyphic script, used primarily for documents written on papyrus. When the Romans, Byzantines, and Arabs ruled over Egypt, the native forms of the written language eventually died. However, a vestige of them was retained in the liturgical language of Coptic.

Early Egyptian Writing

The earliest forms of documented writing in Egypt are found in the Early Dynastic tombs in the necropolis of Abydos. The oldest example is believed to be a tomb known as "U-j," which belonged to one of the first Egyptian kings, who ruled just before 3,100 BC. The earliest inscriptions are quite simple, consisting of little more than a few words at most, but the hieroglyphic system of writing appears to have been already fully formed.

The early Egyptian hieroglyphic script consisted of both ideographic and phonetic signs rendered in about 200 signs. The hieroglyphic script could be quite adaptable, which often confounds modern scholars of the language. For instance, the sign that corresponds to a "t" sound was a hieroglyph of a loaf of bread: it could, therefore, be employed phonetically as a "t" sound in a word or as an ideogram to indicate bread or something to do with bread.

Early on the hieroglyphic script was employed for a sign known as the serekh. A serekh was simply one of the king's many names, written in a square somewhere on a royal monument. Serekhs are found on inscriptions in the tombs and monuments of the kings of the First Dynasty (c. 3,100-2980 BC), the most famous of which is the Narmer Palette, which is believed to be a depiction of Narmer/Menes, the first king of the united Egyptian state. Although stone was the earliest medium on which the Egyptian hieroglyphic script was rendered, it was not the only or even most common.

Monumental inscriptions were carved in the stone of Egyptian temples and on stelae, but the countless administrative documents, as well as literature and other texts, were written on papyrus. Papyrus is a reed that was once quite abundant in Egypt's Nile Valley and could function as a form of paper. In fact, the modern word "paper" is actually derived from Greek word "papyrus." In order to utilize papyrus as paper, it simply had to be cut down and rolled out, which allowed it to be used in individual sheets. Scribes could write on either side of a papyrus roll and it could also be used as a palimpsest - if the writer made a mistake, he could simply erase what he wrote and restart.

Writing evolved quickly through the Early Dynastic Period, and by Egypt's Old Kingdom (c. 2686-2125 BC), the texts were longer, more complex, and much more common. The most developed writings from the Old Kingdom also happened to be the texts that reveal the most about ancient Egyptian religion during the period. Beginning in the Fifth Dynasty (c. 2494-2345 BC), the scribes began inscribing the interiors of the pyramids with religious texts known today as the Pyramid Texts. The Pyramid Texts described the importance of the afterlife as well as the primacy of many of the deities such as Osiris, Re, Isis, and Seth.

But religious inscriptions were not the only important texts created during the Old Kingdom; a genre of writings known as "didactic literature" or "instructions" also became popular. These texts, such as "The Instruction of Ptahhotep," instruct the reader how to live life as an upstanding, moral and ethical Egyptian. The Pyramid Texts and the didactic texts of the Old Kingdom provided a base for writing and literature in the Middle Kingdom (c. 2055-1650 BC), which is considered by many modern scholars to be the classical age of the ancient Egyptian written language.

Writing in the Middle Kingdom

The Middle Kingdom proved not only to be the high point of the ancient Egyptian language and writing system, but it was also the period when some of the greatest literary works in the civilization were created and new literary genres were invented. The linguistic flowering in the Middle Kingdom was particularly marked during the reign of Senusret I (ruled c. 1919-1875 BC) in the Twelfth Dynasty. The Egyptians expanded on the monumental and religious inscriptions and didactic texts of the Old Kingdom, and they introduced new genres of literature while refining the written language.

Didactic literature continued to be written, but the compositions were longer, more complex, and written better overall. One of the best known Middle Kingdom didactic texts is actually also a fictional tale known as The Eloquent Peasant. It tells the tale of a peasant who was robbed by a noble and although lower in class than his adversary, is quite articulate and able to gain an audience with the pharaoh, where he ultimately wins his case. Other notable fictional prose stories that were first written in the Middle Kingdom include The Shipwrecked Sailor, The Story of Sinuhe, and Three Tales of Wonder.

Middle Kingdom scribes also developed a new literary genre that can be described as historical fiction or pseudo-history. Many of these stories, such as The Prophecies of Neferti are set in the Old Kingdom, where one or more of the main characters warn of the impending chaos of the First Intermediate Period (c. 2181-2055 BC). In The Admonitions of Ipuwer the writer used the effective literary devices of metaphors, similes, and comparisons to demonstrate how hopeless the social and political situation was in the First Intermediate Period. Although the Middle Kingdom collapsed when the Hyksos invaded, the literary base that was created in the Twelfth Dynasty provided an impetus for the Egyptian written language to survive and evolve for the remainder of pharaonic history.

