Elements of geometry / from the Latin translation of Commandine. To which is added, a treatise of the nature of arithmetic of logarithms, likewise another of the elements of plain and spherical trigonometry; with a preface ... By Doctor John Keil ... The whole revised ... [with a] preface, by Samuel Cunn.

  • Euclid
Date:
1741
Catalogue details

Licence: Public Domain Mark

Credit: Elements of geometry / from the Latin translation of Commandine. To which is added, a treatise of the nature of arithmetic of logarithms, likewise another of the elements of plain and spherical trigonometry; with a preface ... By Doctor John Keil ... The whole revised ... [with a] preface, by Samuel Cunn. Source: Wellcome Collection.

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    The 7th, 8th, and 9th Booh treat of fuch Properties of Numbers which are neceflary for the Demonftrations of the 10th, which treats of Incommenfurables ; and the' 13th, 14th, and 15th, of the five Platonic Bodies» But though the Doftrine of Incommenfura¬ bles, becaufe expounded in one and the fame Plane, as the firft fix Elements were, claimed by a Right of Order, to be handled before Planes interfered by Planes, or the more com¬ pounded Do&rine of Solids; and the Proper¬ ties of Numbers were neceflary to the Regi- foning about Incommenfurables: Yet becaufe only one Propofition of thefe four Books, viz. the 1 ft of the 10th, is quoted in the 1 ith and 12th Books; and that only once, viz. in the Demonftration of the 2d of the 12th; and that * ft Propofition of the 10th, is fupplied by a Lemma in the 12th: And becaufe the 7th, 8th, 9th, 10th, 13th, 14th, 15th Books have not been thought (by our greateft Matters) necef- fary to be read by fuch as defign to make na¬ tural Philofophy their Study, or by fuch. as would apply Geometry to practical Affairs, Dr. Keil, in his Edition, gave us only thefe eight Books, viz. the firft fix, and the nth and |2th. And as he found there was wanting a Trea- tife of thefe Parts of the Elements, as they were written by Euclid himfelf; he publifhed his Edition without omitting any of Euclid's Demonftrations, except two ^ one of which was a fecond Demonftration of the 9th Propor fition of the third Book; and the other a Demon¬ ftration of that Property of Proportionals cal¬ led Cohverfm (contained in a Corollary to the