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Robert Hooke was important philosopher, architect and studied mathematics. He was born on 1635 and lived a long life up for his time until 1703. He studied many important subjects and came up with "Hookes law". This is the law of physics
{F to the 8th power=-kx}. He also was a very important piece of discovering the building blocks of life, cells.

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Andreas Vesalius was a man born in Brussels, Belgium. He was an atomist which means he investigated the human body by dissection and he also studied medicine. He wrote a very important work called "On The Fabric Of The Human Body." As a student He compared Greek texts to their Arabic translation.

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Rene Descartes was a person who defined the human being and did major work on the scientific method. Descartes also created the priori method, which contrasted with Newton's, Bacons and British Empiricists methods. Descartes also set out to purify algebra and explicitly stated in the discourses that all of his science and physics is in the existence of God.

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In the 1700's Joseph Priestley discovered the gas we know as 'oxygen.' He also isolated and characterized eight other gasses. His first scientific work was 'The History of Electricity.' (1767)

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Johannes Kepler was a astronomer who is famous for his three laws of planetary motion.

https://www.nasa.gov/kepler/education/johannes

https://www.youtube.com/watch?v=DLO_GDF0qq8

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Lived 1608 - 1647.
The 1600s were marked by ferocious conflicts between old superstitions and new sciences. A small number of people began using observations and experiments to reveal how Nature worked and in doing so changed the way we understand our world.

Evangelista Torricelli was one of these people. He invented the mercury barometer and deduced from experiments that his device revealed the height of our planet's atmosphere. In 1644, he concluded that we live at the bottom of a sea of air.

Torricelli's hectic few years of scientific activity began when Galileo was an old man and ended when Isaac Newton was a young boy.

Torricelli was the first person to explain correctly why the wind blows, and he discovered an extraordinary and controversial geometrical figure, Gabriel's horn, which has a finite volume but infinite surface area.

Beginnings

Evangelista Torricelli was born on October 15, 1608 in the great Italian city of Rome.

His mother was Giacoma Ruberti (born Torricelli). His father was Gaspare Ruberti, a weaver. Evangelista was the eldest of their three sons; he took his mother's surname - it was not exceptionally rare in Rome for children to do this. Two of the family's three sons took their mother's surname, while one took the surname Ruberti.

Sometimes biographers incorrectly state that Evangelista was born in the small northern Italian city of Faenza. This is actually where he was educated and where his mother was born - he regarded Faenza as his spiritual birthplace.

Education

Evangelista's parents grasped that their son was unusually intelligent, but they were too poor to pay for school.

Enter Evangelista's uncle, Gian Francesco Torricelli, priest of the Abbey of Saint Ippolito in Faenza, Evangelista mother's birthplace. Gian Francesco was a graduate of the famous University of Padua and was ideally placed to help with Evangelista's education.

Evangelista moved north to live with his Gian Francesco, who began his education by teaching him the basics.

In 1619, age 11, Evangelista began attending Faenza's Jesuit school. In 1623, he began studying mathematics.

Gian Francesco soon learned from Evangelista's teachers that his nephew was an extraordinarily talented mathematician. Gian Francesco got in touch with a friend, Professor Benedetto Castelli of Sapienza College in Rome - both men were in the same Catholic Camaldolese order.

Mathematics and Physical Sciences

In 1626, age 18, Evangelista Torricelli moved to Rome to be taught mathematics and physical sciences by Professor Castelli. This was a fantastic break for the young Torricelli: Castelli had been taught these subjects by Galileo.

Torricelli could not afford fees, so he worked as Castelli's secretary for six years, until 1632. Near the end of this period, he took over Castelli's lecturing duties whenever Castelli was sick or traveling.

Galileo: First Contact

At the beginning of 1632, Galileo Galilei changed the course of scientific and religious history by publishing Dialogue Concerning the Two Chief World Systems. Within a year, this book and everything else he had ever written were suppressed by the Catholic Church.

Galileo was declared "vehemently suspect of heresy." The trigger for the Church's outrage was that part of Galileo's book discussed the Copernican view that the solar system is centered on the sun rather than the earth, a view Galileo said he agreed with.

Soon after the book was published and before it was banned, Torricelli, age 23, read it hungrily, working through all its implications for himself. He soon found himself in a position to write to the great man. In his professor's absence, Torricelli replied to a letter Galileo had sent to Professor Castelli.

In the letter, Torricelli explains that Professor Castelli is absent and so he, as Castelli's secretary, must reply. He introduces himself and tells Galileo that he has read his new book "with delight." Torricelli's letter is a gift for future biographers, because so little of his early life is recorded. Torricelli informs Galileo (and us) that he has studied the works of the great Ancient Greek mathematicians, such as Archimedes', and has studied the works of Ptolemy, Tycho Brahe, and Kepler. He says that he agrees with the Copernican view of the solar system.

This was the only time Torricelli ever openly supported the Copernican view. Soon enough, to do so would risk death.

Torricelli's Lifetime in Context

Evangelista Torricelli's Contributions to Science

The Barometer and Earth's Sea of Air

Torricelli is best known for his invention and, even more importantly, his explanation of the mercury barometer. He did this in in 1643.

Torricelli's device measures atmospheric pressure, which is related to the weight of the miles of air in the atmosphere pressing down on us.

Torricelli's Barometer

Looking at the results of his experiment, Torricelli rather brilliantly concluded that the barometer acts as a balance. On one side of the balance is the downward push of a column of mercury about 76 cm high. On the other is the downward push of Earth's atmosphere.

Torricelli was right. In modern terms we can measure at sea level that the average weight of Earth's atmosphere is 1.03 kg on every square centimeter of surface (14.7 lb on every square inch.)

Torricelli's explanation contradicted Galileo's theory that the mercury column was held in the tube by the suction power of the vacuum above it. Galileo had also been contradicted by Giovanni Baliani of Genoa in 1630, who advanced similar ideas to Torricelli, albeit less developed, about the effects of air pressure. Whether Torricelli had heard of Baliani's ideas is unknown.

In a series of experiments Torricelli and his friend Vincenzo Viviani proved that the vacuum at the top of the tube was not the cause of the mercury column's height.

"We live immersed at the bottom of a sea of air, which by experiment undoubtedly has weight, and so much weight that the densest air in the neighborhood of the surface of the earth weighs about one four-hundredth part of the weight of water... On the surface of the liquid which is in the bowl there rests the weight of a height of fifty miles of air."

Air Exerts a
Surprisingly Powerful Pressure

Otto von Guericke, who lived in the same era as Torricelli, demonstrated just how forceful air pressure can be when he performed a famous experiment. He placed two metal hemispheres together and created a vacuum between them with a pump. Two teams each containing eight horses could not overcome the pressure from our planet's atmosphere holding the hemispheres together.

Air Pressure Extremes

Atmospheric pressure changes as weather systems come and go, which means the height of the mercury column in barometers changes with it.

The world record high pressure (at sea level) is 813 mm of mercury, recorded in Russia in 2001.

In the center of tornados, very low pressures exist. The world record low pressure (at sea level) outside a tornado is 652 mm of mercury, recorded in the Pacific Ocean during a hurricane in 1979.

Since the height of a barometer's mercury column is a measure of the weight of the air above us, it's not surprising that if you climb a mountain the mercury column's height will fall. At the summit of Mount Everest, at a height of 8,848 m, you would expect a barometer's mercury column to be just 250 mm high.

Air pressure is used in weather forecasting. Rising pressure tends to mean the weather will be fair. Falling pressure is more likely to point to wetter conditions.

Why does the Wind Blow?

In Torricelli's day people believed that the wind was caused by vapors released by the damp earth.

Torricelli gave the correct explanation as part of a series of lectures. These were published in 1823, long after his death, as Lezioni accademiche di Evangelista Torricelli.

Torricelli observed prevailing wind directions for some time in the city of Florence and gathered reports from around Europe.

Moreover, he took into account his observation that when the doors of large buildings are opened on hot days, cold air rushes outward through the doorway.

He said that winds are caused by what today we call convection currents, whose circulation he described. Put simply, he said that hot air is less dense than cold air, so hot air rises from the earth's surface - he said it could rise to heights of three or four miles - and is replaced by cooler air. The result is that air moves from regions where its density is high to regions where it is low and this moving air is the wind.

Archimedes and Torricelli's Principle

Torricelli made a number of startling discoveries in mathematics and mechanics, publishing many in his Opera geometrica (Geometry Work).

As a mathematician, his greatest influence was Archimedes, whose work by then was almost two millennia old. Torricelli believed Archimedes had worked " ad occultandum artis arcanum" - in other words using some hidden or secret art. Torricelli was right - Archimedes' work The Method, in which he revealed his remarkable techniques, was only rediscovered in 1906 in the renowned Archimedes Palimpsest.

The concept of center of gravity was discovered by Archimedes. Torricelli, following in his footsteps, discovered a new principle, Torricelli's principle, which says:

A system of bodies in equilibrium can only move spontaneously on the earth's surface if its center of gravity descends.

How Fast Should Water Flow Through an Opening?

Torricelli observed water flowing through openings in water tanks and figured out that the water should move through the opening with the same velocity as if it had fallen under gravity from the height of the water above the opening.

This allowed him to prove in Opera geometrica that the rate a liquid flows through an opening is proportional to the square root of the depth of the liquid. This proportionality is called Torricelli's law.

As a result of his law, Torricelli has a good claim to be recognized as the founder of modern fluid dynamics.

An Infinity Paradox

Gabriel's horn (or Torricelli's trumpet) starts wide and diminishes forever without reaching an end. Torricelli revealed this object to the world in 1644, provoking awe, bewilderment, jeers and acrimony.

The horn has finite volume, infinite length and infinite surface area.

In the 1600s, mathematicians were distinctly uncomfortable with infinity - Torricelli described his discovery as a paradox.

Some philosophers refused to believe Gabriel's horn could exist at all. Thomas Hobbes, of the empiricist school, believed knowledge can only come from experience. Since we cannot experience infinity, Hobbes argued we cannot make any trustworthy statement about it in general or accept Torricelli's discovery in particular. Attempting to defeat mathematics with mockery, Hobbes said of Gabriel's Horn:

"For to understand this for sense, it is not required that a man should be a geometrician or a logician, but that he should be mad."

