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.

    25/465 (page 5)
    PROPOSITION I. 4 Problem. *Tq defcribe an Equilateral Lriangle upon a given finite Right Line. IET AB be the given finite Right Line, upon which it is required to defcribe an a Equilateral Triangle. About the Centre A, with the Diftance A B, defcribe the Circle B C D * • and about the * 3 Pojh Centre B, with the fame Diftance BA, defcribe the Circle ACE; and from the Point C, where the two Circles cut each other, draw the Right Lines CA, CB+. + ,jy. Then becaufe A is the Centre of the Circle DBC, AC ihall be equal to AB$. And becaufe B is the J 15 Def, Centre of the Circle C A E, B C ihall be equal to B A: but C A hath been proved to be equal to AB; there¬ fore both CA and CB are each equal to AB. But Things equal to one and the fame Thing, are equal between themfelves, and confequently CA is equal toCB- therefore the three Sides C A, A B, B C, are equal between themfelves. And fo the Triangle BAC is an Equilateral one, and is defcribed upon the given finite Right Line A B; which was to be done. PROPOSITION II. Problem. -At a given Pointy to put a Right Line equal to a Right Line given. T ET the Point given be A, and the given Right Line BC; it is required to put a Right Line at the Point A? equal to the given Right Line B C.