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 . o BC, meeting BDat E. [I. 31. and joined B~ C Then the triangle ABC is equal to the triangle EBC,because they are on the same base BC, and between thesame parallels BC, AE. [I. 37. But the triangle ABC is, equal to the triangle i>-SC { also the triangle DBC is equal to the triangleEBC, [Axiom 1. the greater to the less; which is AE is not parallel to BC. In the same manner it can be shewn, tha
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 . o BC, meeting BDat E. [I. 31. and joined B~ C Then the triangle ABC is equal to the triangle EBC,because they are on the same base BC, and between thesame parallels BC, AE. [I. 37. But the triangle ABC is, equal to the triangle i>-SC { also the triangle DBC is equal to the triangleEBC, [Axiom 1. the greater to the less; which is AE is not parallel to BC. In the same manner it can be shewn, that no otherstraight line through A but AD is parallel to BC-ytherefore AD is parallel to BC. Wherefore, equal triangles &c, PROPOSITION 40. THEOREM. Equal triangles, on equal bases, in the siime straight line,and on the same side of it, arebetween the same parallels. Let the equal triangles ABC, DEF be on equal basesBC, EF, in the same straight ^ine BE. and on the sameside of it: they shall be between the same parallels. Join AD. A D ^X> shall be parallel to BE. For if it is not. through Adraw AG parallel to BE,meeting ED at (r [I. join BOOK I. 40, 41. 43 ITien the triangle ABC is equal to the triangle GEF,because they are on equal bases BC, EF, and betweenthe same parallels. [I. 38. But the triangle ABC is equal to the triangle DEF. [ also the triangle DEF is equal to the triangleGEF, [Axiom 1. the greater to the less: which is AG is, not parallel to BF. In the same manner it can be shewn that no otherstraight line through A but AB is parallel to BF jtherefore AD is parallel to BF. Wherefore, equal triangles &c. PROPOSITION 41. THEOREM. If a parallelogram and a triangle he on the same baseand between the same parallels, the parallelogram sliall heduiible of the triangle. Let the parallelogram ABCD and the triangle EEC the same base BC, and between the same parallelsliC. AE : the parallelogram ABCD shall be dou
Size: 2410px × 1037px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, booksubjectgeometry, booksubjectmathematicsgree