Modern mathematicians see infinity as an everyday aspect of their work.

Gabriel's horn is made by taking the function y = ¹⁄ x and rotating it around the x-axis for x=1 to ∞.

Parabolas and Projectiles

The study of parabolas began with the Ancient Greeks. In renaissance Italy, parabolas once again fascinated mathematicians. Galileo, building on the work of Niccolo Tartaglia, showed that projectiles, such as cannon balls, follow a parabola-shaped path.

Torricelli made a number of advances in the study of parabolas and projectiles. He recorded these in De motu gravium, published as part of Opera geometrica. The gunnery tables he produced were not improved upon until the 1700s.

Below you can see his 'safety parabola' in blue. Torricelli imagined a cannon ball shot many times, always emerging from the cannon at the same speed, but at different angles to the ground. He deduced that you can draw a 'safety parabola' which will form an envelope around all the possible parabolic trajectories. Anyone outside the envelope is safe from the cannonball, whatever angle the cannon is fired at. The safety parabola is of mathematical interest because it was the first envelope discovered. Torricelli also showed that all possible parabolic trajectories of the cannonball are tangent to the safety parabola.

Honors

The torr unit of pressure is named after Torricelli.

Originally it was defined as the pressure equal to one millimeter of mercury at 0 °C. It is now defined as ¹⁄ ₇₆₀ of a standard atmosphere (101325 Pa).

In 1958, Italy issued a new stamp, shown here, to commemorate the 350th anniversary of Torricelli's birth.

Some Personal Details and the End

Torricelli never married and had no children.

He loved old literature - many of the books he owned were Latin and Ancient Greek classics. His book collection also revealed his enthusiasm for architecture and military technology.

In 1641, three months before Galileo's death, Torricelli traveled to live at his home in the city of Florence to act as his eyes and writer in his final days - Galileo had been completely blind for three years and under house arrest for eight years.

Despite his house arrest, Galileo was the mathematician and philosopher to the Grand Duke Ferdinando II of Tuscany. After Galileo's death, Torricelli was appointed to the post, with an ample salary and an apartment in the Medici Palace in Florence. He was also appointed Chair of Mathematics at the University of Pisa. He remained in these posts until his untimely death.

Torricelli was acclaimed among his friends as a scintillating conversationalist. Before his death, he was working on comedies for performance. Sadly, they no longer exist.

Evangelista Torricelli died in Florence 10 days after his 39th birthday on October 25, 1647. He was feverish for about 20 days before his death, probably resulting from typhoid or pneumonia. During the fever he was sometimes rational, sometimes delirious.

Fearing he would not recover, he wrote his will 11 days before the end came. He left almost all he had to his two brothers, Carlo and Francesco, a sum to his great friend Doctor Buonaiuti, who had treated him during his illness, a sum to his servant Dianora, and his old shoes, socks and similar items to Ceccotto the sweeper.

To his friend Lodovico Serenai, who was responsible for executing his will, he left a ring and his books. He told Serenai to erase any and all the notes he had made in book margins criticizing the Jesuit scholars Niccolò Cabeo and Athanasius Kircher - Torricelli did not want future generations to learn of his profound contempt for them.

Evangelista Torricelli was buried in the Basilica of San Lorenzo in Florence. He died at the peak of his intellectual powers.

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Please use the following MLA compliant citation:

"Evangelista Torricelli." Famous Scientists. famousscientists.org. 31 Aug. 2019. Web.
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Further Reading
Charles Coulston Gillispie, Editor in Chief
Dictionary of Scientific Biography, Vol. 13
Scribner, 1981

Franco Gabici, Fabio Toscano
Scienziati di Romagna
Alpha Test, 2006

Fabio Toscano
L'erede di Galileo: vita breve e mirabile di Evangelista Torricelli
Sironi Editore, 2008

Raffaele Pisano, Paolo Bussotti
Notes on Mechanics and Mathematics in Torricelli as Physics Mathematics Relationships in the History of Science
Problems of education in the 21st Century, Vol. 61, pp 88-97, 2014

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Lived 1608 - 1647. The 1600s were marked by ferocious conflicts between old superstitions and new sciences. A small number of people began using observations and experiments to reveal how Nature worked and in doing so changed the way we understand our world. Evangelista Torricelli was one of these people.

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http://teacherlink.ed.usu.edu/tlnasa/reference/imaginedvd/files/starchild/docs/StarChild/whos_who_level2/copernicus.html
Copernicus was born in Thorn, Poland, on February 19 1473. The son of a wealthy merchant, studied mathematics and astronomy at the University of Krakow. He first circulated the principles of his heliocentric or Sun-centered solar system opposed to geocentric, Earth-centered solar system sometime between 1507 and 1515. Although he died more than 450 years ago, he is still considered the founder of modern astronomy.

https://www.youtube.com/watch?v=M0p6NKANE08

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The Galileo Project | Science | Tycho Brahe

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Tyge (Latinized as Tycho) Brahe was born on 14 December 1546 in Skane, then in Denmark, now in Sweden. He was the eldest son of Otto Brahe and Beatte Bille, both from families in the high nobility of Denmark. He was brought up by his paternal uncle Jörgen Brahe and became his heir.

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Tycho Brahe, the scandalous astronomer - Dan Wenkel

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Lived 1632 - 1723.
Antonie van Leeuwenhoek is the somewhat improbable father of microbiology. A moderately educated owner of a textile business, he learned how to make his own unique microscopes which offered unparalleled magnification. Using these microscopes he made a number of crucially important scientific discoveries, including single-celled animals and plants, bacteria, and spermatozoa.

His microscopy methods were so finely tuned that after he discovered bacteria, this type of organism would not be observed again by any other scientist for over 100 years.

Beginnings

Antonie van Leeuwenhoek was born on October 24, 1632, in the small city of Delft in the Dutch Republic. His father was Philips Antonisz van Leeuwenhoek, a basket maker. His mother was Margaretha Bel van den Berch, whose prosperous family were beer brewers.

Antonie's early life was rather rocky: his father died when he was just five years old. His mother remarried, and Antonie spent some time living with an uncle. His uncle was a lawyer and helped Antonie with basic literacy and numeracy, reinforcing the education he had received in local schools. By the time Antonie was 16, his step-father had also died.

Antonie learned no languages other than Dutch, which suggests he was never expected to go to university: he would have needed to learn at least Latin for this.

Business Career

In 1648, at the age of 16, Leeuwenhoek moved to the famous Dutch trading city of Amsterdam to begin work in a textile shop. He learned his trade well and was promoted to the trusted position of cashier and book-keeper.

In 1654, aged 21, he returned to Delft, where he would spend the rest of his long life. This was a significant year for Leeuwenhoek. Not only did he return to his hometown, but he got married, and, putting his business experience in Amsterdam into practice, he opened his own textile shop in Delft. In addition to cloth he sold buttons, ribbons, and other accessories.

Over the next few years Leeuwenhoek became an influential figure in Delft. In 1660, aged 28, he was appointed to manage the operations of Delft's council meeting hall. In return for only a small amount of work - the actual physical work of the job was delegated to other people - he received a generous salary.

A man of many talents, Leeuwenhoek was also appointed to supervise Delft's wine trade and levy the appropriate taxes on imported wine.

While running his shop and working for the city of Delft, Leeuwenhoek became a qualified land surveyor at about 40 years of age, just before he started his scientific work.

Antonie van Leeuwenhoek's Science

The Discovery of the Leeuwenhoek Lens

Leeuwenhoek's biological discoveries were completely dependent on his ability to make lenses of extraordinarily high quality.

He never told anyone how he made his lenses. The secret went with him to the grave. In fact, to throw competitors off the scent, he used to talk about how he had to grind glass for a very long time to make his lenses. This was almost certainly not true.

People in the textiles trade had, for hundreds of years, used glass pearls - small spheres of glass - as lenses to examine cloth in fine detail. Leeuwenhoek used glass pearls frequently in his day-to-day business to examine the density of threads and the quality of cloth.

In 1665 the great English scientist Robert Hooke released Micrographia, showcasing drawings he had made of the natural world seen through the lens of his microscope.

Leeuwenhoek visited England in 1668 and most likely saw a copy of Micrographia: it had become the first scientific bestseller. Importantly for Leeuwenhoek, it contained drawings Hooke had made of his microscopic examinations of cloth.

Micrographia contains a description of how a powerful microscope could be made using a single spherical lens - similar to the glass pearls Leeuwenhoek was already familiar with:

...if you take a very clear piece of a broken Venice Glass, and in a lamp draw it out into very small hairs or threads, then holding the ends of these threads in the flame, till they melt and run into a small round globule, or drop, which will hang at the end of the thread; and if further you stick several of these upon the end of a stick with a little sealing wax, so as that the threads stand upwards, and then... grind off a good part of them, and afterward on a smooth metal plate, with a little tripoly, rub them till they come to be very smooth; if one of these be fixed with a little soft wax against a small needle hole, pricked through a thin plate of brass, lead, pewter, or any other metal, and an object, placed very near, be looked at through it, it will both magnify and make some objects more distinct then any of the great microscopes.

(In Hooke's day people sometimes wrote VERY long sentences indeed!)

We cannot tell whether Leeuwenhoek was aware of Hooke's words - he could not read English. However, it is now believed that he used Hooke's technique to make his lenses.

Hooke himself did not use lenses made by this method because they were inconvenient: the distance between the lens and the viewed object had to be very short and the observer's eye had to be pushed very close to the lens, causing Hooke's eyes to quickly become strained.

Hooke used a compound microscope (one with two lenses) which more closely resembles the microscopes we use today.

Leeuwenhoek, however, was more than happy to use small, spherical lenses to make single-lens microscopes. He kept the details of how he manufactured his lenses secret, but today we can be reasonably sure that he did the following:

used a hot flame to heat the middle part of a glass rod until molten

pulled the ends of the rod in opposite directions, forming a long, thin thread of molten glass

continued pulling the ends while the molten thread in the middle grew thinner and thinner, finally breaking

placed one of the thread ends back into the flame, resulting in the end of the thread forming a small glass sphere

This sphere was a lens, which may have required some polishing. The smaller the sphere, the greater the magnification.

When he started making lenses, Leeuwenhoek may have hoped to use them to examine textiles more closely than anyone had ever done before.