Writing in the New Kingdom and Beyond

Most extant copies of Egyptian papyrus texts that modern scholars study and use in their research are New Kingdom (c. 1550-1069 BC) copies of Middle Kingdom compositions. Although new literary works from the genres discussed above were created, most noteworthy New Kingdom texts were composed on monuments. New Kingdom scribes, though, did create an extensive corpus of historical and "proto-historiographical" texts. Most of the New Kingdom historiographical texts were in the form of king-lists and annals of military campaigns. All genres of Egyptian literature continued to be produced through the Late Period (664 BC-early Christian Era), with historiographical writing becoming even more developed. King-lists continued to be written and a new genre of folk history and pseudo-history formed. One of the most interesting aspects of literature and writing in the New Kingdom, though, was the apparent expansion of overall literacy.

Although the overall literacy rate in ancient Egypt was probably never higher than one percent, a fairly large corpus of written material from the workmen's village of Deir el-Medina has revealed much about the daily lives of non-noble Egyptians in the Nineteenth and Twentieth dynasties of the New Kingdom. The village was the home to the men and their families who built the tombs in the Valley of the Kings. More than 470 letters, notes, and records written by the workers, which were recorded on papyri and ostraca (pottery sherds) in the hieratic script, demonstrate that the Egyptians' lived lives not unlike those of the modern world. Although the actual compositions may not approach the level of the literary genres discussed earlier, at least in terms of proper grammar and syntax, they demonstrate that literacy was not just the purview of the nobles.

The Evolution of Script in Ancient Egypt

In addition to the great changes that took place in Egyptian literature over the course of the ancient civilization's long history, how the language was written, its script, also evolved. The hieroglyphic script was the first script the Egyptians employed to articulate their thoughts in writing and was the most enduring.

Although the hieroglyphic script could be unwieldly due to the details of each character, it was quite adaptable - the texts could be written in any direction. The hieroglyphic text proved to be so durable that the last inscription is dated to the fourth century AD, long after Christianity became the dominant religion of the Nile Valley.

Because the hieroglyphic text could be so cumbersome, a cursive script known as hieratic was developed by 2686 BC. Hieratic was used primarily on papyrus for administrative and literary texts and although a hieratic text could be composed much quicker using it than hieroglyphs, it was only written right to left, which limited its versatility in some ways.

The hieratic script eventually evolved into another cursive script known as demotic. Demotic replaced hieratic in most economic texts by the Twenty-Sixth Dynasty (664-525 BC), but it eventually even began to replace the hieroglyphic script in religious texts and some monuments. Demotic was used into the third century AD when it was all but replaced by Greek. Although all of the Egyptian written scripts that were invented during the pharaonic period were extinct by the early Christian Era, the Coptic language, which is the liturgical language of the Egyptian Orthodox Church, continued to use the native language with a modified Greek script.

Conclusion

The evolution of writing in ancient Egypt was quite complex and featured many theoretical and philosophical branches and forks. Writing appeared somewhat suddenly and then quickly evolved to compromise several different genres. As the different literary genres evolved throughout Egyptian history, so too did the manner in which the language was writing. Egyptian scribes used three different scripts to articulate their language and later adapted the Greek script when they became Christians. Today, scholars are amazed at the number of literary works the Egyptians produced and have yet to uncover all of the nuances of the Egyptian written language.

References

# data[].attributes.attachment_link.description
Ancient Egypt was one of the world's first two literate societies, having discovered the art/science of writing around the year 3,100 BC, not long after the first scripts were invented in Mesopotamia. But writing in Egypt developed very differently than in Mesopotamia.

# data[].attributes.attachment_link.readable_text
Examples for

Wolfram|Alpha has broad knowledge and deep computational power when it comes to math. Whether it be arithmetic, algebra, calculus, differential equations or anything in between, Wolfram|Alpha is up to the challenge. Get help with math homework, solve specific math problems or find information on mathematical subjects and topics.

Complex Analysis

Analyze functions and expressions containing imaginary numbers or complex variables.
More examples

# data[].attributes.attachment_link.description
Examples for Wolfram|Alpha has broad knowledge and deep computational power when it comes to math. Whether it be arithmetic, algebra, calculus, differential equations or anything in between, Wolfram|Alpha is up to the challenge. Get help with math homework, solve specific math problems or find information on mathematical subjects and topics.

# data[].attributes.attachment_link.title
How ancient Egypt shaped our idea of beauty

# data[].attributes.attachment_link.description
Pop culture is steeped in images of smoky-eyed pharaohs and their queens. Were the ancient Egyptians insufferably vain – or are we simply projecting our own values onto them?

