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 . to the triangle DBC. Wherefore, triangles &c. PEOPOSITIOX 38. THEOREM. Triangles on equal bases, and letween the same par-allels, are equal to one another. Let the triangles ABC, DEF he on equal bases BC^EF, ai. i^etween the same parallels i?i^, AD : the triangleABC shall be equal to the triangle DEF. Produce ^2) both ways to the points ^ ^ 2) H G,H; through B draw BGparallel to CA, andthrough F draw FHparallelto^i>. [1
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 . to the triangle DBC. Wherefore, triangles &c. PEOPOSITIOX 38. THEOREM. Triangles on equal bases, and letween the same par-allels, are equal to one another. Let the triangles ABC, DEF he on equal bases BC^EF, ai. i^etween the same parallels i?i^, AD : the triangleABC shall be equal to the triangle DEF. Produce ^2) both ways to the points ^ ^ 2) H G,H; through B draw BGparallel to CA, andthrough F draw FHparallelto^i>. [ Then each of thefigures GBCA, DEFH is a parallelogram. [Definition. And they are equal to one another because they are onequal bases BC, EF, and between the same parallelsBF, GH. [I. 36. And the triangle ABC is half of the parallelogram GBCA,because the diameter ^^ bisects the parallelogram ; [I. the triangle DEF is half of the parallelogram DEFH^because the diameter DF bisects the the halves of equal things are equal. [Axiom 7. Therefore the triangle ABC i& equal to the triangle DEF. Wherefore, triangles &c.
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