An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 292
e. Then, since the anglesPAO, PBO are respectively complementary to half the anglesAOP, BOP, the angle AOE is equal to half the angle AOB, andis therefore equal to the angle APB.Hence we have, P {AB, CD] = 0 {AB, CD]. Hence, since the cross ratio of the pencil P {AB, CD] is constant for all… … 18—2 276 pascals theorem. the points of intersection of the pairs of lines AB, DE; BC, EF; CD, FA ;are collinear. (Pascals theorem. Cf. § 181.) Let AB, DE intersect in X; BC, EF in V; and CD, FA in 2. Then the pencils Z {FY, CE], C {FB, DE} are equicross becausethey have the common transversal EF;…
Geometry
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