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 . in the triangles DBC, ACB,DB is equal to AC, [Construction. and BCis common to both, the two sides DB, BC are equal to the two sides AC, CB^each to each ; and the angle DBC is equal to the angle -4 C^; [ the base DC is equal to the base AB, and thetriangle DBC is equal to the triangle ACB, [I. 4. the less to the greater; which is absurd. [Aodom, 9. Therefore AB is not unequal to AC, that is, it is equal to it.
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 . in the triangles DBC, ACB,DB is equal to AC, [Construction. and BCis common to both, the two sides DB, BC are equal to the two sides AC, CB^each to each ; and the angle DBC is equal to the angle -4 C^; [ the base DC is equal to the base AB, and thetriangle DBC is equal to the triangle ACB, [I. 4. the less to the greater; which is absurd. [Aodom, 9. Therefore AB is not unequal to AC, that is, it is equal to it. Wherefore, if tico angles &c. Corollary. Hence every equiangular triangle is alsoequilateral. PROPOSITION 7. the same hase, and on the same side of it, there can-not he two triangles having theirsides which are terminated at oneextremity of the hase equal to oneanother, and likewise those whichare terminated at the other ex-tremity equal to one another. If it be possible, on the samebase AB, and on the same side ofit, let there be two triangles A CB,ADB, having their sides CA, DA,which are terminated at the extremity A of the base, equal. BOOK I. 7, 8. 13 to one another, and likewise their sides CB^ DB, which areterminated at B equal to one another. Join CD. In the case in whici the vertex of each tri-angle is without the other triangle ; because ACi?> equal to AD, [Hypothesis. the angle ACD is equal to the angle ADC. [I. 5. But the angle ACD is greater than the angle BCD, [Ax. the angle ADC is also greater than the angleBCD, much more then is the angle BDC greater than the angleBCD. Again, because BC is equal to BD, [Hypothesis. the angle BDC is equal to the angle BCD. [1. r>. But it has been shewn to be greater; which is impossible. But if one of the vertices asD, be within the other triangleACS, produce AC, AD to E. F. Then because AC \9, equal to^2>, in the triangle ^r^Z>, [ angles BCD, FDC, on theother side of the base CD,
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Keywords: ., bookcentury1800, booksubjectgeometry, booksubjectmathematicsgree
