HIRE, Philippe de la. Sectiones conicae, in novem libros distributae, in quibus quidquid hactenus observatione dignum cum a veteribus, tum a recentioribus Geometris traditum est, novis contractisque demonstrationibus explicatur; multis etiam & exquisitis propositionibus recens inventis illustratur.
Paris: Steph. Michallet, 1685. First edition.

A fine copy of this major work on conic sections. "The method of projection and section was taken up by Philippe de La Hire (1640-1718), who was a painter in his youth and then turned to mathematics and astronomy. Like Pascal, La Hire was influenced by Desargues and did a considerable amount of work on the conic sections. Some of it, in publications of 1673 and 1679, employed the synthetic mannerof the Greeks but with new approaches, such as the focus-distance definition of the ellipse and hyperbola, and some of it used the analytic geometry of Descartes and Fermat. His greatest work, however, is the Sectiones Conicae (1685) and this is devoted to projective geometry. Like Desargues and Pascal, La Hire first proved properties of the circle, chiefly involving harmonic sets, and then carried these properties over to the other conic sections by projection and section. Thus he could carry the properties of the circle over to any type of conic section in one method of proof. Though there were a few omissions, such as Desargues's involution theorem and Pascal's theorem, in this 1685 work of La Hire we find practically all the now familiar properties of conic sections synthetically proved and systematicalyy established. In fact, La Hire proves almost all of Apollonius' 364 theorems on the conics. He also has the harmonic properties of quadrilaterals. In all, La Hire proved about 300 theorems. He tried to show that projective methods were superior to those of Apollonius and the new analytic methods of Descartes and Fermat which had already been created. ... On the whole, La Hire's results do not go beyond Desargues's and Pascal's. However, in pole and polar theory he has one major new result. He proves that if a point traces a straight line, then the polar of the point will rotate around the pole of that straight line." (Kline: Mathematical Thought from Ancient to Modern Times, pp.298-99). Honeyman 1886, Macclesfield 5/1186.

Large folio: 380 x 262 mm. Uncut in eighteenth century boards. (8), 245, 248-249, (1) pp., Qqq paginated 245/247 as the Macclesfield copy.