Lemma XXVI.
To place the three angles of a triangle both in kind and magnitude, in reſpect of as many right line given by poſition, provided they are not all parallel among themſelves, in ſuch manner that the ſeveral angles may touch the ſeveral lines. (Pl. 12. Fig. 2.)
Three indefinite right lines AB, AC, BC, are given by poſition, and it is required ſo to place the triangle DEF that its angle D may touch the line AB, its angle E the line AC, and its angle F the line BC. Upon DE, DF and EF, deſcribe three ſegments of circles DRE, DGF, EMF, capable of angles equal to the angles BAC, ABC, AVB reſpectively. But thoſe ſegments are to deſcribed towards ſuch ſides of the lines DE, DF, EF, that the letters DRED may turn round about in the ſame order with the letters BACB; and the letters DGFD in the ſame order with the letter ABCBA; and the letters EMFE in the ſame order with the letters ACBA; then completing thoſe ſegments into entire circles, let the two former circles cut one the other in G, and ſuppose P and Q to be their centres. Then joining GP, PQ take Ga to AB, as GP is to PQ; and about the centre G, with the interval Ga deſcribe a circle that may cut the firſt circle DGE in a. Join aD cutting the ſecond circle DFG in b, as
