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Traité Analytique des Sections Coniques et de leur Usage pour la Resolution des Equations dans les Problêmes tant déterminez qu'indéterminez. Ouvrage Posthume.


Paris, Jean Boudot et Jean Boudet fils, 1707. 4to. Contemporary full calf. A bit of cracking to front hinges, so that cords are seen, but cover not loosening. Spine with 6 raised bands, richly gilt compartments. Wear to top of spine. Two small old paperlabels, one to upper compartment, one to frontcover. Covers slightly rubbed. (4),459,(5) pp. Large woodcut vignette on titlepage, 2 other vignettes, one engraved , one in woodcut. 32 folded engraved plates and one smaller folded plate (Fig. A). An old owners stamp on flyleaf. Internally clean and fine. A few tiny brownspots. Wide-margined and printed on good paper. ¶ Scarce first edition of l'Hôspital's second book - his second successfull textbook - the manuscript of which was left completed at his death in 1704. His first book "Analyse des infiniment petits pour l’intelligence des lignes courbes", 1696 was the first textbook of the differential calculus, and his name lives on in the name of the rule for finding the limiting value of a fraction whose numerator and denominator tend to zero. His mathyematical teacher was Jean Bernoulli.

The year in which Newton published the anti-Cartesian "Arithmeticus" there appeared in France a conspicuously successfull textbook on Cartesian geometry along the lines of that of Guisnée. This was the "Traité Analytique des Sections Coniques".... a book which contains less original material than that of Guisnée, but which is more extensive and closer to the modern manner of treatment. The work had been intended for publication at the time the authors famous calculus textbook appeared in 1696, but l'Hospital's illness apparently led to delay and it appeared posthumously in 1707. It is Cartesian in emphasis and although it consists of but one volume, follows generally the tripartite plan of Lahire and Ozanam: first an algebraic quasi-analytic treatment of the Conic Sections along the lines of Apollonian theory; then an analytic study of the loci, and finally a long section on the customary construction by conics of the roots of cubic and quartic polynominal equations... LHospital sometimes used two axes and seems to have recognized the interchangeability of these, but he betrays some hesitation... In general, L'Hospital (like Descartes) was more interested in analytic geometry as a measure of ecpressing loci algebraivcally than as a method of deriving the properties of a curve from its equation." (Carl B. Boyer "History of Analytic geometry", pp. 150-154.

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