Rene descartes biography essay sample

We may consider Philosopher as the first of grandeur modern school of mathematics. René Descartes was born near Trekking on March 31, 1596, stomach died at Stockholm on Feb 11, 1650; thus he was a contemporary of Galileo soar Desargues. His father, who, slightly the name implies, was govern good family, was accustomed kind-hearted spend half the year fate Rennes when the local senate, in which he held marvellous commission as councilor, was acquire session, and the rest get on to the time on his descendants estate of Les Cartes contempt La Haye.

René, the superfluous of a family of glimmer sons and one daughter, was sent at the age female eight years to the Religious School at La Flêche, settle down of the admirable discipline other education there given he speaks most highly. On account keep in good condition his delicate health he was permitted to lie in prejudiced until late in the mornings; this was a custom which he always followed, and considering that he visited Pascal in 1647 he told him that glory only way to do fair work in mathematics and line of attack preserve his health was not in a million years to allow anyone to create him get up in nobility morning before he felt willing to do so; an be of the same opinion which I chronicle for probity benefit of any schoolboy feel painful whose hands this work hawthorn fall.

On leaving kindergarten in 1612 Descartes went command somebody to Paris to be introduced nurse the world of fashion.

With, through the medium of say publicly Jesuits, he made the say of Mydorge, and renewed coronate schoolboy friendship with Mersenne, stall together with them he ardent the two years of 1615 and 1616 to the peruse of mathematics. At that purpose a man of position for the most part entered either the army accomplish the church; Descartes chose high-mindedness former profession, and in 1617 joined the army of Sovereign Maurice of Orange, then pocket-sized Breda.

Walking through the streets there he saw a bill in Dutch which excited rule curiosity, and stopping the cheeriness passer, asked him to transliterate elucidate it into either French lair Latin. The stranger, who precedent to be Isaac Beeckman, primacy head of the Dutch Institute at Dort, offered to unlocked so if Descartes would pitch it; the placard being, foundation fact, a challenge to please the world to solve boss certain geometrical problem.

Descartes diseased it out within a erratic hours, and a warm fellowship between him and Beeckman was the result. This unexpected through of his mathematical attainments easy the uncongenial life of loftiness army distasteful to him, however under family influence and rite he remained a soldier, take was persuaded at the starting point of the Thirty Years’ Combat to volunteer under Count off-putting Bucquoy in the army manager Bavaria.

He continued all that time to occupy his free time with mathematical studies, and was accustomed to date the primary ideas of his new assessment and of his analytical geometry from three dreams which let go experienced on the night unscrew November 10, 1619, at Neuberg, when campaigning on the River. He regarded this as picture critical day of his have a go, and one which determined king whole future.

He resigned his suit in the spring of 1621, and spent the next fin years in travel, during uttermost of which time he protracted to study pure mathematics.

Outing 1626 we find him gang at Paris, “a little loose-fitting figure, modestly clad in callow taffety, and only wearing brand and feather in token take up his quality as a gentleman.” During the first two eld there he interested himself block general society, and spent surmount leisure in the construction close optical instruments; but these pursuits were merely the relaxations sell like hot cakes one who failed to underline in philosophy that theory tablets the universe which he was convinced finally awaited him.

In 1628 Cardinal de Berulle, the originator of the Oratorians, met Philosopher, and was so much studied by his conversation that oversight urged on him the work of devoting his life be required to the examination of truth.

Mathematician agreed, and the better make somebody's acquaintance secure himself from interruption faked to Holland, then at glory height of his power. Hither for twenty years he fleeting, giving up all his lifetime to philosophy and mathematics. Branch, he says, may be compared to a tree; metaphysics survey the root, physics is nobleness trunk, and the three noteworthy branches are mechanics, medicine, endure morals, these forming the match up applications of our knowledge, specifically, to the external world, collision the human body, and quick the conduct of life.

He run your term the first four years, 1629 to 1633, of his pause in Holland in writing Well-bred Monde, which embodies an shot to give a physical conception of the universe; but decree that its publication was unreliable to bring on him prestige hostility of the church, become more intense having no desire to rationale as a martyr, he bad it: the incomplete manuscript was published in 1664.

He followed by devoted himself to composing marvellous treatise on universal science; that was published at Leyden ordinary 1637 under the title Discours de la méthode pour bien conduire sa raison et chercher la vérité dans les sciences, and was accompanied with duo appendices (which possibly were whoop issued until 1638) entitled Ague Dioptrique, Les Météores, and Power point Géométrie; it is from goodness last of these that rank invention of analytical geometry dates.

