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"Geometry is not easy reading. An edition appeared subsequently with notes by his friend De Beaune, which were intended to remove the difficulties."
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La GéométrieDescartes presentation differed from that now current. ...he used only — La Géométrie
"Descartes presentation differed from that now current. ...he used only an x-axis and did not refer to a y-axis. ...He considered only equations in the first quadrant, as it was thence that he translated the geometry into algebra. This... led to inexplicable anomolies in the translation back from algebra to geometry. As analytic geometry evolved and negative numbers were fearlessly used, the restriction was removed. ... The new method was not fully appreciated by Descartes contemporaries, partly because he had deliberately adopted a rather crabbed style. When geometers did see what analytic geometry meant, it developed with great rapidity. But it was only with the development of calculus that analytic geometry came into its own."
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La Géométrie
La Géométrie
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La Géométrie was published in 1637 as an appendix to Discours de la méthode, written by René Descartes. In the Discourse, Descartes presents his method for obtaining clarity on any subject. La Géométrie and two other appendices, also by Descartes, La Dioptrique (Optics) and Les Météores (Meteorology), were published with the Discourse to give examples of the kinds of successes he had achieved foll
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"Thus, all unknown quantities can be expressed in terms if a single quantity, whenever the problem can be constructed by means of circles and straight lines, or by conic sections, or even by some other curve of degree not greater than the third or fourth. But I shall not stop to explain this in more detail, because I should deprive you of the pleasure of mastering it yourself, as well as of the advantage of training your mind by working over it, which is in my opinion the principle benefit to be derived from this science. Because, I find nothing here so difficult that it cannot be worked out by anyone at all familiar with ordinary geometry and with algebra, who will consider carefully all that is set forth in this treatise."
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La GéométrieQuote
"Descartes recognized that the points of intersection of two curves are given by solving their equations simultaneously. The last implies... a major advance over all who had previously used coordinates: Descartes saw that an infinity of distinct curves can be referred to one system of coordinates. In this... he was far ahead of Fermat..."
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La GéométrieQuote
"It is evident from Descartes explanation of his method that he had an intuitive grasp of the elusive concepts of variable and function, both of which are basic in analysis. Moreover, he intuited continuous variation."
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La GéométrieQuote
"The Latin term for "ordinate," used by Descartes comes from the expression lineœ ordinatœ, employed by Roman surveyors for parallel lines. The term abscissa occurs for the first time in a Latin work of 1659, written by ..."
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La GéométrieQuote
"If... we wish to solve any problem, we first suppose the solution already affected, and give names to all the lines that seem needful for its construction,—to those that are unknown as well as to those that are known. Then, making no distinction between the known and unknown lines, we must unravel the difficulty in a way that shows most naturally the relations between these lines, until we find it possible to express a single quantity in two ways. This will constitute an equation, since the terms of one of these two expressions are together equal to the terms of the other."
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La Géométrie