An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 37
A B C This relation may also be written in the forms: {APQ).BG^{BPq).AG + {CPQ).BA (2), {APQ).BC = (BPQ).AG-{GPQ).AB (3). 36. Ex. 1. If A, B, C he any three points on a straight line, x any otherstraight line, and 0 any given point; show that {OBC).Ax+{OCA).Bx+{OAB). Cx=0. Ex. 2. If ABCD be a… … Let the diagonals meet in G. Then Q is the middle point of BD. Hence,by § 35 (2), we have 2 (PAQ)={()AB)-^{OAD). But since AC=iAG, {OACr)=2{0AG). Ex. 3. Prove the following construction for finding the sum of anynumber of triangular areas {POA}, {FOB), {POO), &c. From A drawAB equal and…
Geometry
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