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 . the samepoint Z>, it is plain that each ofthe parallelograms is double ofthe triangle BDC:and they are therefore equal to one another. But if the sides AD, EF, opposite toof the parallelo-gi-ams ABCD,EBQF be notterminated atthe same point,then, becauseABCD is a par-allelogram ^D is equal to BC,for the same reason EF\^ equal to BC\therefore AD is equal to EF\ [Axiom-l. therefore the whole, or the remainder, AE is equal to thewh
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 . the samepoint Z>, it is plain that each ofthe parallelograms is double ofthe triangle BDC:and they are therefore equal to one another. But if the sides AD, EF, opposite toof the parallelo-gi-ams ABCD,EBQF be notterminated atthe same point,then, becauseABCD is a par-allelogram ^D is equal to BC,for the same reason EF\^ equal to BC\therefore AD is equal to EF\ [Axiom-l. therefore the whole, or the remainder, AE is equal to thewhole, or the remainder, DF. [Axioms 2, 3. And AB is equal to DC; [I. 34. therefore the two sides EA, AB are equal to the two sides^Z>,i>Ceach to each; and the exterior angle FDC is equal to the interior andopposite angle EAB ; [I. 29. therefore the triangle EAB is equal to the triangleFDC. [r. 4. Take the triangle FDC from the trapezium ABCF,and from the same trapezium take the triangle EABfand the remainders are equal; [Axiom 3. that is, the parallelogram ABCD is equal to the parallelo-gram EBCF. Wherefore, parallelograms on the game base &c. [I. 34. 40 EUCLIDS ELEMENTS.
Size: 2738px × 913px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, booksubjectgeometry, booksubjectmathematicsgree
