Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/200

134

To place the three angles of a triangle both in kind and magnitude, in repect of as many right line given by poition, provided they are not all parallel among themelves, in uch manner that the everal angles may touch the everal lines. (Pl. 12. Fig. 2.)

Three indefinite right lines AB, AC, BC, are given by poition, and it is required o 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, decribe three egments of circles DRE, DGF, EMF, capable of angles equal to the angles BAC, ABC, AVB repectively. But thoe egments are to decribed towards uch ides of the lines DE, DF, EF, that the letters DRED may turn round about in the ame order with the letters BACB; and the letters DGFD in the ame order with the letter ABCBA; and the letters EMFE in the ame order with the letters ACBA; then completing thoe egments into entire circles, let the two former circles cut one the other in G, and uppose 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 decribe a circle that may cut the firt circle DGE in a. Join aD cutting the econd circle DFG in b, as