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Description: PMM 129 - THE INVENTION OF ANALYTIC GEOMETRY. First edition, a fine, large copy, of Descartes' first and most famous work. Following the Discours, now celebrated as one of the canonical texts of Western philosophy, are three 'Essais', the last of which, La Géométrie, contains the birth of analytical or co-ordinate geometry, "of epoch-making importance" (Cajori, History of Mathematics, p. 174), designated by John Stuart Mill as "the greatest single step ever made in the progress of the exact sciences". It "rendered possible the later achievements of seventeenth-century mathematical physics" (Hall, Nature and nature's laws (1970), p. 91). The first of the Essais, La Dioptrique, contains Descartes' discovery of 'Snell's law' of refraction of light (earlier than Snell); the second, Les Météores, contains Descartes' explanation of the rainbow, based on the optical theories developed in the first Essai. "It is no exaggeration to say that Descartes was the first of modern philosophers and one of the first modern scientists; in both branches of learning his influence has been vast . The revolution he caused can be most easily found in his reassertion of the principle (lost in the middle ages) that knowledge, if it is to have any value, must be intelligence and not erudition. His application of modern algebraic arithmetic to ancient geometry created the analytical geometry which is the basis of the post-Euclidean development of that science. His statement of the elementary laws of matter and movement in the physical universe, the theory of vortices, and many other speculations threw light on every branch of science from optics to biology. Not least may be remarked his discussion of Harvey's discovery of the circulation of blood, the first mention of it by a prominent foreign scholar. All this found its starting point in the 'Discourse on the Method for Proper Reasoning and Investigating Truth in the Sciences'. Descartes's purpose is to find the simple indestructible proposition which gives to the universe and thought their order and system. Three points are made: the truth of thought, when thought is true to itself (thus cogito, ergo, sum), the inevitable elevation of its partial state in our finite consciousness to its full state in the infinite existence of God, and the ultimate reduction of the material universe to extension and local movement" (PMM). Provenance: Lessing J. Rosenwald (small morocco monogram bookplate); given to the Library of Congress (bookplate and duplicate stamp); Richard Green (Christie's NY, 17 June 2008, The Richard Green Library, lot 87, $116,500). In October 1629 Descartes began work on The World, which included not only his Treatise on Light, first published as Le Monde in 1664, and the Treatise on Man, first published two years earlier as Renatus Descartes de Homine, but also the material on the formation of colours in the Meteors and the material on geometrical optics in the Dioptrics, both subsequently published in 1637 along with the Discourse and the Geometry. Descartes sets out the details of the treatise he was working on from mid-1629 to 1633 in part 5 of the Discourse: "I tried to explain the principles in a Treatise which certain considerations prevented me from publishing, and I know of no better way of making them known than to set out here briefly what it contained. I had as my aim to include in it everything that I thought I knew before I wrote it about the nature of material things. But just as painters, not being able to represent all the different sides of a body equally well on a flat canvas, choose one of the main ones and set it facing the light, and shade the others so as to make them stand out only when viewed from the perspective of the chosen side; so too, fearing that I could not put everything I had in mind in my discourse, I undertook to expound fully only what I knew about light. Then, as the opportunity arose, I added something about the Sun and the fixed stars, because almost all of it comes from them; the heavens, because they transmit it; the planets, comets, and the earth, because they reflect light; and especially bodies on the earth, because they are coloured, or transparent, or luminous; and finally about man, because he observes these bodies" (quoted in Gaukroger (ed.), Rene Descartes: The World and Other Writings, p. xi). But The World was never published in Descartes' lifetime. "During the years immediately following the condemnation of Galileo, Descartes held fast to his initial view that the cardinals had made a mistake, though one that was potentially dangerous for himself. His fundamental idea was that the decision involved a misunderstanding of the role of the Bible as a source of scientific knowledge. He also argued that he was not bound to accept the Roman decision as a matter of faith, and he hoped that it would be reversed in due course so that he could publish his World without fear of censure. He had to concede, however, that as long as there was no change of mind about Galileo by the church, the World would remain 'out of season' . In these circumstances, the next-best option was to consider ways in which parts of his work that were not theologically sensitive could be released to the public. Accordingly, during the years from 1633 to 1637, Descartes spent most of his time on this project. His efforts came to fruition with the publication of the Discourse on the Method for Guiding one's Reason and Searching for Truth in the Sciences, together with the Dioptrics, the Meteors, and the Geometry, which are samples of this Method (1637) . [It] omitted what Descartes called the 'foundations of my physics', that is, the controversial view of the universe that included heliocentrism. He offered instead some examples of the results that one could expect from his basic theory when applied to specific areas such as dioptrics. For good measure, he made sure that the book appeared anonymously. "The standard practice among scholars
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