Soon, however, he felt the same compulsion as Hooke to examine natural objects in never-before-seen detail.

Leeuwenhoek's Microscopes

Microscopes made from Leeuwenhoek's tiny spherical lenses - the smallest lenses measured just 1 mm across - were easily capable of magnifying objects by a factor of about 200 - 300, while Hooke's compound microscope magnified only by a factor of about 40 - 50.

Remarkably, Leeuwenhoek could use his lenses to resolve details as small as 1.35 μm. (This meant that, for example, he could easily see red blood cells, which are typically 6 - 8 μm in diameter.)

Leeuwenhoek's Art of Microscopy

What is still uncertain even today is how Leeuwenhoek lit the objects he was studying. This was a vitally important part of his unique art of microscopy. Another was his unrivaled skill in setting up for viewing:

drops of liquid, such as blood or pond-water, or

solid samples, such as plant material or animal muscles, cleanly cut with a razor blade into very thin sections, transparent enough for light to travel through so their details could be seen and drawn.

Leeuwenhoek made over 500 tiny microscopes during his lifetime. They were awkward to use and inconvenient, which is why today we use compound microscopes. Despite their drawbacks, in Leeuwenhoek's expert hands, they revealed an entirely new biological world.

The Microscopic World Discovered by Leeuwenhoek

Leeuwenhoek was a tradesman who had no formal training in science and had never been to college.

Nevertheless, the quality of his observations was so high and his discoveries so compelling that his research became well-known through letters he sent to the Royal Society in London. These were translated into English and published in the Society's journal, Philosophical Transactions.

Interestingly, many of Leeuwenhoek's letters were read first by Robert Hooke, who was the Curator of Experiments and then Secretary of the Society. Hooke actually learned Dutch so he could read Leeuwenhoek's letters for himself.

Leeuwenhoek's first communication was in 1673, replicating some of the work Hooke had covered in Micrographia, including Leeuwenhoek's detailed drawings of bee stings, a fungus, and a human louse.

The following year Leeuwenhoek began to describe outstanding new discoveries he had made.

Single-Celled Life
In 1674, aged 41, Leeuwenhoek made the first of his great discoveries: single-celled life forms. Nowadays these organisms are grouped with the protists - these are mainly single-celled plants and animals. Echoing the initial disbelief Hooke's Micrographia had met, many members of the Royal Society refused to believe in the existence of Leeuwenhoek's microscopic creatures. It took until 1677 before their existence was fully accepted. This happened after Robert Hooke returned to his microscopes, which he had given up because of eye strain, and verified Leeuwenhoek's observations.

The Shape and Size of Red Blood Cells
In 1674 Leeuwenhoek examined red blood cells, which had been discovered six years earlier by his fellow Dutchman, Jan Swammerdam. With his superior lens, Leeuwenhoek was able to give a clearer description of the cells than ever before and was the first person to determine their size accurately.

Bacteria
In 1676 Leeuwenhoek discovered bacteria in water. The bacteria were at the limit of observation of his microscope - he estimated that it would take more than 10,000 of them to fill the volume of a small grain of sand. Such was the brilliance of his work that nobody else observed bacteria until another century had passed.

Spermatozoa
In 1677 Leeuwenhoek discovered spermatozoa, later concluding that eggs are fertilized when entered by sperm.

"...I observed certain animalcules, within whole bodies I saw so quick a motion as to exceed belief; they were about the size of a large grain of sand, and their bodies being transparent, that the internal motion could plainly be seen. Among other things, I saw in the body of one of these animalcules a bright and round corpuscle, placed near the head, and in which a very wonderful swift motion was to be seen, consisting of an alternate extension and contraction. This particle I concluded to be the heart..."

Lymphatic Capillaries
In 1683 Leeuwenhoek discovered the lymphatic capillaries, which contained "a white fluid, like milk."

By observing the life-cycles of maggots and fleas Leeuwenhoek proved that such creatures are not spontaneously generated, as many people believed at the time. He showed these creatures go through a process of reproduction from eggs to maggots to pupae to adults.

By dissecting aphids he discovered parthenogenesis. He found parent aphids containing the embryos of new aphids although eggs had not been fertilized.

By observing the flow of blood in tiny capillaries, Leeuwenhoek confirmed William Harvey's work on blood circulation.

The Birth of a New Science

Leeuwenhoek's discoveries, combined with Hooke's earlier discovery of microscopic fungi, signaled the creation of a new science: microbiology.

Some Personal Details and The End

Leeuwenhoek married Barbara de Mey in 1654, when he was 21 years old. They had five children, but only one - their daughter Maria - survived beyond infancy.

Barbara died in 1666, after twelve years of marriage. Five years later Leeuwenhoek married Cornelia Swalmius, with whom he had no children. It was during his second marriage that Leeuwenhoek's interest in science seems to have developed.

In February 1680 Leeuwenhoek was elected to The Royal Society in London. He took great pride in this; it meant that he had won recognition as a true scientist. He never visited the Royal Society. He was happy to continue his work in Delft.

Leeuwenhoek's second wife, Cornelia, died in 1694, when Leeuwenhoek was 61 years old.

Antonie van Leeuwenhoek died aged 90 on August 26, 1723. He was buried in the Old Church in Delft.

Although he had not been born into a scientific family nor had he received an education in science, his death was that of a true scientist. He communicated to the Royal Society such a careful, detailed description of the medical condition that was affecting him, eventually causing his death, that it is now called Van Leeuwenhoek's disease. This is a rare condition which causes involuntary twitching of muscles.

Leeuwenhoek was survived by his daughter Maria, who had not married. She looked after her aging father and helped him to run the family's textile business. Leeuwenhoek had become a wealthy man and Maria inherited this wealth.

"...my work, which I've done for a long time, was not pursued in order to gain the praise I now enjoy, but chiefly from a craving after knowledge, which I notice resides in me more than in most other men. And therewithal, whenever I found out anything remarkable, I have thought it my duty to put down my discovery on paper, so that all ingenious people might be informed thereof."

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Further Reading
Samuel Hoole
The Select Works of Antony van Leeuwenhoek
The Philanthropic Society, London, 1807

Antony van Leeuwenhoek and his "Little animals"
Clifford Dobell
Harcourt, Brace and Company, New York, 1932

Bentley Glass
Review of the Leeuwenhoek Legacy
The Quarterly Review of Biology, Vol 69, (1) March 1994

Howard Guest
The Discovery of Microorganisms by Robert Hooke and Antoni van Leeuwenhoek, Fellows of the Royal Society
Notes Rec. R. Soc. Lond. 58 (2), 2004

IML Donaldson
Robert Hooke's Micrographia of 1665 and 1667
J R Coll Physicians Edinb (40) 2010

Creative Commons licensed images
Image of Antonie van Leeuwenhoek at Microscope from the Wellcome Trust, Creative Commons Attribution 4.0 International.

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Lived 1632 - 1723. Antonie van Leeuwenhoek is the somewhat improbable father of microbiology. A moderately educated owner of a textile business, he learned how to make his own unique microscopes which offered unparalleled magnification. Using these microscopes he made a number of crucially important scientific discoveries, including single-celled animals and plants, bacteria, and spermatozoa.

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https://www.britannica.com/biography/Isaac-Newton

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Joseph Priestley | A Momentous Encounter | The Mystery of Matter

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See how Priestley's friendship with Benjamin Franklin led to his own career in science.

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In full:

Galileo Galilei

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Galileo (born February 15, 1564, Pisa [Italy]-died January 8, 1642, Arcetri, near Florence) Italian natural philosopher, astronomer, and mathematician who made fundamental contributions to the sciences of motion, astronomy, and strength of materials and to the development of the scientific method. His formulation of (circular) inertia, the law of falling bodies, and parabolic trajectories marked the beginning of a fundamental change in the study of motion. His insistence that the book of nature was written in the language of mathematics changed natural philosophy from a verbal, qualitative account to a mathematical one in which experimentation became a recognized method for discovering the facts of nature. Finally, his discoveries with the telescope revolutionized astronomy and paved the way for the acceptance of the Copernican heliocentric system, but his advocacy of that system eventually resulted in an Inquisition process against him.

Early life and career

Galileo was born in Pisa, Tuscany, on February 15, 1564, the oldest son of Vincenzo Galilei, a musician who made important contributions to the theory and practice of music and who may have performed some experiments with Galileo in 1588-89 on the relationship between pitch and the tension of strings. The family moved to Florence in the early 1570s, where the Galilei family had lived for generations. In his middle teens Galileo attended the monastery school at Vallombrosa, near Florence, and then in 1581 matriculated at the University of Pisa, where he was to study medicine. However, he became enamoured with mathematics and decided to make the mathematical subjects and philosophy his profession, against the protests of his father. Galileo then began to prepare himself to teach Aristotelian philosophy and mathematics, and several of his lectures have survived. In 1585 Galileo left the university without having obtained a degree, and for several years he gave private lessons in the mathematical subjects in Florence and Siena. During this period he designed a new form of hydrostatic balance for weighing small quantities and wrote a short treatise, La bilancetta ("The Little Balance"), that circulated in manuscript form. He also began his studies on motion, which he pursued steadily for the next two decades.

In 1588 Galileo applied for the chair of mathematics at the University of Bologna but was unsuccessful. His reputation was, however, increasing, and later that year he was asked to deliver two lectures to the Florentine Academy, a prestigious literary group, on the arrangement of the world in Dante's Inferno. He also found some ingenious theorems on centres of gravity (again, circulated in manuscript) that brought him recognition among mathematicians and the patronage of Guidobaldo del Monte (1545-1607), a nobleman and author of several important works on mechanics. As a result, he obtained the chair of mathematics at the University of Pisa in 1589. There, according to his first biographer, Vincenzo Viviani (1622-1703), Galileo demonstrated, by dropping bodies of different weights from the top of the famous Leaning Tower, that the speed of fall of a heavy object is not proportional to its weight, as Aristotle had claimed. The manuscript tract De motu ( On Motion), finished during this period, shows that Galileo was abandoning Aristotelian notions about motion and was instead taking an Archimedean approach to the problem. But his attacks on Aristotle made him unpopular with his colleagues, and in 1592 his contract was not renewed. His patrons, however, secured him the chair of mathematics at the University of Padua, where he taught from 1592 until 1610.