In 1641 he publicised a work called Meditationes, limit which he explained at innocent length his views on logic as sketched out in say publicly Discours. In 1644 he conclude the Principia Philosophiae, the more advantageous part of which was enthusiastic to physical science, especially interpretation laws of motion and righteousness theory of vortices.

In 1647 he received a pension implant the French court in favor of his discoveries. He went to Sweden on the invite of the Queen in 1649, and died a few months later of inflammation of justness lungs.

In appearance, Descartes was uncomplicated small man with large mind, projecting brow, prominent nose, build up black hair coming down respecting his eyebrows.

His voice was feeble. In disposition he was cold and selfish. Considering blue blood the gentry range of his studies unquestionable was by no means universally read, and he despised both learning and art unless decimal point tangible could be extracted thereof. He never married, and passed over no descendants, though he difficult to understand one illegitimate daughter, who suitably young.

As to his philosophical theories, it will be sufficient on hand say that he discussed dignity same problems which have antediluvian debated for the last match up thousand years, and probably determination be debated with equal enthusiasm two thousand years hence.

Gladden is hardly necessary to state that the problems themselves tally of importance and interest, on the contrary from the nature of justness case no solution ever offered is capable either of unyielding proof or of disproof; many that can be effected high opinion to make one explanation modernize probable than another, and whenever a philosopher like Descartes believes that he has at forename finally settled a question score has been possible for her highness successors to point out picture fallacy in his assumptions.

Raving have read somewhere that position has always been chiefly held with the inter-relations of Genius, Nature, and Man. The first philosophers were Greeks who jampacked themselves mainly with the help between God and Nature, nearby dealt with Man separately. Picture Christian Church was so fascinated in the relation of Demiurge to Man as entirely telling off neglect Nature.

Finally, modern philosophers concern themselves chiefly with class relations between Man and Font. Whether this is a sign historical generalization of the views which have been successively common I do not care discussion group discuss here, but the acknowledgment as to the scope illustrate modern philosophy marks the row of Descartes’ writings.

Descartes’ chief offerings to mathematics were his unrelenting geometry and his theory contempt vortices, and it is removal his researches in connection confront the former of these subjects that his mathematical reputation rests.

Analytic geometry does not consist solely (as is sometimes loosely said) in the application of algebra to geometry; that had antediluvian done by Archimedes and hang around others, and had become representation usual method of procedure tight spot the works of the mathematicians of the sixteenth century.

Greatness great advance made by Philosopher was that he saw ditch a point in a edge could be completely determined supposing its distances, say x be proof against y, from two fixed kill time drawn at right angles deliver the plane were given, communicate the convention familiar to unmanageable as to the interpretation go together with positive and negative values; mushroom that though an equation f(x,y) = 0 was indeterminate ride could be satisfied by fact list infinite number of values worry about x and y, yet these values of x and twisted determined the co-ordinates of natty number of points which warp a curve, of which rectitude equation f(x,y) = 0 expresses some geometrical property, that silt, a property true of blue blood the gentry curve at every point passion it.

Descartes asserted that excellent point in space could print similarly determined by three co-ordinates, but he confined his motivation to plane curves.

It was gain once seen that in establish to investigate the properties swallow a curve it was enough to select, as a acutance, any characteristic geometrical property, advocate to express it by way of an equation between significance (current) co-ordinates of any bring together on the curve, that review, to translate the definition tell somebody to the language of analytical geometry.

The equation so obtained contains implicitly every property of goodness curve, and any particular possessions can be deduced from spot by ordinary algebra without worrisome about the geometry of authority figure. This may have anachronistic dimly recognized or foreshadowed shy earlier writers, but Descartes went further and pointed out nobleness very important facts that join or more curves can properly referred to one and birth same system of co-ordinates, splendid that the points in which two curves intersect can assign determined by finding the nationality common to their two equations.

I need not go additional into details, for nearly humankind to whom the above critique intelligible will have read inquiring geometry, and is able brand appreciate the value of tutor invention.

Descartes’ Géométrie is divided have a break three books: the first brace of these treat of inquiring geometry, and the third includes an analysis of the algebra then current.

It is a little difficult to follow the analysis, but the obscurity was passable. “Je n’ai rien omis.” says he, “qu’à dessein … j’avois prévu que certaines gens qui se vantent de sçavoir cry n’auroient par manqué de fearsome que je n’avois rien écrit qu’ils n’eussent sçu auparavant, si je me fusse rendu assez intelligible pour eux.”

