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 . [I. 34. 40 EUCLIDS PROPOSITION 36. THEOREM. Parallelograms on equal bases, and between the sameparallels, are equal to one another. Let ABCD, EFGH be parallelof^rams on equal basesBC, FG, and between the same i)arallel3 AH, EG: t;ieparallelogram ABCD shall be equal to the parallelogramEFGH. Join BE, CH. Then, because BGis equal to FG, [ FG to EH, [ BG is equal to EH; [Axiom 1. B C F G and they are parallel
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 . [I. 34. 40 EUCLIDS PROPOSITION 36. THEOREM. Parallelograms on equal bases, and between the sameparallels, are equal to one another. Let ABCD, EFGH be parallelof^rams on equal basesBC, FG, and between the same i)arallel3 AH, EG: t;ieparallelogram ABCD shall be equal to the parallelogramEFGH. Join BE, CH. Then, because BGis equal to FG, [ FG to EH, [ BG is equal to EH; [Axiom 1. B C F G and they are parallels, [ and joined towards the same parts by the straight linesBE, CH. But straight lines which join the extremities of equal andparallel straight lines towards the same parts are them-selves equal and parallel. [I. BE, CH are both equal and EBCH is a parallelogram. [ it is equal to ABCD, because they are on the samebase BC, and between the same parallels [I. 35. For the same reason the parallelogram EFGH is equalto the same EBCH. Therefore the parallelogram ABCD is equal to the par-allelogram EFGH [Axiom 1. Wherefore, parallelog
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