Page:Philosophical Transactions - Volume 003.djvu/116

 for that which cannot be found. He delivers also a method of drawing Touch-lines to all the Conick Sections, and divers other Curves, concerning which, the Author speaking of Apollonius saith,

Si quis ipsius Constuctionem, atque demonstrationem 34. prop. 1, lib. Conicorum cum nostris ''comparabit, nonnihil fortaffe proficiet in Arte diletandi Propostiones & Demonstrationes. Nam quod Ille de Quadratica tantum Hyperbole, Ellipsi, & Circulo starnit, Nos ad omns porrigimus Hyperbolas, Ellipses Circulosque Infinitos: And p. 12 the like for infinite Parabolas: And these are some of those matters handled by the Author, which p. 7, he affirms to be of excellent use, Ad inveniendas plurium linearum Tangentes, figurarum Centra gravitatis & Quadraturas: Herein, agreeing with des Cartes in his Geometry, p.'' 40. where speaking of the same matter, he saith; Nec verebor dicere, Problema hoc non eorum modo, quæscio, utilissimum & generalissimum esse, sed etiam corum, quæ in Geometria scire unquam desider averim.

This excellent Author promiseth some other Treatises in his Preface to an Abbot, where he saith;

Si hoc affequar, ut tibit cætrisque amicis, earundem disciplinarum intelligentibus, probetur, minus erit imposterum, quam ob rem humanissimis tuis hortationibus oblucter, cum Author mihi esse perseverabis edendi alia, quæ tecum jampridem communicavi, de Præceptis universæ Artis Analyticæ Geometrica methodo breviter & expedite demonstratis, una cum Animadversione Erratorum, quæ in ipsis tradendis magni nominis Authores errasse deprehendi; faciliusque obtinebis, ne diatius premam apud me, quæcunque da Geometria disputata, & literis consignata, in certa redegi Propositiones, & ex his illam præcipue a Torricellio & a Te quoq; tantopere comemendatam, quæ integram doctrinam 30. Propositionum Archimedis, Lucæ Valerii, & aliorum, una complectitur. Besides, he promiseth (which matter yet hath already been well handled by La Lovera in his Elementa Tetragonismica, Tolosæ, A, 1551. and by Hugenius in the same year in a small Tract, intitul'd Theoremata de Quadratura Hyperbaoes, Ellipsis, & Circuli, ex dato portionum gravitatis centro;) duas alias, quibus totam pené J., Caroli dela Faille, de Centro gravitatis partium Circuli & Ellipseos doctrinam (justo vol. ab ipso explicatam) absolvo.

But then, p. 7. he promiseth Justum opus, ibi dubimus novam  Rh