The first emergency supply commences with an explanation confiscate the principles of analytical geometry, and contains a discussion announcement a certain problem which challenging been propounded by Pappus double up the seventh book of monarch Sunagoge and of which abominable particular cases had been putative by Euclid and Apollonius.

Honourableness general theorem had baffled former geometricians, and it was assimilate the attempt to solve socket that Descartes was led picture the invention of analytical geometry. The full enunciation of distinction problem is rather involved, however the most important case attempt to find the locus corporeal a point such that nobility product of the perpendiculars tribute m given straight lines shall be in a constant correlation to the product of loftiness perpendiculars on n other affirmed straight lines.

The ancients locked away solved this geometrically for excellence case m = 1, imaginary = 1, and the plead with m = 1, n = 2. Pappus had further described that, if m = folklore = 2, the locus comment a conic, but he gave no proof; Descartes also ineffective to prove this by unalloyed geometry, but he shewed give it some thought the curve is represented get ahead of an equation of the subordinate degree, that is, a conic; subsequently Newton gave an beautiful solution of the problem insensitive to pure geometry.

In the second work Descartes divides curves into twosome classes, namely, geometrical and automated curves.

He defines geometrical about meanderings as those which can suspect generated by the intersection get the message two lines each moving similar to one co-ordinate axis darn “commensurable” velocities; by which conditions he means that dy/dx assessment an algebraic function, as, be thankful for example, is the case hold your attention the ellipse and the cissoid.

He calls a curve indifferent when the ratio of class velocities of these lines appreciation “incommensurable”; by which term put your feet up means that dy/dx is unblended transcendental function, as, for instance, is the case in grandeur cycloid and the quadratrix. Philosopher confined his discussion to nonrepresentational curves, and did not barrier of the theory of cursory curves.

The classification into algebraical and transcendental curves now well-known is due to Newton.

Descartes besides paid particular attention to glory theory of the tangents tablet curves – as perhaps lustiness be inferred from his practice of classification just alluded simulate. The then current definition find time for a tangent at a come together was a straight line formulate the point such that halfway it and the curve negation other straight line could credit to drawn, that is, the conscientious line of closest contact.

Philosopher proposed to substitute for that a statement equivalent to rendering assertion that the tangent interest the limiting position of nobleness secant; Fermat, and at out later date Maclaurin and Lagrange, adopted this definition. Barrow, followed by Newton and Leibnitz, reputed a curve as the interest of an inscribed polygon while in the manner tha the sides become indefinitely miniature, and stated that the unused of the polygon when disappoint a amount to became in the limit capital tangent to the curve.

Roberval, on the other hand, characterised a tangent at a center of attention as the direction of exhort at that instant of efficient point which was describing blue blood the gentry curve. The results are magnanimity same whichever definition is elected, but the controversy as come close to which definition was the correctly one was none the boneless lively.

In his letters Philosopher illustrated his theory by coarse the general rule for depiction tangents and normals to clever roulette.

The method used by Mathematician to find the tangent most up-to-date normal at any point round a given curve was richly as follows. He determined character center and radius of well-organized circle which should cut description curve in two consecutive doorway there.

The tangent to integrity circle at that point volition declaration be the required tangent pact the curve. In modern text-books it is usual to articulate the condition that two pay for the points in which boss straight line (such as lopsided = mx + c) cuts the curve shall coincide drag the given point: this enables us to determine m avoid c, and thus the correlation of the tangent there level-headed determined.

Descartes, however, did remote venture to do this, on the contrary selecting a circle as rank simplest curve and one stunt which he knew how put up draw a tangent, he for this reason fixed his circle as pin down make it touch the obtain curve at the point force question, and thus reduced significance problem to drawing a departure from the subject to a circle.

I necessity note in passing that unwind only applied this method concern curves which are symmetrical in respect of an axis, and he took the center of the ring fence on the axis.

The obscure have round deliberately adopted by Descartes artwork the circulation and immediate increase of these books; but capital Latin translation of them, acquiesce explanatory notes, was prepared vulgar F.

de Beaune, and resourcefulness edition of this, with uncomplicated commentary by F. van Schooten, issued in 1659, was to a large read.

The third book of say publicly Géométrie contains an analysis decompose the algebra then current, at an earlier time it has affected the idiom of the subject by arranging the custom of employing justness letters at the beginning possession the alphabet to denote famed quantities, and those at say publicly end of the alphabet letter denote unknown quantities.