Although Galileo's salary was considerably higher there, his responsibilities as the head of the family (his father had died in 1591) meant that he was chronically pressed for money. His university salary could not cover all his expenses, and he therefore took in well-to-do boarding students whom he tutored privately in such subjects as fortification. He also sold a proportional compass, or sector, of his own devising, made by an artisan whom he employed in his house. Perhaps because of these financial problems, he did not marry, but he did have an arrangement with a Venetian woman, Marina Gamba, who bore him two daughters and a son. In the midst of his busy life he continued his research on motion, and by 1609 he had determined that the distance fallen by a body is proportional to the square of the elapsed time ( the law of falling bodies) and that the trajectory of a projectile is a parabola, both conclusions that contradicted Aristotelian physics.

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Galileo | Biography, Discoveries, Inventions, & Facts

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Galileo, the brilliant Italian polymath, revolutionized our understanding of the universe through his groundbreaking discoveries in astronomy and contributions to scientific methodology.

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Galileo was born February 15, 1564 in Pisa, Italy and he contributed to the study of the sciences of motion, astronomy, and the strength of materials, but mostly the development of the scientific method. Galileo also invented the telescope and made a multitude of discoveries these are the rings of saturn and the four moons of jupiter.

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https://www.youtube.com/watch?v=kKKM8Y-u7ds

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Gabriel was a dutch german inventor and insturment maker. he made the first thermometer.

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Anton Van Leeuwenhoek was a very important man to the Scientific Revolution. He was known as the father of biology and he learned how to make his own microscopes and he made important discoveries; single celled animals and plants, bacteria, and spermatozoa. He had discovered bacteria and the organism would not be discovered by any other scientist for another 100 years because they were so finely found.

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Anders Celsius was a swedish astronomer and mathematician.He was known for coming up with celsius scale.Which is a unit of tempature.

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René Descartes' major work on scientific method was the that was published in 1637 (more fully: Discourse on the Method for Rightly Directing One's Reason and Searching for Truth in the Sciences). He published other works that deal with problems of method, but this remains central in any understanding of the Cartesian method of science. The common picture of Descartes is as one who proposed that all science become demonstrative in the way Euclid made geometry demonstrative, namely as a series of valid deductions from self-evident truths, rather than as something rooted in observation and experiment. Descartes is usually portrayed as one who defends and uses an a priori method to discover infallible knowledge, a method rooted in a doctrine of innate ideas that yields an intellectual knowledge of the essences of the things with which we are acquainted in our sensible experience of the world. This metaphysics of essences and the accompanying a priori method are then contrasted to the method of Newton, Bacon and the British empiricists, who denied the metaphysics of essences and the doctrine of innate ideas, and for whom knowledge of the world of sensible appearances was to be located, not by going outside it to a realm of essences, but by applying the method of experiment through which one could trace out the patterns in this world of causes and effects. There is something to this standard picture, but Descartes' thought, like that of the empiricists, goes far beyond this simple description. In fact, Descartes sought to found our knowledge of things as much in experience and in experiment as in things a priori.

Table of Contents

1. Science as Observation and Experiment

a. Laws about Laws

Let us begin in the middle of one of these essays, the Optics, and in particular its Fifth Discourse, "Of Vision." There Descartes asks the reader to turn to experience, observational knowledge. He asks the reader to carefully observe an eyeball, say that of an ox, from which a portion of the rear has been removed with sufficient care to leave the eyeball fluid untouched. The portion removed is covered with a thin piece of paper. Descartes then describes how one can view the image formed on the back of the eyeball of objects at varying distances from the front of the eyeball, how the size of the image varies with distance, becomes fuzzier when the eyeball is squeezed, and so on. These were observations that had not before been recorded: they were part of the "new world" that science was just beginning to explore. The method was to, in the first place, explore it by empirical observation. Look, but look carefully and systematically.

To observe, however, is not to explain, and the new science seeks also to explain. Descartes has prepared the way for this. In earlier Discourses in the Optics, he presented the laws of geometrical optics for reflection and refraction. The former was already well known, but the sine law for refraction was newly discovered. (Huygens was later to complain that Descartes had not referred to Snell, who is now generally credited with the discovery of this law.) Descartes carefully shows how the lens of the eyeball, in conformity with the law of refraction, focuses light arriving from the object to form the image on the retina. The more particular biological facts of sight can be explained by the more general laws of geometrical optics.

The sine law of refraction is the general form of a set of laws: the angle of refraction will depend upon the particular transparent substances through which the light passes. The actual angle for any pair of substances will have to be determined by experiment.

Notice the structure of these inferences. There is a general law to the effect that for any situation of certain generic sort, there are specific laws that have some generic form. This is a law about laws. This law about laws serves as an abstract generic theory, and it yields, in regard to any specific sort of situation falling under the genus, the conclusion that, for such a specific sort of situation, there is a law (this has been called a "Principle of Determinism") and that this law will have a certain generic form and not any other sort of form (this has been called a "Principle of Limited Variety"). These two Principles provide a framework within which the scientist searching after truth works as he or she attempts to locate the law of the relevant generic sort that is there, according to theory, to be discovered. There will be a number of specific possibilities, each of the relevant generic sort. The task will be to turn to experiment to eliminate all possibilities but one by finding counterexamples. The un-eliminated hypothesis will be the specific law one is aiming to discover. In particular, such experiments will determine the constant of refraction that the sine law asserts to be there for specific pairs of transparent substances. Experiment will confirm the un-eliminated specific hypothesis, and this will in turn confirm the more generic theory that predicted the existence of a law of that relevant form.

The direction of the light rays as they pass from one substance to another will be determined not just by the constant of refraction, but also by the curvature of the surface that is the interface boundary. Descartes shows how the shape of a lens contributes to the formation of images. This again is a generic description of the laws applying to many specific situations. Descartes applies this knowledge to account for the various effects that can be produced on the image on the retina, for example, by squeezing the eyeball to distort the lens of the eye in various ways.

In later Discourses in the Optics Descartes goes on to show how this knowledge of patterns or regularities among things and events of the sensible world can be used to design telescopes, recently used effectively by Galileo, and to design lenses that can be used to remedy defects in eyesight. Descartes is using the knowledge of patterns not only to explain things newly noticed in observation, but also to apply it in ways useful to the further scientific exploration of the world (telescopes) and to make ordinary life better (corrective lenses).

The laws about laws that are the laws of reflection and refraction are themselves laws of physics, laws of matter in motion. In his presentation of these laws in the earlier Discourses in the Optics, Descartes uses a speculative model of light as consisting of little particles akin to tennis balls, only much smaller. This kinship is not only one of shape but one of the generic form of the laws that describe the motions of these two sorts of entity. He assumes that the particles of light move in straight lines. In the case of reflection he assumes that the light, that is, these light particles, strike an impenetrable surface and bounce off. In the case of the refraction he assumes the particles pass from a medium of one density to and through one with another density. The deductions Descartes offers are, in particular in the case of refraction, of questionable validity, but that is not to the present point; our interest is in the Cartesian method or methods and not how he actually applies them.

Descartes is clearly open to speculation because the model he uses for light is one that lacked empirical confirmation. He offered little evidence for his model of light. But it has two uses. One is as a heuristic device, to be used to discover laws, such as that of refraction, which can themselves be confirmed in experience. The experimental confirmation of these specific laws will also confirm the laws of the generic theory that has been discovered by means of the heuristic model.

He was clear, in his own mind at least, that the model had hardly be given a demonstration in the sense in which one could give in geometry the sort of demonstration given by Euclid. He wrote to Mersenne:

You ask me whether I think what I have written about refraction is a demonstration. I think it is, at least as far as it is possible, without having proved the principles of physics previously by metaphysics, to give any demonstration in this subject ... as far as any other question of mechanics, optics, or astronomy, or any other question which is not purely geometrical or arithmetical, has ever been demonstrated. But to demand that I should give geometrical demonstrations of matters which depend on physics is to demand that I should do the impossible. If you restrict the use of "demonstration" to geometrical proofs only, you will be obliged to say that Archimedes demonstrated nothing in mechanics, nor Vitello in optics, nor Ptolemy in astronomy, etc., which is not commonly maintained. For, in such matters, one is satisfied that the writers, having presupposed certain things which are not obviously contradictory to experience, have besides argued, consistently and without logical fallacy, even if their assumptions are not exactly true. (27 May 1638)

b. Models of "How Possibly"

The other use which these models have is to yield what might be called "how possibly" explanations. Many explained that sight occurred by immaterial sensory species, images of the objects being observed, being given off by those objects, and impinging upon the eye. The challenge was more or less that something like this must be so because no purely material explanation, in terms of particles interacting mechanically, could be given for the person becoming aware of the form of the object viewed. Descartes' model showed how this could be so because it explained how it possibly could be that there is a mechanical process that accounts for the facts of sight without invoking immaterial entities.

Descartes works out further this "how possibly" model, when he goes on in the Optics to elaborate a vision of the biological workings of a complete physiology that, like the more restricted case of the workings of the eyeball, can be explained by the supposed laws of a mechanistic physics. He lays out the idea that there certain fluids - "animal spirits" - carrying in effect messages from the sense organs to the brain, and to the pineal gland in particular - where he supposes the messages to be read as it were by the mind - this is the point of contact between the mind as a mental substance and the body as a, or more accurately as a part of the, material substance. The pineal gland is where the science of physics and material things stops, and the metaphysics of mind takes over. We need not pursue the line of the perceptual process from body into mind.

These "how possibly" uses of mechanistic models clearly introduce a research program, both of discovering the specific laws they suggest are there and confirming that the models do represent the structure of the world.