# data[].attributes.attachment_link.readable_text
The introduction of writing in Egypt in the predynastic period ( c. 3000 bce) brought with it the formation of a special class of literate professionals, the scribes. By virtue of their writing skills, the scribes took on all the duties of a civil service: record keeping, tax accounting, the management of public works (building projects and the like), even the prosecution of war through overseeing military supplies and payrolls. Young men enrolled in scribal schools to learn the essentials of the trade, which included not only reading and writing but also the basics of mathematics.

One of the texts popular as a copy exercise in the schools of the New Kingdom (13th century bce) was a satiric letter in which one scribe, Hori, taunts his rival, Amen-em-opet, for his incompetence as an adviser and manager. "You are the clever scribe at the head of the troops," Hori chides at one point,

a ramp is to be built, 730 cubits long, 55 cubits wide, with 120 compartments-it is 60 cubits high, 30 cubits in the middle...and the generals and the scribes turn to you and say, "You are a clever scribe, your name is famous. Is there anything you don't know? Answer us, how many bricks are needed?" Let each compartment be 30 cubits by 7 cubits.

This problem, and three others like it in the same letter, cannot be solved without further data. But the point of the humour is clear, as Hori challenges his rival with these hard, but typical, tasks.

What is known of Egyptian mathematics tallies well with the tests posed by the scribe Hori. The information comes primarily from two long papyrus documents that once served as textbooks within scribal schools. The Rhind papyrus (in the British Museum) is a copy made in the 17th century bce of a text two centuries older still. In it is found a long table of fractional parts to help with division, followed by the solutions of 84 specific problems in arithmetic and geometry. The Golenishchev papyrus (in the Moscow Museum of Fine Arts), dating from the 19th century bce, presents 25 problems of a similar type. These problems reflect well the functions the scribes would perform, for they deal with how to distribute beer and bread as wages, for example, and how to measure the areas of fields as well as the volumes of pyramids and other solids.

The Egyptians, like the Romans after them, expressed numbers according to a decimal scheme, using separate symbols for 1, 10, 100, 1,000, and so on; each symbol appeared in the expression for a number as many times as the value it represented occurred in the number itself. For example, stood for 24. This rather cumbersome notation was used within the hieroglyphic writing found in stone inscriptions and other formal texts, but in the papyrus documents the scribes employed a more convenient abbreviated script, called hieratic writing, where, for example, 24 was written .

In such a system, addition and subtraction amount to counting how many symbols of each kind there are in the numerical expressions and then rewriting with the resulting number of symbols. The texts that survive do not reveal what, if any, special procedures the scribes used to assist in this. But for multiplication they introduced a method of successive doubling. For example, to multiply 28 by 11, one constructs a table of multiples of 28 like the following:

The several entries in the first column that together sum to 11 (i.e., 8, 2, and 1) are checked off. The product is then found by adding up the multiples corresponding to these entries; thus, 224 + 56 + 28 = 308, the desired product.

To divide 308 by 28, the Egyptians applied the same procedure in reverse. Using the same table as in the multiplication problem, one can see that 8 produces the largest multiple of 28 that is less then 308 (for the entry at 16 is already 448), and 8 is checked off. The process is then repeated, this time for the remainder (84) obtained by subtracting the entry at 8 (224) from the original number (308). This, however, is already smaller than the entry at 4, which consequently is ignored, but it is greater than the entry at 2 (56), which is then checked off. The process is repeated again for the remainder obtained by subtracting 56 from the previous remainder of 84, or 28, which also happens to exactly equal the entry at 1 and which is then checked off. The entries that have been checked off are added up, yielding the quotient: 8 + 2 + 1 = 11. (In most cases, of course, there is a remainder that is less than the divisor.)

For larger numbers this procedure can be improved by considering multiples of one of the factors by 10, 20,...or even by higher orders of magnitude (100, 1,000,...), as necessary (in the Egyptian decimal notation, these multiples are easy to work out). Thus, one can find the product of 28 by 27 by setting out the multiples of 28 by 1, 2, 4, 8, 10, and 20. Since the entries 1, 2, 4, and 20 add up to 27, one has only to add up the corresponding multiples to find the answer.