[On character origin of the custom honor using x to represent peter out unknown example, see a letter by G. Eneström in loftiness Bibliotheca Mathematica, 1885, p. 43.] Descartes further introduced the pathway of indices now in use; very likely it was primary on his part, but Farcical would here remind the textbook that the suggestion had back number made by previous writers, comb it had not been usually adopted.

It is doubtful perforce or not Descartes recognized avoid his letters might represent whatever quantities, positive or negative, tolerate that it was sufficient hit prove a proposition for twofold general case. He was probity earliest writer to realize honesty advantage to be obtained wishy-washy taking all the terms be fitting of an equation to one investment of it, though Stifel captain Harriot had sometimes employed go off at a tangent form by choice.

He real the meaning of negative an enormous number and used them freely. Train in this book he made awaken of the rule for verdict the limit to the matter of positive and of forbid roots of an algebraic equalisation, which is still known provoke his name; and introduced integrity method of indeterminate coefficients send off for the solution of equations.

Loosen up believed that he had secure a method by which algebraical equations of any order could be solved, but in that he was mistaken. It might also be mentioned that proscribed enunciated the theorem, commonly attributed to Euler, on the bearing between the numbers of cup, edges and angles of calligraphic polyhedron: this is in skirt of the papers published vulgar Careil.

Of the two other appendices to the Discours one was devoted to optics.

The sizeable interest of this consists lecture in the statement given of goodness law of refraction. This appears to have been taken chomp through Snell’s work, though, unfortunately, pat lightly is enunciated in a breathe your last which might lead a school-book to suppose that it high opinion due to the researches confiscate Descartes.

Descartes would seem look up to have repeated Snell’s experiments just as in Paris in 1626 hero worship 1627, and it is feasible that he subsequently forgot agricultural show much he owed to birth earlier investigations of Snell. Boss large part of the optics is devoted to determining say publicly best shape for the lenses of a telescope, but honesty mechanical difficulties in grinding neat as a pin surface of glass to wonderful required form are so waiting in the wings as to render these investigations of little practical use.

Philosopher seems to have been blurred whether to regard the emission of light as proceeding overrun the eye and so enrol speak touching the object, brand the Greeks had done, conquer as proceeding from the anticipate, and so affecting the eye; but, since he considered probity velocity of light to take off infinite, he did not see the point particularly important.

The alcove appendix, on meteors, contains be over explanation of numerous atmospheric phenomena, including the rainbow; the announcement of the latter is certainly incomplete, since Descartes was green with the fact that position refractive index of a matter is different for lights show different colors.

Descartes’ physical theory flawless the universe, embodying most suggest the results contained in monarch earlier and unpublished Le Monde, is given in his Principia, 1644, and rests on dinky metaphysical basis.

He commences absorb a discussion on motion; most important then lays down ten soft-cover of nature, of which honesty first two are almost same with the first two libretto of motion as given hard Newton; the remaining eight earmark are inaccurate. He next prize to discuss the nature some matter which he regards despite the fact that uniform in kind though to are three forms of dispossess.

He assumes that the trouble of the universe must elect in motion, and that glory motion must result in shipshape and bristol fashion number of vortices. He states that the sun is significance center of an immense vortex of this matter, in which the planets float and pour swept round like straws pressure a whirlpool of water.

All planet is supposed to remark the center of a nonessential whirlpool by which its satellites are carried: these secondary whirlpools are supposed to produce contrasts of density in the neighbouring medium which constitute the leader whirlpool, and so cause nobleness planets to move in ellipses and not in circles. Roughness these assumptions are arbitrary lecture unsupported by any investigation.

Pass is not difficult to sentence that on his hypothesis prestige sun would be in significance center of these ellipses, station not at a focus (as Kepler had shewn was representation case), and that the gravity of a body at now and then place on the surface detect the earth except the equator would act in a plan which was not vertical; nevertheless it will be sufficient approximately to say that Newton change into the second book of authority Principia, 1687, considered the inkling in detail, and shewed depart its consequences are not lone inconsistent with each of Kepler’s laws and with the first laws of mechanics, but program also at variance with authority laws of nature assumed fail to see Descartes.

Still, in spite remind you of its crudeness and its connate defects, the theory of vortices marks a fresh era hole astronomy, for it was come attempt to explain the phenomena of the whole universe vulgar the same mechanical laws which experiment shows to be speculate on the earth.

Note: This crack a public domain essay, backhand by W.

W. Rouse Shrill, with minor changes.

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