An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 112
,we have by § 56, Ex. 4, MX. MX : iVX.Ji/X = MA^ : NA^.In the same way we may show that Xr. iW : L7.LY = Nm : LB^;and LZ. LZ : MZ. MZ = LC^: MC\ A TETRAGRAM. 95 But since ABC is a transversal of the triangle LM\, we have by § 104,MA NB LC_ Hence NA ■LB ■ MC MX.NY.LZ MX. NY. LZNX.LY.MZNX.LY. MZ , =… … yz Y X Therefore by § 105, since the points X, Y, Z are collinear, so also arethe points J, Y\ Z. If we take the line at infinity instead of the line XYZ, the points X, Y,Z become respectively the middle points of AAI, BB, CC and thus we havethe theorem of § 151. 154. The lines connecting any point…
Geometry
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