Cyclomathesis : or, An easy introduction to the several branches of the mathematics; being principally designed for the instruction of young students, before they enter upon the more abtruse and difficult parts thereof . and h. Then (becaufe in the point B,OB zz OD,)mn (or Bn — Bm) rz fr. Alfp #> (or ^ — eq) :^ (or D^ — Db) : : O* : *D : : AB : AD : : fr or»/.» : bg. Therefore qp zz mr?, therefore pn, qm(which are the projected lines of gr, bf,) are parallel, [ Principle j>/. thePRINCIPIA. 15 [ib. we fhall have the folution required] For the bgi fuppofed now to be given
Cyclomathesis : or, An easy introduction to the several branches of the mathematics; being principally designed for the instruction of young students, before they enter upon the more abtruse and difficult parts thereof . and h. Then (becaufe in the point B,OB zz OD,)mn (or Bn — Bm) rz fr. Alfp #> (or ^ — eq) :^ (or D^ — Db) : : O* : *D : : AB : AD : : fr or»/.» : bg. Therefore qp zz mr?, therefore pn, qm(which are the projected lines of gr, bf,) are parallel, [ Principle j>/. thePRINCIPIA. 15 [ib. we fhall have the folution required] For the bgi fuppofed now to be given, may be tranf- into the firft figure HGI, by making as Odto dgi To is OD to DG parallel to the radius AO. [ib. For as often as two conic lections] For thefeconic fed ions being transformed into fimpler ones,give the point of inteifection •, and thereby is hadan ordinate drawn from that point of interferonin the transformed curves, correfponding to the in-terferon of the given curves. [Pr. 25.] Let KG, KH be two tangents meet- in K, yx the third tangent meeting ba in y. Letthe lines KH, KG be projected in ki lb ; and yb*yx into kl> ib; then you have the parallelogrambikl •, then proceed according to the propofition. [ib. For by the p-operties of the conic feclions]by cor. 4. Pr. 44. Conies I. [ib. But according as the points] This is plain, f the nature of the ellipfis and hyperbola-, and figure cannot be a parabola, by recyclomathesisore12emer
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