There was another point to the development of these "how possibly" models. The Roman physician Galen had written a work On the Usefulness of Bodily Parts, which thoroughly examined anatomical and physiological functioning. It was based on dissection, mainly of animals, and some experiment, and a good deal of speculation. Overall, it argued the thesis not only that the parts of the body are useful to the survival and good life of the animal or human being, but more strongly that the existence of these parts was to be explained by their utility--they existed in virtue of the fact that they contributed to the Good. While connected to the past, the cause of their existence was the form of the Good, their final cause, drawing them from the future into the present. Galen's work was openly teleological, a perspective developed by Plato, first in the Phaedo against Anaxagoras, and extended by Aristotle, against the mechanism of Democritus and Epicurus and Lucretius. While rejecting the anti-theological positions adopted by these latter Greek and Roman philosophers, Descartes sided with them in opposing teleological explanations. To be sure, anatomy and physiological processes did contribute to the survival and well being of animals and human beings, but their explanation was entirely in terms of mechanistic causes. Descartes' "how possibly" explanations aim to establish that our understanding of bodily processes needs no teleology because research can proceed here much as it proceeds in physics. That is, the science of human physiology is the same in kind as the science of stones.

c. Application to Human Physiology

Descartes was prepared to extend his guess to the whole set of natural processes defining the human being (save for rational thought and action under control of the conscious will). In the early 1630s he composed a Treatise on Man ( Traité de l'homme), which he suppressed on learning of Galileo's condemnation in 1633. It appeared only posthumously, in 1664, when it was published along with another unfinished work, this one from 1647/8, The Description of the Human Body ( La Description du Corps Humaine). The latter is sometimes titled "On the Formation of the Fetus," though this is misleading as this is only part, albeit an important part, of what the work covers. The Treatise begins deliberately with the supposition that God has built a statue which is a "machine made from earth," with a heart, a brain, and so on, but a contrivance which in detail works much like a clock, only in more complicated ways. The complex mechanisms are assumed to be able to approximate those of a human, but as it is imagined as a machine we will not be tempted to attribute its motions to the various mysterious powers, vegetative and sensitive souls, and so on, as did Aristotle and the Scholastics. Descartes' program aimed to show that all but rational and deliberately willed and self-conscious behavior could, in principle, at least, be explained as material processes operating according to mechanistic laws. He therefore elaborates "how possibly" such a machine might work. He describes how a "man of earth" analogous to clocks and to the automata, powered by water and doing various things, constructed by engineers for the gardens of the rich, but incredibly more complex, might be constructed by God and how it might work. The mechanisms envisioned by Descartes for this "man machine" in the Treatise are quite complex, although in comparison to what we now know of these mechanisms, they are simplistic and crude. The Description is a more curious work, dealing with the development of the human being from sperm through fetus to grown adult person. It consists mainly of assertions and coarse sketches of the mechanisms supposed to be involved. It was still a "how possibly" explanation, but it certainly was less persuasive than other parts of Descartes' sketches of a non-Galenic, non-Aristotelian mechanistic vision of the human body.

Descartes laid out the basic framework for empirical investigation in the main body of the Discourse on Method, in the Fifth Part. He makes specific reference to William Harvey's experiments that established the circulation of the blood, against the views of Galen, drawing attention to the eliminative role of observations in determining which, among several possible cases, is the one which is true. He indicates the need for a background generic theory to guide research by providing a principle of determinism and a principle of limited variety. Descartes is well aware of the logical structure of the research process for investigating the natural world, and discovering the laws of that world.

The background theory that is needed is the thesis that the world operates through mechanical processes and mechanisms that obey the laws of physics. Discoveries such as that of Harvey confirm these generic laws that guide the research. But there is more to it than that. This is where Descartes slips from the idea of science as empirical to the idea of science as a priori, from the idea of science as a method rooted in observation and experiment to the idea of a science whose method is rooted in the demonstrations of pure reason.

2. Cartesian Rationalism

a. A Priori Method

Descartes argues that the laws in the basic mechanistic framework that he takes to hold for sciences like optics and physiology - these laws about laws that guide empirical research in these sciences - are not themselves empirical but are rather necessary truths that are knowable a priori. Thus far we have seen that Descartes is well aware of the logical structure of the experimental method in natural science. To that extent he is not a philosopher who asserts that the a priori method applies everywhere. But he is nonetheless correctly to be counted among the rationalists. In fact he argues that in principle at least all laws could be known a priori. It is just that the world of ordinary things is too complicated in its structure for us, with our finite minds and limited capacity to grasp the a priori structure of the world, to deduce from self-evident premises the laws of the mechanisms underlying ordinary observable things and processes. We can know a priori the law about laws that there are more specific laws with the generic structure of physical mechanisms, of machines. But what those specific laws are requires empirical research; they are too complex logically to be knowable a priori by us, with our finite capacities.

Descartes argues that all things, including the material world we know by sense, have an inner essence or form, and its presence explains the structure of things as they ordinarily appear. These essences or forms are known not by sense but by reason. Reason is precisely the capacity to grasp these essences which are the reasons for things, the reasons why there are these patterns and regularities in the sensible world rather than others. He takes for granted that when the form is known that form is literally in the mind of the knower: there is an identity of the knower and the known. To grasp the essence of a thing is to know a priori the structure and behavior of the thing of which it is the essence. Material things are all modes of a single substance, the essence of which is extension. When we grasp the axioms of geometry as necessary truths, we are grasping the logical and ontological structure of the material world. Descartes is like Aristotle in attributing essences to things, but for Aristotle knowledge of the essence is given by syllogisms and by real definitions of species in terms of genus and specific difference. For Descartes, the structure is given by the truths of geometry.

Descartes holds in the Fifth Part of the Discourse on Method that the basic laws of physics are those of the geometry of objects in motion. These laws, he suggests, can be deduced from our knowledge of God. He creates a world the essence of which is given by the laws of geometry together with the principle that in any change quantity of motion is conserved. This conservation principle is thought to follow from the unchanging nature and stability of God the creator. There is a much more detailed derivation in the Principles of Philosophy. It is far from adequate. Descartes' knowledge of the laws of physics and of mechanics falls far short of Newton's. Perhaps this shows the weakness of the a priori method proposed by Descartes for obtaining the basic framework laws for science, the framework that provides the starting point of the experimental method and of the "how possibly" explanations he offers for material processes. Many have thought so.

In the Principles of Philosophy he goes so far as to attempt a derivation of the basic laws for planetary motions, based on the mechanistic supposition that the planets are material objects moved in circular fashion by vortices in a surrounding material fluid. Newton was soon enough to present his Mathematical Principles ( Principia Mathematicae) to the world. Descartes had been able to present only a set of non-mathematical principles, but Newton demonstrated that the vortex account, whatever its pretensions to being established a priori, was, given his three laws of motion, inconsistent with the facts of elliptical orbits as established by observation by Kepler. After Newton had succeeded in his attempt to "demonstrate the frame of the system of the world" (as he set out to do in Book III of his Principia Mathematicae), little was heard, save for a rearguard of French Cartesians, of the vortex theory. It became an historical curiosity.

Be that as it may, it could be concluded that Descartes had merely misapplied his method a priori, not that it was incorrect. Some later thinkers such as William Whewell argued this point. The method did not disappear in the way the vortex theory disappeared.

b. Geometrical Deduction

In one sense, this method is like the method of geometry that Euclid had given to the world in that one began with self-evident truths as axioms and then deduced by equally self-evident steps a set of theorems. Descartes referred to this as the "synthetic method" of doing geometry and (he had hoped) physics. He attempted this in outline in the Discourse on Method and in detail in his Principles, taking as his axiom the existence of God as an unchanging and stable creator of the natural world. The mechanistic framework for carrying on empirical research followed.

However, there is the issue of how the premises are discovered. Euclid never showed how this was to be done. But the later Greek mathematician Pappus, to whom Descartes referred on the issue of method in the Rules for the Improvement of the Understanding, had suggested that the method of finding premises reversed as it were the deductions of the synthetic method. This was the "analytic method." On the synthetic method one begins with premises that are accepted as true and works deductively towards conclusions, the theorems. Having reached the theorem, one has constructed a demonstration of that proposition. This synthetic method takes as given the premises from which it starts. But often to find a demonstration one must locate the premises from which the demonstration is to be constructed. This task of discovery was the point of the analytic method. On this method, one takes the conclusion to be demonstrated not as something accepted as true but merely as an hypothesis. One then works deductively towards the premises which one hopes to find for constructing a demonstration. Having arrived at the appropriate self-evident premises, one reverses the steps to obtain a synthetically organized demonstration of the hypothesis from which the analytic process started. And now that one has this demonstration, the proposition is transformed from a mere hypothesis to one that can be accepted as true. A particular version of the analytic method occurs in a reductio ad absurdum proof. Here one begins from an hypothesis and derives a contradiction; one then concludes that the hypothesis must be false, and that its denial is true. And as a special case of reductio ad absurdum, one begins with a proposition taken hypothetically and derives a conclusion that contradicts a known truth, concluding thereby that the original hypothesis is false. Descartes proposed to use this method to discover the axioms for his synthetic deductions: he is inspired by its uses in algebra, but extends it to his proof that the truths of geometry, arithmetic and physics, while self-evident, can themselves be demonstrated to be incorrigibly true from still more fundamental premises. The synthetic method was fine enough for the presentation of demonstrations in a science where the basic axioms are already known, and Descartes was to use this method, or thought he was so using it, in those parts of the Principles of Philosophy where he offered demonstrations of the basic truths of physics. Needless to say, his "proofs" have for the most part come to be seen as inadequate. But the analytic method was necessary from the discovery of the required premises. This is the method he proposes in the Discourse on Method as basic to firmly grounding the edifice of knowledge; and it is the method he uses in his presentation of the search after fundamental and incorrigible truths in the Meditations on First Philosophy, though here again he has generally been taken to be less successful in his application of the method than he himself hoped to be and expected he was. But his advocacy of the methods have continued to have their influence, in mathematics and algebra, and perhaps in physics, if not in first philosophy. Nevertheless, no one now expects to construct in either physics or geometry or first philosophy the rationalist ideal of an a priori demonstrative science.

c. Deduction in the Discourse and Meditations

As for the analytic method, Descartes was to use the first of the treatises appended to the Discourse on Method to illustrate the power of this method. This was the treatise on Geometry. This work in mathematics is remarkable, and it too was to revolutionize the way people thought about both algebra and geometry.

Descartes first set out to purify algebra. This was to be done by separating its patterns of thought from the particular subject matter to which it could be applied. He first separated what is given from which is to be discovered, developing the still current notation of a, b , c, ... for known quantities and x, y, z, ... for unknowns. He also reformed the notation for exponents replacing verbal terms such as "square" and "cube," and so forth, by superscripts ..., eliminating the geometrical connotations of the verbal terms. We continue to use this Cartesian notation.

