Geometrical Lectures; Explaining the Generation, Nature, and Properties of Curve Lines

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1735 edition. Excerpt: ... the fourth a -U -- cr n. Which ine quality nevertheless is so much the less as AE (or n) is the greater. c c a -- -- = n. a cc nn a + -- =--. a a. cc n 3 + --=--. a a a c c n* a = _. a ai fig 212. This Series may be explained according to the second Way aforegoing, and that by exhibiting the fame Curves L X L, M XM, N X N of such a Nature, that drawing GK any how perpendicular to AH j GLmay be-- l Lt GM = 3 A G -/' -, and G N = - DEGREES Cub. For if AG q A G H A R be a half right Angle, and G E O be any how drawn perpendicular to A H, and it be made GE: c:: c: E O; and you describe a Hyperbola OO thro' O within the Asymtotes A D, AR; the Intersections of this and the said Curves LXL, MXM, NXN, will determine the respective Roots a. For drawing LG.MG, NG perpendicular to AH; the intercepted Parts AG will be respectively equal to the several a ?. After the like manner may all the subsequent Series be explain'd. But we shall continue on the Business only according to the first Way. Fifth Series. Make the Angle R Al half aright one, Fig 213. and let AD be perpendicular to Al, and make AC =c. Then drawing GZ any how parallel to A D, let A G (or G Z): A C:: AC: ZK, and thro' K'describe an HyperbolaKYK within the AngleDAR. Then let the Curves CL YH x, AM YH DEGREES AN YH V be such, that G L be a Medial, G M a BimeU dial,