Computations involving fractions are carried out under the restriction to unit parts (that is, fractions that in modern notation are written with 1 as the numerator). To express the result of dividing 4 by 7, for instance, which in modern notation is simply 4/7, the scribe wrote 1/2 + 1/14. The procedure for finding quotients in this form merely extends the usual method for the division of integers, where one now inspects the entries for 2/3, 1/3, 1/6, etc., and 1/2, 1/4, 1/8, etc., until the corresponding multiples of the divisor sum to the dividend. (The scribes included 2/3, one may observe, even though it is not a unit fraction.) In practice the procedure can sometimes become quite complicated (for example, the value for 2/29 is given in the Rhind papyrus as 1/24 + 1/58 + 1/174 + 1/232) and can be worked out in different ways (for example, the same 2/29 might be found as 1/15 + 1/435 or as 1/16 + 1/232 + 1/464, etc.). A considerable portion of the papyrus texts is devoted to tables to facilitate the finding of such unit-fraction values.

These elementary operations are all that one needs for solving the arithmetic problems in the papyri. For example, "to divide 6 loaves among 10 men" (Rhind papyrus, problem 3), one merely divides to get the answer 1/2 + 1/10. In one group of problems an interesting trick is used: "A quantity ( a h a) and its 7th together make 19-what is it?" (Rhind papyrus, problem 24). Here one first supposes the quantity to be 7: since 1 ¹/ ₇ of it becomes 8, not 19, one takes 19/8 (that is, 2 + 1/4 + 1/8), and its multiple by 7 (16 + 1/2 + 1/8) becomes the required answer. This type of procedure (sometimes called the method of "false position" or "false assumption") is familiar in many other arithmetic traditions (e.g., the Chinese, Hindu, Muslim, and Renaissance European), although they appear to have no direct link to the Egyptian.

The geometric problems in the papyri seek measurements of figures, like rectangles and triangles of given base and height, by means of suitable arithmetic operations. In a more complicated problem, a rectangle is sought whose area is 12 and whose height is 1/2 + 1/4 times its base (Golenishchev papyrus, problem 6). To solve the problem, the ratio is inverted and multiplied by the area, yielding 16; the square root of the result (4) is the base of the rectangle, and 1/2 + 1/4 times 4, or 3, is the height. The entire process is analogous to the process of solving the algebraic equation for the problem ( x × ³/ ₄ x = 12), though without the use of a letter for the unknown. An interesting procedure is used to find the area of the circle (Rhind papyrus, problem 50): 1/9 of the diameter is discarded, and the result is squared. For example, if the diameter is 9, the area is set equal to 64. The scribe recognized that the area of a circle is proportional to the square of the diameter and assumed for the constant of ¹/ ₇ , first proposed by proportionality (that is, π/4) the value 64/81. This is a rather good estimate, being about 0.6 percent too large. (It is not as close, however, as the now common estimate of 3 Archimedes, which is only about 0.04 percent too large.) But there is nothing in the papyri indicating that the scribes were aware that this rule was only approximate rather than exact.

A remarkable result is the rule for the volume of the truncated pyramid (Golenishchev papyrus, problem 14). The scribe assumes the height to be 6, the base to be a square of side 4, and the top a square of side 2. He multiplies one-third the height times 28, finding the volume to be 56; here 28 is computed from 2 × 2 + 2 × 4 + 4 × 4. Since this is correct, it can be assumed that the scribe also knew the general rule: A = ( h/3)( a ² + a b + b ²). How the scribes actually derived the rule is a matter for debate, but it is reasonable to suppose that they were aware of related rules, such as that for the volume of a pyramid: one-third the height times the area of the base.

The Egyptians employed the equivalent of similar triangles to measure distances. For instance, the seked of a pyramid is stated as the number of palms in the horizontal corresponding to a rise of one cubit (seven palms). Thus, if the seked is 5 ¹/ ¹/ ₃ cubits (Rhind papyrus, problem 57). The Greek sage ₄ and the base is 140 cubits, the height becomes 93 Thales of Miletus (6th century bce) is said to have measured the height of pyramids by means of their shadows (the report derives from Hieronymus, a disciple of Aristotle in the 4th century bce). In light of the seked computations, however, this report must indicate an aspect of Egyptian surveying that extended back at least 1,000 years before the time of Thales.

Egyptian seked Encyclopædia Britannica, Inc.

# data[].attributes.attachment_link.title
Mathematics - Mathematics in ancient Egypt

# data[].attributes.attachment_link.description
Mathematics - Mathematics - Mathematics in ancient Egypt: The introduction of writing in Egypt in the predynastic period (c. 3000 bce) brought with it the formation of a special class of literate professionals, the scribes.

# data[].attributes.body
https://www.cnn.com/style/article/ancient-egypt-beauty-ritual-artsy/index.html

# data[].attributes.attachment_link.title
How ancient Egyptian cosmetics influenced our beauty rituals | CNN

# data[].attributes.attachment_link.description
Cosmetics from thousands of years ago still influence our rituals today.