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The first six books of the elements of Euclid : with a commentary and geometrical exercises ; to which are annexed a treatise on solid geometry, and short essays on ancient geometrical analysis, and the theory of transversals (1861)

Lardner, Dionysius, 1793-1859 · London : Print. for Taylor and Walton · leaf 335

An illustration from The first six books of the elements of Euclid : with a commentary and geometrical exercises ; to which are annexed a treatise on solid geometry, and short essays on ancient geometrical analysis, and the theory of transversals, 1861, leaf 335
oved of the other lines of the figure. Theorem. (25) If two points C and F be given in position, and an indefinite rightline M N parallel to CF being drawn, a series of points P, P, P, fyc.be assumed upon it at equal distances, and right lines diverging from Fpass through these points P, P, P, fyc,… … APPENDIX III. 329 Draw any transversal C A. Then Co .. Co .. Co .. Co . . &c.From o draw a m parallel to F C or M N, and from n draw n pparallel toFm. Because F C and a m are parallel, we have F C : a m = F a : a m.But since P P = P P, and a m is parallel to PP, a n=n m,and since np is parallel…

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