 | George Darley - Euclid's Elements - 1836 - 172 pages
...it and E are, by ART. 96, reciprocally proportional ; that is, BA is to ED as EF is to BC. This, &c. ART. 107. Two triangles which have an angle in one...equal angles reciprocally proportional, are equal. In the above figure, let ABC, DEF, be two triangles, which hare the angle at B equal to the angle at... | |
 | John Playfair - Geometry - 1836 - 148 pages
...(5. Def. 5.), and BA is to AE, as GF to FL (5. Def. 5.) ; wherefore because the triangles ABE, FGL, have an angle in one equal to an angle in the other, and their sides about these equal angles proportionals ; the triangle ABE is equiangular (7. 5.), and therefore... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...similar, the angles A and F are equal, and BA : AE : : GF : FL : wherefore, because the triangles ABE, FGL have an angle in one equal to an angle in the other, and the sides about those angles proportionals, the triangle ABE is (VI. 6.) equiangular, and therefore... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...angle GFL ; and BA is to AE, as GF to FL (VI. Def. 9) ; wherefore, because the triangles ABE, FGL, hare an angle in one equal to an angle in the other, and their sides about these equal angles proportionals, the triangle ABE is equiangular (VI. 6), and therefore... | |
 | Euclides - 1838 - 264 pages
...6 '* eil'1al* l0 the angle GFL, and BA : AE : : GF : FL; therefore, because the triangles ABE, FGL have an angle in one equal to an angle in the other, and their sides about these equal angles proportionals, the tri» 6 angle ABE is equiangular,* to the triangle... | |
 | Dionysius Lardner - Curves, Plane - 1840 - 386 pages
...which have their sides proportional, have their angles respectively equal. (253.) If two triangles have an angle in one equal to an angle in the other, and the sides which include that angle proportional each to each, the triangles will be similar. That is,... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...GFL (def. 1. 6.), and BA : AE : : GF : FL (def. 1. 6.) : wherefore, because the triangles ABE, FGL have an angle in one equal to an angle in the other, and their sides about these equal angles proportionals, the triangle ABE is equiangular (6. 6.), and therefore... | |
 | Euclides - 1842 - 316 pages
...1 . Def. 6.) and BA is to AE, as GF to FL (1. Def. 6.): wherefore, because the triangles ABE, FGL, have an angle in one equal to an angle in the other, and their sides about these equal angles proportionals, the triangle ABE is equiangular (6. 6.), and therefore... | |
 | Joseph Gwilt - Architects - 1842 - 1114 pages
...identical; which is absurd, since their angles arc unequal. 941. РЯОР. LXIII. Triangles which hare an angle in one equal to an angle in the other, and the sides about these angles proportional, are equiangular. If in the two triangles ВАС, NMP (fig.... | |
 | Euclides - 1845 - 546 pages
...(vi. def. 1.) and BA is to AE, as GF to FL : (vi. def. 1.) therefore, because the triangles ABE, FGL have an angle in one equal to an angle in the other, and their sides about these equal angles p oportionals, the triangle ABE is equiangular to the triangle... | |
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FGL have an angle in one equal to an angle in the other, and their... 
