SCHOOTEN, Frans van.

De Organica Conicarum Sectionum in Plano Descriptione, Tractatus. Geometris, Opticis; Praesertim verò Gnomonicis & Mechanicis Utilis. Cui subnexa est Appendix, de cubicarum Aequationum resolutione.

Leiden: Elzevir, 1646. First edition.

A very fine copy of this beautiful book concerned with the so-called organic description (or generation) of curves. This was an important topic, since in order to determine the point of intersection of curves in the construction of geometrical solutions, it was natural to think of the curves as generated by a continuous motion driven by some instrument. It is the continuity of the motion generating the curves that guarantees a point of intersection can be located exactly. Descartes had devised several mechanisms for generating curves. In De Organica, which Newton read, van Schooten had presented several mechanisms for generating conic sections. This research field was connected with practical applications, for instance, lens grinding and sundial design, but it was also sanctioned by classical tradition and motivated the highly abstract needs underlined by Descartes. Newton was able to devise a mechanism for generating conics and to extend it to higher-order curves. In this work Schooten gave the now standard method of drawing an ellipse with the piece of string whose ends are attached to two pegs, and it is the first printed work that contains a mechanical description of the ellipsis, parabola and hyperbola without considering them as conics. The book is among the 24 highlights of the Elsevier Heritage Collection.*Honeyman 2807; Macclesfield 873; Willems 607.

Small 4to. Contemporary vellum, pp [16] 117 [3:blank]. Fine and clean, entirely unrestored.