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 . bythe sides of that tchich has the greater base, shall begreater than the angle contained by the sides equal tot/iem, of the other. Let ABC, DEF be two trianrjles, which have the twosides AB, AC equal to tlie two sides DE, DF, each toeach, namely, AB to DE, and AC to DF, but the baseBC greater than the base EF\ the angle BAC shallbe greater thau the angleEDF. For if not, the angle-B^ Cmust be either equalto the angle EDF or lesst
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 . bythe sides of that tchich has the greater base, shall begreater than the angle contained by the sides equal tot/iem, of the other. Let ABC, DEF be two trianrjles, which have the twosides AB, AC equal to tlie two sides DE, DF, each toeach, namely, AB to DE, and AC to DF, but the baseBC greater than the base EF\ the angle BAC shallbe greater thau the angleEDF. For if not, the angle-B^ Cmust be either equalto the angle EDF or lessthan the angle the angle BA C is notequal to the angle EDF,for then the base BC would be equal to the base EF; [I. 4. but it is not; {Hypothesis. therefore the angle BAC is not equal to the angle is the angle BAC less than the angle EDF,for then the base BC would be less thau the base EF; [I. it is not; [Hypothesis. therefore the angle BAC is not less thau the angle it has been shewn that the angle BAC is not equalto the angle the angle ^^Cis greater than the angle EDF. Wherefore, if tico triangles &c. PROPOSITIOX 26. THEOREM. If two triangles have two angles of the one equal to twoangles of the other, each to each, and one side equal toone side, namely, either the sides adjacent to the equalangles, or sides which are opx)osite to equal angles in each,then shall the other sides be equal, each to each, and alsothe third angle of the one equal to the third angle of theother. Let ABC, DEF be two triangles, which have theangles ABC, BCA equal to the angles DEF, EFD, each BOOK L 26. 29
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