Descartes then set out to apply this purified algebra in the solution of geometrical problems. The details need not concern us. For us it suffices to look at the problem he first addresses. This problem, which was posed originally by Pappus, is one of finding a curve of a point y relative to a point x, subject to certain geometrical constraints. To solve this problem he invents and uses the notion of a coordinate system. In effect he creates an arithmetical interpretation of geometry. (Descartes himself uses only an " x- axis"; the familiar extension of this idea to using two orthogonal " x" and " y" axes - what we now call "Cartesian coordinates" - were a later development of Descartes' pioneering idea.) Descartes shows how the finding of this curve can be done algebraically by solving certain equations. The point for us is that the solving of an equation is a matter of applying Pappus' "analytic method." Given a, b, c, ... , standing in certain arithmetical relations to one another, the equation in x and y asserts that there are values satisfying these conditions, that is, that there are solutions to the equation. This is the theorem to be proved. One proceeds by taking it as an hypothesis that x and y are solutions, and works out what those solutions are. This is the analytic process. Having found the solutions, one then has the premises from which the theorem to be proved follows. Deriving the theorem from the newly discovered premises is the synthetic process.

The algebraic methods that Descartes developed enabled him to present a series of entirely novel and original moves in geometry. Descartes' work in its applications is itself significant, but what was revolutionary was the new methods for solving problems in geometry and algebra. It is easy to prove theorems, but the greatness of a mathematician is the new methods of proof that he or she introduces. By this standard Descartes was indeed a great mathematician. Thinking in terms of equations, one can see why Descartes valued the analytic method over the synthetic, for the latter amounted to a footnote to the former. The analytic method was the one to be used if one was aiming to discover new truths; once these are discovered the synthetic method can be used to present this knowledge to students. As a method for discovering truth, the synthetic procedure was largely useless, the searcher after truth will need, and will use, the analytic method. This why Descartes argues that the analytic method is the appropriate method for discovering the a priori necessary truths that are the starting point for any genuine science, not only a science like geometry but also as providing the necessary theoretical truths required by the eliminative methods of empirical experimental science.

Descartes makes some important remarks in reply to some objections to the argument of the Meditations. Prior to publication of the Meditations, Descartes had circulated the manuscript to various other philosophers; they raised objections, and he wrote replies. He published his Meditations together with these Objections and Replies. In one of the Objections, the issue is raised why Descartes did not present his work in geometrical fashion, proceeding from axioms to theorems, using the synthetic method. In his Replies, Descartes explains he could have done so, but preferred to present his thoughts in the analytic method, which gives the order of discovery, through which the mind rises from hypotheses to the premises that are then used to prove synthetically the hypotheses that were the starting point of the inferences. He does, however, accede to the request of the Objection and does give a synthetically organized presentation of his inferences.

In this synthetic presentation the first proposition that he establishes is God's existence, which he takes to be something involved in the very idea of God as a being who, of His own nature, has all perfections. He then proceeds to the causal arguments for God's existence, and then to the proposition that God guarantees the truth of all propositions self-evidently implied by our ideas. Naturally enough this reverses the order of the Meditations themselves, which proceed in the order of the analytic method.

This means that the order of the Meditations is from propositions taken hypothetically to the proposition which is to form the first proposition to be discovered to be true and from which the hypotheses are then to be proved, that is, transformed from hypotheses to known truths.

Descartes reports in the First of the Meditations how he discovers that he can doubt almost everything about the material world that surrounds him. At the beginning of the Second Meditation his attention suddenly shifts from the world given in sense experience to the world given in inner awareness. He here discovers a proposition that he cannot doubt, namely the proposition that he expresses by "I think." Since this thinking is a mode it must clearly be a mode of something, a substance: "I think, therefore I am." Further, his thinking is inconceivable apart from himself, unlike, for example, extended things such as his body. He draws the further inference that he is a thinking thing. That is, he apparently is a substance, not a rational animal as Aristotle said, but a being or substance that is purely rational, one the essence of which is to aim to grasp the reasons for things. He carefully points out that this distinction between mind and body, based on the separability in thought of thinking from extension is only tentative. It may be that the world is not such as it here self-evidently appears to be. Thinking and extension may in the end be necessarily connected and it may be that modes can exist apart from substances, inconceivable though these things apparently seem to be. All this is to be here taken hypothetically, as a starting point in the analytic process leading to the discovery of a premise or premises that will serve to guarantee their truth and to justify the Meditator accepting them as truth.

This is where the Meditator is at the beginning of the Third Meditation. He or she can conclude, however, that as he or she is an imperfect being. Being a being that aims to know the doubt with which he or she is presently seized, it is clear he or she does not exist as his or her essence naturally implies that he or she should exist but lacks something the presence of which would be his or her Good. The idea that one has of oneself is that of an imperfect being; but to conceive an imperfect being requires one to be able to conceive a perfect being, just as conceiving something to be a non-square requires one to have the idea of a square. The presence of the negative idea requires the presence of the positive idea. So, the Meditator has the idea of a being that lacks no Good, no perfection--for any way of being this entity has that way either actually or formally. (Recall here that an idea, which, as Descartes speaks, formally exists as a property of the mind, exists objectively as the form or essence of a substance; the idea is true only if that the substance of which it is the essence actually exists in sense that it has actually the properties the essence determines that it ought to have; the idea is false if the substance has properties contrary to those that the essence requires it to have.)

The Meditator now infers the existence of such a perfect being from the fact that he as a finite being must be caused by such a perfect being, and from the fact that he or she could have present in his or her thoughts the idea of such a being only if it were placed there by such a being. But the existence of a perfect being is only established hypothetically - the arguments depend upon causal principles that, while self-evident, have not yet been established as true - following hypothetically from propositions that are themselves only hypothesis, the existence of God at this point in the inferences of the Meditations can only be an hypothesis - a further stage as one is led on by the analytic method to the discovery of what one hopes will be a truth upon which all other truths can be made demonstratively to rest.

The Fourth Meditation is a sort of aside in which Descartes clears away an apparent difficulty. There appears to be an inconsistency between the idea of a perfect being causing one with the idea that one falls into error and doubt: shouldn't a perfect being create beings that do not fail to be what essentially they ought to be? Descartes replies that such error is not caused by God but by ourselves. Located in a world that often hastens us on, we must regularly conclude before full evidence is available. Our will moves us to judge and such judgments often outrun what reason can justify. Now, God has given us free will, and this is a greater good than is mere avoidance of error. God's will does not cause us to err, it is our own will that does that, so the idea of a perfect God creating us is compatible with our being beings that fall into error. The apparent difficulty disappears, and we can return to the process of analysis that is, one hopes, leading one to a premise which can serve to demonstrate the hypotheses through which one is being led by a series of apparently necessary connections.

This brings us to the Fifth Meditation. Thinking of oneself as a finite being one is led to the idea of God and then to the idea of God as one's creator and as one who is created with the idea of such a perfect being within oneself. But now before one's mind is the idea of a being with creative powers that lacks nothing, lacks no perfection. It must therefore in particular cause itself to be and to be in this state of full perfection. But if it has the creative power to maintain itself as a being which lacks nothing, if, in other words, it is a being which as a creating being is infinitely powerful, then there is nothing else that could cause it not to be in any way at all. We have within us this idea and as we plumb its depths we recognize that this is an idea of a being the creative powers of which guarantee that it exists, it is the idea of a being that guarantees the truth of this very idea. Our other ideas are ideas of finite beings none of which can guarantee their own existence and the ideas of which might therefore be false; but this one idea, this one essence that is before the mind, is the idea of a being infinite in its creative powers and which is therefore the essence of a being that can guarantee its own existence, which in turn therefore guarantees the truth of the idea of itself.

Here, then, in the existence of God, we have reached the end point of our analytic process in a truth which guarantees its own truth and upon which all other truths can be made to rest. This truth can therefore form the incorrigible base upon which all our knowledge claims can be made to rest. Descartes can now hastily draw things to a close: God as a perfect being, could not create non-being: it is a contradiction to suppose non-being could be brought into being. But for a rational being, a thinking substance, to err is for it to not know: it is a form of non-being. So God could not create a rational being for which principles clearly and distinctly perceived to be true were after all false: that would be to create a being which systematically erred about the structure of the world. So what is clear and distinct, what is self-evident, and compels its acceptance by the Meditator and indeed by any rational being, is guaranteed to be true. In particular, the laws of geometry, of extended substance, are guaranteed to be true. And further, the incompatibility of thought and extension as essence of substances, which, in the Second Meditation, while clear and distinct, is only apparently true can now be affirmed as not merely apparently true but as actually true.

With God, we have reached at the conclusion of the analytic process the starting point of the synthetic presentation that Descartes gives in his Replies to the Objections. In that synthetic presentation, the sequence ends with the conclusion (theorem) that what is clear and distinct must be true.

Two points need to be mentioned. First, the move of "I think, therefore I am" ( cogito, ergo sum) is not a direct insight into the Meditator's own being. It is, rather, an inference, based on the principle that every mode (property) exists only if it is in a substance. Since it is based on a metaphysical principle the truth of which has not yet been established, it could not provide a starting point for constructing the edifice of knowledge.

Second, the existence of God is in the end not established by argument. The so-called ontological argument of the Fifth Meditation is not in fact an argument. It is rather a case where we have direct insight into the essence of God - what is formally the idea of God is objectively the essence of God - , where we recognize that here we have an essence that guarantees its own existence as an infinitely powerful being and thereby guarantees the truth of the idea through which we think it. Other ideas we have are no doubt true, but none save this one alone guarantees its own truth - guarantees it in a way that requires no argument. With God we reach a point where no further premises are either available or needed.

The Cartesian method to science thus indeed yields an a priori science. It is a deductive method but one that involves both analysis and synthesis.

3. Method of Doubt

We have so far studiously avoided one feature of the Cartesian method. This is the so-called "method of doubt." Descartes takes very seriously the notion that progress in science will be hindered if we allow our minds to be clouded by the worthless standards inherited from the past and from our teachers. Thus, he begins the Geometry with his clarification of the notion of a power, removing the irrelevant geometrical connotations attached to expressions like " x cubed" and replacing them with the perspicuous notation of " x ³ " that we continue to use to this day. Again, he believed it to be important to shed ourselves of all forms of teleological thinking - he chastised Harvey for falling away from the mechanistic reasoning he used to establish the circulation of the blood and into teleological thinking when he came to discuss the action of the heart.

