Ball, W. W. Rouse (Walter William Rouse), 1850-1925 · London, Macmillan · leaf 72
CH. Ill] GEOMETRICAL RECREATIONS 49 OE perpendicular to AG produced. Draw OF perpendicularto AB produced. Join OB, 00. Following the same argument as before, from the equalityof the triangles A OF and AOE, we obtain AF=AE\ and,from the equality of the triangles BOF and GOE, we obtainFB = EG.… … Thus in all cases, whether or not BO and AO meet, andwhether they meet inside or outside the triangle, we haveAB—AG\ and therefore every triangle is isosceles, a resultwhich is impossible. Fifth Fallacy^, To prove that irj^ is equal to tt/S. On thehypothenuse, BG, of an isosceles right-angled…
Mathematical recreations · Geometry · Astrology · Space and time · Matter · Magic squares
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