The elements of Euclid for the use of schools and colleges : comprising the first two books and portions of the eleventh and twelfth books; with notes and exercises . sides of the one equal to two sides ofth. other, each to each, and the angles opposite to a pair of equalsid^,s equal; then if the angles opposite to the other pair of equalaides be both acute, or bo&i obtuse, or if one of them be a righiangle, the two triangles are equal in aU respects. Let A EC and DEF betwo triangles; let AB beequal to DE, and 5C equalto EF, and the angle Aequal to the angle D. First, suppose the anglesC and F
The elements of Euclid for the use of schools and colleges : comprising the first two books and portions of the eleventh and twelfth books; with notes and exercises . sides of the one equal to two sides ofth. other, each to each, and the angles opposite to a pair of equalsid^,s equal; then if the angles opposite to the other pair of equalaides be both acute, or bo&i obtuse, or if one of them be a righiangle, the two triangles are equal in aU respects. Let A EC and DEF betwo triangles; let AB beequal to DE, and 5C equalto EF, and the angle Aequal to the angle D. First, suppose the anglesC and F acute angles. If the angle B be equal to the angle E, the triangles A EC,DEF are equal in all respects, by I. 4. If the angle B be n(»tequal to the angle E, one of them must be greater than theother; suppose the angle B greater than the angle E, and makethe angle ABG equal to the angle E. Then the triangles A EG,DEF are equal in all respects, by I. 16, therefore BG is equalto EF, and the angle EGA is equal to the angle EFD. But theangle EFD is acute, by hypothesis ; therefore the angle BGA isfcoute. Therefore the angle BGC is obtuse, by I. 13. But it baa. 262 NOTES OM
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Keywords: ., bookcentury1800, booksubjectgeometry, booksubjectmathematicsgree
