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directrix. Through E and F draw KEH,FGL parallel to CD, making the parts EHand FG each equal to CB. Bisect CK, CLin N and M, through which points, paral-lel to CD, draw NO, MP, making the for-mer a mean proportional between GV andKH, and the latter a mean proportionalbetween CV and LG : join OP, cutting theaxis CD in Q, and through Q. draw B QSparallel to FE, cutting NO in S, and MPproduced in R, so shall R and S (by ar-ticle 21.) be points in the proposed curve.In the same manner, by bisecting CN andCM, and finding a mean proportional be-tween CV and NO, and another betweenCV and MP, two other points may befound in the catenary. Also by bisectingNK and LM, and finding mean proportion-als between NO, KH and MP, LG, twoother points in the curve may be found, theone between S and E, and the other be-tween R and F. And by continually bi-secting the divisions on LK, and findingmean proportionals as before, as manypoints as we please may be found betweenV and E, or between VF.

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