variablesDescartes - Descartes' use of z, y, x. The...

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Descartes' use of z, y, x. The following is from Cajori (vol 1, page 381): The use of z, y, x . . . to represent unknowns is due to René Descartes, in his La géometrie (1637). Without comment, he introduces the use of the first letters of the alphabet to signify known quantities and the use of the last letters to signify unknown quantities. His own langauge is: ". ..l'autre, LN, est (1/2) a la moitié de l'autre quantité connue, qui estoit multipliée par z, que ie suppose estre la ligne inconnue." Again: ". ..ie considere . .. Que le segment de la ligne AB, qui est entre les poins A et B, soit nommé x, et quie BC soit nommé y ; . .. la proportion qui est entre les costés AB et BR est aussy donnée, et ie la pose comme de z a b ; de façon qu' AB estant x, RB sera bx / z, et la toute CR sera y = bx / z . . .." Later he says: "et pour ce que CB et BA sont deux quantités indeterminées et inconnuës, ie les nomme, l'une y ; et l'autre x. Mais, affin de trouver le rapport de l'une a l'autre, ie considere aussy les quantités connuës qui determinent la description de cete ligne courbe: comme GA que je nomme a, KL que je nomme b, et NL, parallele a GA, que ie nomme C. " As co-ordinates he uses later only x and y. In equations, in the third book of the Géométrie, x predominates. In manuscripts written in the interval 1629-40, the unknown z occurs only once. In the other places x and y occur. In a paper on Cartesian ovals, prepared before 1629, x alone occurs as unknown, y being used as a parameter. This is the earliest place in which Descartes used one of the last
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This note was uploaded on 02/04/2011 for the course PB HLTH 140 taught by Professor Tarter during the Fall '10 term at University of California, Berkeley.

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variablesDescartes - Descartes' use of z, y, x. The...

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