BOOK III.] OF NATURAL PHILOSOPHY. 467 — CK = 2b, CK — DL = 36, DL + EM = 46, — EM + FN = 56, &c. ; then 6 — 2b == c, &c., and so on to the last difference, which is here /*. Then, erecting any perpendicular RS, which may be considered as an ordinate of the curve required, in order to find the length of this ordinatc, suppose the intervals HI. IK, KL, LM, (fee., to be units, and let AH = a. -KS=f>, \p into — IS = q, ±q into + SK = r, \r into + SL = s, \s into 4- SM = t ; proceeding, to wit, to ME, the last perpendicular but one, and prefixing negative signs before the terms HS, IS, &c., which lie from S towards A; and affirmative signs before the terms SK, SL, (fee.. which lie on the other side of the point S ; and, observing well the signs, RS will be = a + bp + cq + dr + es + ft, + (fee. CASE 2. But if HI, IK, (fee., the intervals of the points H, I, K, L,