Selected propositions in geometrical constructions and applications of algebra to geometry. Being a key to the appendix of Davies' Legendre (1875)
Legendre, A. M. (Adrien Marie), 1752-1833, Davies, Charles, 1798-1876 · New York, Chicago [etc.] A.S. Barnes & company · leaf 75
68 KEY. clearing of fractions and transposing, we have2x2 + 2y2 -z2 = 4a2 •■ • • (1) 2x2 +■ 2z2 - y< 4b2 • • (2) 2y2 + 2z2 -x2 -4c2 . • . (3);subtracting equation (2) from (1), we have multiplying equation (3) by 2, and adding to (2) 3y2 + 6z2 - 8c2 + 462 •subtracting equation (4) from (5), 9z2… … z = ± f y/2b2 + 2c2 - -a2 X z= ±jv^ + 262 - -c2 y = ± J v/2a^ + 2c2 — 62. Obr. Through G and E, the middle points of AC and BC, drawGE; then will GE be parallel to the base AB (Bk. IV^. Prop. 16) :and since AC is equal to twice CG, AD will be equal to twice GP,or its equal PE. But the triangles AOD…
Geometry
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