He therefore recommended that one undertake a cleansing intellectual project in the attempt to move towards truth by first eliminating error and indeed all possibility of error. This could be done by rejecting as false all propositions that could in any way be doubted. This is Descartes' first rule of method in the Discourse on Method. This is stated as the injunction:

[N]ever to accept anything as true if I did not have evident knowledge of its truth: that is, carefully to avoid precipitate conclusions and preconceptions, and to include nothing more in my judgments than what presented itself to my mind so clearly and so distinctly that I had no occasion to doubt it.

By eliminating all dubitable beliefs, truths would of course be excised along with the false, but then in the re-building of the edifice of knowledge that was to follow those truths would be recovered, free from the errors of the past.

This was an exercise to be undertaken by oneself, simply taking oneself to be a rational being. But if one is rational, one is also animal, even if being an animal is not part of one's essence. The animal makes demands - one must eat and drink, one must sleep, perchance to dream, one must live with others, one might even take a lover. One could not do this if all beliefs were eliminated. So Descartes also recommends that one go along with this second best, the beliefs that one needs to survive and to have a decent and pleasant life - interrupted only occasionally by bouts of meditating on the foundations of knowledge, or the basic laws of physics - just as one must in the end do science empirically, through observation and experiment, even though it is only uncertainly founded. Reason demands for itself the method of doubt, but the remainder of one's being makes unavoidable demands that require one to ignore the promptings of reason to try to doubt everything. The reasonable person will accede to those demands, just as reason must attempt a universal doubt. It is also part of Descartes' method that one does accede to those extra-rational demands. The reasonable person could not do otherwise: there is in the end more to being human than simply being rational.

So we have the structure of the Meditations as follows:

[Hypothesis:] There is an evil genius who is deceiving me about the truth of clear and distinct ideas. [From this hypothesis I now infer] if I am being deceived, then I am thinking; if I am thinking, then I exist; if I (as a finite creature) exist, then there exists a God (an infinite being) who creates me; - [here the existence of God is hypothetical, but having reached the idea of God as an infinite cause of all being, including myself, I can see as I grasp this idea that it non-hypothetically requires its own truth] - God (as an infinite creator) guarantees His own being and therefore exist - [here we have reached a certain and incorrigible categorical truth]; but [now upon this truth all other truths hinge] an infinite being is a perfect being and therefore cannot create finite beings who are systematically deceived; therefore our clear and distinct ideas are true; therefore there is no evil genius.

4. Conclusion

Many now see Descartes as having posed the skeptical challenge that still confronts philosophers, with the hypothesis of the evil genius taking the skeptical challenge as far, or as deep, as it can go. For Descartes, however, it was more like the deep night through which the soul must pass on its way to light, the light of reason, and to God as the reason for all things and the source of that light, and then, through God, to the scientific study of the world. Few have been able to follow him: he has not convinced. For most, the radical skepticism created by Descartes' method of doubt and the demon hypothesis is a sham: Descartes creates the problem for himself when he suggests that the world can be distinguished ontologically into the world of ordinary experience and a world of essences or forms that lies beyond this ordinary world but which constitutes the reasons for its being. If the reasons for our ordinary world being as it is are not to be found in that world, then they are not to be found at all, and the radical skepticism is a consequence of a search after what cannot be found: the skepticism is not there to be conquered, as Descartes thought, but to be dismissed as an unreasonable longing for a world of certainty that is not there.

But if we say this, then we must also say that method of doubt is not wholly to be dismissed in this way. While the radical skepticism that Descartes proposes cannot be reasonable, we should nonetheless take his method seriously enough that we remain diffident in our judgments - that we not take things dogmatically, but rather critically, ready to recognize evidence that can challenge the rational acceptability of those judgments. So long as we do not take 'clear' and 'distinct' as rigidly as Descartes does, it is not a bad rule "to include nothing more in one's judgments than what presents itself to one's mind so clearly and distinctly that one has no reason to doubt it" (to paraphrase Descartes' rule in the Discourse). This is what reasonable persons do. It is now the norm, it was not the norm before Descartes.

Nor, taking Descartes' other rules of method just as cautiously, is it difficult to see the wisdom in these rules of method - the rules in the Discourse that one should "divide each of the difficulties examined into as many parts as possible and as may be required in order to resolve them better"; that one ought "to direct one's thoughts in an orderly manner, by beginning with the simplest and most easily known objects in order to ascend little by little, step by step, to knowledge of the most complex, and by supposing some order even among objects that have no natural order of precedence"; and that one ought "throughout to make enumerations so complete, and reviews so comprehensive, so that one could be sure of leaving nothing out." Following these rule may not lead one to discover the existence of God, as Descartes thought, but they remain rules that recommend themselves to searchers after any sort of truth about the world, even where those truths are metaphysically more modest than those that Descartes sought.

This was perhaps the most important contribution of Descartes to the opening up of thought in the modern and early modern period. If Descartes was not as modest in his cognitive aspirations as his method of doubt requires, then that only shows that Descartes too had his failings as a human being - it is not to denigrate the contribution he made to the emergence of the modern mind as one that is committed to finding truth, and that is open, and ready to submit to criticism. Descartes' rationalism has had its day; few would now advocate the method a priori that he advocated. Yet, if they are taken cautiously, the Cartesian precepts for the search after truth that he presents in the Discourse on Method can still be recommended for the clarity of thought that results from our conforming to these standards.

Science is no longer something that aims to become a priori and incorrigibly certain. But Descartes also saw science as a human enterprise in which the search after truth is rooted in observation and experiment. This part of the Cartesian vision remains with us. So, too, does his notion that progress towards truth comes through the testing of hypotheses and the elimination of the false through the production in experiments, deliberate or natural, of counterexamples. Of course, this idea, that science searches after truth through the elimination of error, was not Descartes' alone. He shared it with Bacon. Indeed, Bacon's vision was in one respect clearer, since he did not see the need to root the scientific theories that guide research into some a priori ontological structure of being. The theories that guide research are simply laws among laws - to be sure, they are laws about laws, but for all that they are empirical generalizations like any other law.

At the same time, it must be said that Descartes was much the better at applying the experimental method that both he and Bacon advocated. Descartes made real contributions to empirical science, for example, in optics and in the physiology of the eyeball, where Bacon made no such contribution.

Moreover, the Cartesian vision of the world as one to be understood in terms of physical mechanisms, while no longer taken to be one that needs any a priori defense of the sort Descartes himself proposed, has become and remains as the basic framework of science: if it has not been confirmed a priori, it has certainly been confirmed a posteriori, and it is still the guiding vision of science - this in spite of the challenges, still often to be heard, that the complexity of this or that cannot be reduced to, or be understood in terms of, "mechanistic materialism." In the years after Descartes' death, his mechanistic formulations of problems in physiology swept out the obfuscating categories of the older forms of thought, of teleology in particular, in ways that could not be circumvented. Some tenured professors in the universities continued to hang on to the old scholastic ways of thought, but elsewhere the new science of Descartes swept away the dross. The modern science of physiology was created by the Cartesian vision, and in fact is still sustained by it - though, to be sure, physics is no longer simply a science of mechanical motions, it has grown to include quantum mechanics and molecular biology - but physics is still a science that enables us to say that science of physiology is no different in kind from the sciences of stones and of atoms and of planets.

Descartes' own contributions to physics, both in optics and mechanics, were considerable. In mechanics, his work was definitely blocked by his failure to even think that a notion of mass was essential to any mechanics that was to move from kinematics to dynamics. In optics, his mechanistic ideas clearly interfered with his attempts to understand colors. These problems, in both mechanics and optics, awaited Newton for their solution.

In mathematics his contributions remain with us to this day, not merely as part of a guiding vision - though that is certainly there - but as part of the working tools of every mathematician. One has only to think of his innovations in notation, for example, of exponents, or the methods of analytic geometry, for example, the use of a system of ("Cartesian") coordinates. Modern algebra and modern geometry are inconceivable without Descartes' contributions. The mathematics and mathematical methods that he invented shaped his reflections on the proper method in science and in philosophy. It is also true, one must add, that his reflections on the methods proper to philosophy shaped his work in algebra and geometry.

Descartes' reflections on the methods proper to science and to philosophy were, as he himself claimed, highly original, and highly influential. They shape our thinking about these same things up to the present, and will no doubt continue to shape them. They amount to the demand that we seek clarity in our thought, that we be diffident rather than dogmatic in our judgments, that when we search after truth then we should do so systematically, from the simpler to the complex, in a way befitting the subject matter, and that a science like physiology is to be understood as in no way different in kind from the science of stones. If we ignore these Cartesian precepts of method, then that is to our own peril, or at least to the impoverishment of our own thought.

5. References and Further Reading

a. Primary Sources

Descartes' complete works can be found in Oeuvres de Descartes. Ed. C. Adam and P. Tannery. 12 vols. (Paris: J. Vrin, 1897-1913; reprinted 1964-1974).
See also the Correspondance. Publiée avec une introd. et des notes, par Ch. Adam et G. Milhaud, 8 vols. (Paris: F. Alcan, 1936-63).

Descartes, René. The Philosophical Writings. 3 vols. Vols 1 and 2 trans. J. Cottingham, R. Stoothoff and D. Murdoch; vol. 3 trans J. Cottingham, R. Stoothoff, D. Murdoch, and A. Kenny (Cambridge: Cambridge University Press, vols. 1 and 2, 1984, vol. 3, 1992).
This is now the standard English translation. Vol. 1 contains Early Writings; Rules for the Direction of Our Native Intelligence; The World and Treatise on Man; Discourse on Method and (in part) the appended treatises on Optics, Geometry, and Meteorology;Principles of Philosophy (in part); Comments on a Certain Broadsheet; Description of the Human Body; and The Passions of the Soul. Vol. 2 contains (in full) the Meditations on First Philosophy and the Objections and Replies. Vol. 3 contains much of the philosophically and scientifically interesting portions of Descartes' correspondence.

Descartes, René. Discourse on Method, Optics, Geometry, and Meteorology. Trans. with Intro. by Paul J. Olscamp. (Indianapolis, IN: Bobbs-Merrill, 1965)
This contains complete English translations of the Discourse on Method and the three appended treatises.

