"Science, may be compared to a tree; metaphysics is the root, physics is the trunk, and the three chief branches are mechanics, medicine, and morals, these forming the three applications of our knowledge, namely, to the external world, to the human body, and to the conduct of life ."
The man who wrote the words quoted above, was the third and last child born to his parents. His mother died as a result of his birth. It was recorded that as a child he showed an inquisitive mind, and was called by his father, "my philosopher." This was at the beginning of the 1600's in France.
He was sent to school at the age of eight, the school of La Fleche which Henry IV had founded. He continued there from 1604 to 1612. In 1613 he had moved to Paris and here made the acquaintance of Mydorge, one of the foremost mathematicians of France. -
"The man Mydorge was known for his work in geometry which was directed to the study of conic sections. -[like a cone]- His work on the subject, first published in two volumes in 1631 and enlarged to four in 1639, was reprinted several times under the title De sectionibus conicis. His works on conic sections contain hundreds of problems published for the first time, as well as a multitude of ingenious and original methods that later geometers frequently used. Mydorge became the premier mathematician of his day. He studied the properties and nature of light and refraction, and he studied vision. He also carried out extensive astronomical observations."
Quote from The Galileo Project online resource
After meeting Mydorge the man devoted the years 1615 and 1616 to the study of mathematics. In 1617, at age 21 he left France for the Netherlands.
It was during his time in the Netherlands that his mathematical career began, and it was also the period that is noted as the birth of modern mathematics.
Who is he? Have you heard of him?
At the height of its power he moved to Holland. There he lived for twenty years , giving up all his time to philosophy and mathematics. And with these subjects alone his focused his writings.
He spent the time from 1629 to 1633 writing Le Monde, a work embodying an attempt to give a physical theory of the universe.
But finding its publication was likely to bring on him the hostilitv of the Church [as Galileo found ], and having no desire to pose as a martyr, he abandoned it. The incomplete manuscript was later published in 1664.
Galieo was convicted of heresy in 1933.
The publication we now know under the English title as The World, or Treatise on Light
He then devoted himself to composing a treatise on universal science; this
was puiblished at Leyden in 1637 under the title Discourse de la methode pour
bien conduire sa raison et chercher la verite dans les scierices,
and was accompanied with three appendices entitled La Dioptrique, Les Mel1ores, and La Geometrie.
It is from the last of these that the invention of analytical geometry dates. In 1641, he published a work called Meditations, in which he explained
at some length his views of philosophy as sketched out in the Discourse. In
1644, he issued the Principia Philosophiae, the greater part of which was devoted to physical science especially the laws of motion and the theory of vortices.
In his theory of vortices, he commences with a discussion of motion, and then
lays down ten laws of nature, of which the first two are almost identical with the
first two as laid dowwnby Newton. Or so it has been recorded.
The remaining eight are inaccurate. He next proceeds to a discussion of the nature of matter which he regards uniform in kind though there are three fornms of it. He assumes that the rnatter:of the universe is in motion, that this motion is constant in amount, and that the motion results in a number of vortices. He states that the sun is the center of an immense whirlpool of this matter, in which the planets float and are swept round like straws in a whirlpool of water. Each planet is supposed to be the center of a secondary whirlpool by which its satellites are carried, and so on.
It is said that all of these assumptions are arbitrary and unstupported by any investigation.
It is a little strange that a man who began his philosophical reasonings by doubting all things and finally comning to cogito, ergo sum. should have made assumptions so groundless.
Descartes was a philosopher of a very high type, yet his fame will
ever rest on his researches in mathematics.
The first important problem solved by Decartes in his geometry is the problem of Pappus,-:
"Given severalstraight lines in a plane, to find the locus of a point such that perpendiculars, or, more generally, straight lines at given angles, drawn from the point to the given lines, shall satisfy that the product of certain of them shall be in given ratio to the product of the rest."
"The most important case of this problem is to find the locus of a point such that the product of the perpendiculars on m given lines be in a constant ratio to the product of the perpendiculars on n' other given straight lines.
The ancients had solved this geometrically for the case m=1, n= l, and the case m =1, n = 2.
Pappus had further stated that if m-n = 2, the locus was a conic, but he gave no proof. Descartes also failed to prove this by pure geomnetry, but he showed that the curve was represented by an equation of the second degree, that is, was a conic. Subsequently Newton gave an elegant solution of the problem by pure geometry."*
[*Ball's Short'Account of the History of Mathematics]
In algebra, Descartes expounded and illustrated the general methods of
solving equations up to those of the fourth degree (and believed that his method
could go beyond), stated the law which connects the positive and negative roots
of an equation with the change of signs in the consecutive terms, known as Descartes' Law of Signs, and introduced the method of indeterminate coefficients for
the solution of equations.
In appearance, Descartes was a small man with large head, projecting
brow, prominent nose, and black hair coming down to his eyebrows. His voice
was feeble.
Considering the range of his studies he was by no means widely
read, had no use for Greek, as is shown by his disgust when he found that Queen
Christinia devoted some time each day to its study, and despised both learning
and art unless something tangible could be extracted from them.
In philosophy he did not read much of the writings of others. In disposition, he was cold and selfish, He never married, and left no descendants, though he, had one illegitimate daughter, Francine, who died in 1640, at the age of five.
In 1649, through the instigation of his close personal friend, Chanut, he
received an invitation to the Swedish court, and in September of that year he
left Egmond for the north. Here, on the 11th of February, 1650, he died of inflamation of the lungs brought about by too close devotion to the sick room of
his friend Chanut, who was dangerously ill with the same disease.
The bulk of this gossamer article is sourced from The American Mathematical Monthly 1898. You can find and read that full article as well right here.
And more resources on Descartes may be read here
"Science, may be compared to a tree; metaphysics is the root, physics is the trunk, and the three chief branches are mechanics, medicine, and morals, these forming the three applications of our knowledge, namely, to the external world, to the human body, and to the conduct of life ." -Rene Decartes
