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2019-11-05 13:23:06
VERY OLD- RARE CARNOT'S GEOMETRY / MATHEMATICS- 1803
Géométrie (Geometrie) De Position. By Carnot, L. N. M. , 1803, J. B. M. Duprat, first edition, Small quarto hardcover, xxxviii, 2, 489, (15 plates) leather spine over marbeled boards: tight binding, clean and unfoxed pages (high rag content) , the covers have a modicum of shelfwear, faint cracking of gutters, else VG-. A handsome copy. All 15 folding plates are present and in excellent condition. Text in French. "This work deals with projective rather than descriptive geometry. According to Laptev & Rozenfel'd (1996) , Carnot is responsible for initiating the use of cross-ratios: ..first to introduce the cross (anharmonic) ratio of four points of a line taking account of its sign, thereby sharpening Pappus' concept. He then proved that this ratio is invariant for the four points obtained by cutting four lines of a pencil of lines with different secants. In this way he established the harmonic properties of the complete quadrilateral. " He also wrote on the metaphysics of infinite calcalus and on fortified defenses.
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