Descartes, René. Principles of Philosophy. Trans. with Notes by V. R. Miller and R. P. Millar. (Synthese Historical Library - Texts and Studies in the History of Logic and Philosophy, vol. 24. Dordrecht, The Netherlands: D. Reidel, 1983).
This contains a complete English translation of the 1644 text.

b. Bibliographical Study

Sebba, G. Bibliographica Cartesianae: A Critical Guide to the Descartes Literature, 1800-1958(The Hague: Nijhoff, 1964).
An indispensable bibliography.

c. Secondary Sources

Roger. Descartes' Meditations: Background Source Materials. (Cambridge: Cambridge University Press, 1998).

Beck, L. J. The Method of Descartes: A Study of the Regulae. (Oxford: Oxford University Press, 1952).

Broughton, Janet. Descartes's Method of Doubt. (Princeton: Princeton University Press, 2002).

Cottingham, John, ed. The Cambridge Companion to Descartes. (Cambridge: Cambridge University Press, 1992).

Crombie, A. C., "The Mechanistic Hypothesis and the Scientific Study of Vision," Proceedings of the Royal Microscopical Society, 2 (1907), pp. 3-112.

Curley, E. M. Descartes Against the Skeptics. (Cambridge, MA: Harvard University Press, 1978).

Foster, Michael. Lectures on the History of Physiology, during the Sixteenth, Seventeenth and Eighteenth Centuries. (Cambridge: Cambridge University Press, 1901).

Garber, Daniel. "Semel in vita: The Scientific Background to Descartes' Meditations." In Essays on Descartes' Meditations, ed. Amélie Oksenberg Rorty. (Berkeley: University of California Press, 1986).

Garber, Daniel. Descartes' Metaphysical Physics. Chicago: University of Chicago Press, 1992).

Gaukroger, Stephen. Cartesian Logic: An Essay on Descartes's Conception of Inference. (Oxford: Clarendon Press, 1989).

Gewirtz, A. "Experience and the Non-Mathematical in the Cartesian Method," Journal of the History of Ideas, 2 (1941), pp. 183-210.

Hall, Thomas J. Ideas of Life and Matter. 2 vols. (Chicago: University of Chicago Press, 1969).
The impact of Cartesian ideas in the seventeenth century is discussed in vol. 1.

Gaukroger, Stephen, ed. Descartes: Philosophy, Mathematics and Physics. (Sussex: The Harvester Press, 1980).

Gilson, Étienne. Études sur le Role de la Pensée Médiévale dans la Formation du Système Cartésien (Paris: J. Vrin, 1930).

Gilson, Étienne. René Descartes' Discours de la Méthode; Texte et Commentaire. (Paris: Librairie Philosophique J. Vrin, 1947).

Grant, Edward. Much Ado about Nothing: Theories of Space and Vacuum from the Middle Ages to the Scientific Revolution. (Cambridge: Cambridge University Press, 1981).

Koyré, Alexandre. Entretiens sur Descartes. (New York: Brentano's, 1944).

Koyré, Alexandre. From the Closed World to the Infinite Universe. (Baltimore: Johns Hopkins University Press, 1957).

Lennon, Thomas. The Battle of the Gods and Giants: the Legacies of Descartes and Gassendi, 1655-1715. (Princeton: Princeton University Press, 1993).

Popkin, Richard H. The History of Scepticism from Erasmus to Spinoza. (Berkeley: University of California Press, 1979).

Smith, Norman Kemp. New Studies in the Philosophy of Descartes: Descartes as Pioneer. (London: Macmillan, 1952). Voss, Stephen. ed. Essays on the Philosophy and Science of René Descartes (Oxford University Press, 1993).

Wilson, Fred. The Logic and Methodology of Science in Early Modern Thought: Seven Studies (Toronto: University of Toronto Press, 1999).

Wilson, Margaret D. Descartes. (London: Routledge & Kegan Paul, 1978).

Author Information

Fred Wilson
Email: fwilson@chass.utoronto.ca
University of Toronto
Canada

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René Descartes' major work on scientific method was the that was published in 1637 (more fully: Discourse on the Method for Rightly Directing One's Reason and Searching for Truth in the Sciences). He published other works that deal with problems of method, but this remains central in any understanding of the Cartesian method of science.

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Anders Celsius
1701-1744
Anders Celsius, born in Uppsala, was one of a large number of scientists (all related) originating from Ovanåker in the province of Hälsingland. The family name is a latinised version of the name of the vicarage (Högen). His grandfathers were both professors in Uppsala: Magnus Celsius the mathematician and Anders Spole the astronomer. His father, Nils Celsius, was also professor in astronomy. Celsius, who was said to have been very talented in mathematics from an early age, was appointed professor of astronomy in 1730.
He began his "grand tour", lasting for four years, in 1732, and he visited during these years almost all the notable european observatories of the day, where he worked with many of the leading 18th century astronomers.

Soon after his return to Uppsala he participated in the French astronomer Maupertuis' famous expedition 1736 to Torneå, in the most northern part of Sweden. ("The Lapland expedition.") The aim of the expedition was to measure the length of a degree along a meridian, close to the pole, and compare the result with a similar expedition to Peru (today Ecuador) near the equator. The expeditons confirmed Newton's belief that the shape of the earth is an ellipsoid flattened at the poles.

Celsius' participation in this expedition made him famous and was important in his efforts to interest the Swedish authorities in donating the resources necessary to build a modern observatory in Uppsala. He was successful, and the Celsius observatory was ready in 1741, equipped with instruments purchased during his long voyage abroad, comprising the most modern instrumental technology at that time.

In those days geographical measurements, metereological observations and other things, not considered as astronomy today, were included in the work of an astronomy professor. He carried out many geographical measurements for the Swedish General map, and was also one of the first to note that the land of the nordic countries is slowly rising above sea level, a process which has been going on since the melting of the ice from the latest ice age. He believed though, that it was the water that was evaporating.

For his metereological observations he constructed his world famous Celsius thermometer, with 0 for the boiling point of water and 100 for the freezing point. After his death in 1744 the scale was reversed to its present form.

Together with his assistant Olof Hjorter he also was the first to realize that the aurora phenomenon has magnetic causes through observing the inclination of a compass-needle and finding that the larger deviations correlated with stronger aurora activity.

In astronomy he made observations of eclipses and various astronomical objects. He published catalogues of carefully determined magnitudes for a total of 300 stars using his own photometric system (mean error=0.4 mag). The idea of his system consists of using identical transparent glass plates and viewing the ray of light from a star through them. He could then compare the magnitudes of the stars by the number of glass plates needed to extinguishe the light. (The star Sirius, the brightest star in the sky, needed 25 of his plates to be extinguished.)

Celsius published most of his work in the publications of the Royal Society of Sciences in Uppsala, which is the oldest Swedish scientific society founded in 1710, where Celsius was the secretary 1725-1744, and in the publications of the Royal Swedish Academy of Sciences, founded in 1739. He also presided at about twenty dissertations in astronomy where, as was the general rule in those days, he was the main author. His popular book Arithmetics for the Swedish Youth was typical of the spirit of his period, the Enlightenment.
Celsius was a very active supporter for introducing the Gregorian calender in Sweden but he wasn't successful until 1753, almost ten years after his death, when the Julian calender was abandoned by dropping 11 days.

Anders Celsius died of tuberculosis in april 1744, only 42 years old. His grave is next to his grandfather's, Magnus Celsius, in the church at Gamla Uppsala, about 5 km north of central Uppsala.

References:

Collinder, Per, Swedish Astronomers 1477-1900 , Acta Universitatis Upsaliensis, Ser. C. 19, Uppsala, 1970
Links:

Anders Celsius from English Wikipedia

300th anniversary of the birth of Celsius, November 27, 2001

Beckman, Olof, Anders Celsius (Elementa,84:4,2001)

Nordenmark, N.V.E., Anders Celsius: Professor i Uppsala 1701-1744, 1936

Anders Celsius från svenska WikipediaUppsala Astronomical Observatory: History Home 765k 454k 350k
Painting by Olof Arenius(1701 - 1766)
Uppsala University - Astronomical Observatory

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Anders Celsius 1701-1744 Anders Celsius, born in Uppsala, was one of a large number of scientists (all related) originating from Ovanåker in the province of Hälsingland. The family name is a latinised version of the name of the vicarage (Högen). His grandfathers were both professors in Uppsala: Magnus Celsius the mathematician and Anders Spole the astronomer.

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He was a journalsit, author and a polictic at the time. He came up with ways to test hypothesis like something involving nature he does the opposite effect to see f he is correct. He came up with the idea of hypothesis. He had many offervations and taught many people new stuff to his people back then involve science and polictics.
https://www.khanacademy.org/humanities/monarchy-enlightenment/baroque-art1/beginners-guide-baroque1/a/francis-bacon-and-the-scientific-revolution

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Robert Boyle - Man of Science, Man of Faith

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Robert Boyle has been called the "Father of Modern Chemistry". He was one of a handful of thinkers who pioneered the scientific method and helped displace alchemy and replace it with chemistry. But few are aware of his spiritual pursuits, both as a supporter of Bible translation and a defender of Christianity against Atheism.

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Description of Andreas Vesalius's life and his contributions to modern science and anatomy.

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Francis Bacon and the scientific revolution

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Read and learn for free about the following article: Francis Bacon and the scientific revolution

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Antoine was born into a wealthy family. At age 21 he started to study mathematics and science. in 1771, Lavoisier married 13-year old Marie-Anne Pierette Paulze. She then started to become a colleague to her husband by learning English so she can translate the writings of Priestley, also gaining the ability of art and sculpting. In 1770 to 1790 he explained what is now combustion.  Antoine help invent many things such as metric system and most of chemistry.

http://mattson.creighton.edu/History_Gas_Chemistry/Lavoisier.html
https://www.youtube.com/watch?v=QiiyvzZBKT8

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isaac newton was a famous mathematician and astronomer at the time and he was a huge influence to the scientific revolution.

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Robert Boyle (Stanford Encyclopedia of Philosophy)

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Robert Boyle was born in Lismore, Ireland, on January 25, 1627. He was his parents' fourteenth, penultimate, child, and the last to survive to adulthood. Boyle was the youngest son and, after his sister Margaret died when he was 10, the youngest child of the family.