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 . PROPOSITION 24. THEOREM. If two triangles have two sides of the one equal to ticosides of the other, each to each, but the angle contained hythe tico sides of one of them greater than the angle con-tained hy the two sides equal to them, of the other, the baseof that ichich has the greater angle shall he greater thanthe base of the oilier. Let ABC, DEF be two triangles, which have the twosides AB, AC, equal to the two sides DE, DF
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 . PROPOSITION 24. THEOREM. If two triangles have two sides of the one equal to ticosides of the other, each to each, but the angle contained hythe tico sides of one of them greater than the angle con-tained hy the two sides equal to them, of the other, the baseof that ichich has the greater angle shall he greater thanthe base of the oilier. Let ABC, DEF be two triangles, which have the twosides AB, AC, equal to the two sides DE, DF, each toeach, namelv, AB to DE, and AC to DF, but the anglt^^C greater than the angle EDF: the base BC shall be. BOOK I. 24, 25. 27 greater than the baseEF, Of the two sidesDE, DF, let DE bethe side which is notgieater than the the point D inthe straight line DE,make the angle EDGequal to the angleBAG, [I. 23. and make DG equal to ^C or DF, [I. jom EG, GF. Because ^i> is equal to DE, [Hypothesis. and AC to DG ; {Construction. the two sides BA, AC 2ae equal to the two sides ED, DG,each to each ; and the angle BAC is equal to the angle EDG ; [ the base BC is equal to the base EG. [I. 4. And because DG is equal to DF, [Construction. the angle DGF is equal to the angle DFG. [I. 5. But the angle DGF is greater than the angle EGF. [Ax. the angle DFG is greater than the angle more then is the angle EFG greater than the angleEGF. [Axiom 9. And because the angle EFG of the triangle EFG isgreater than its angle EGF. and that the gieater angle issubtended by the greater side, [I. 19. therefore the side EG is gi-eater than the side EF»But EG was shewn
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