 | Euclides - 1838 - 264 σελίδες
...FGHKL, the angle BAE »iDef 6 '* eil'1al* l0 the angle GFL, and BA : AE : : GF : FL; therefore, because the triangles ABE, FGL have an angle in one equal...sides about these equal angles proportionals, the tri» 6 angle ABE is equiangular,* to the triangle FGL; *4. e! and therefore similar to it ;* wherefore... | |
 | Dionysius Lardner - 1840 - 386 σελίδες
...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,... | |
 | Euclides - 1841 - 378 σελίδες
...is to AE, • i Def as G ^ to FL:* therefore because the triangles ABE, 6. FGL have an angle in the one equal to an angle in the other, and their sides about these equal angles pro• 6. 6. portionals, the triangle ABE is equiangular* to the • 4. 6. triangle FGL, and therefore*... | |
 | John Playfair - 1842 - 332 σελίδες
...BAE is equal to the angle GFL (def. 1. 6.), and BA : AE : : GF : FL (def. 1. 6.) : wherefore, because the triangles ABE, FGL have an angle in one equal...wherefore the angle ABE is equal to the angle FGL : and, because the polygons are similar, the whole angle ABC is equal (def. 1. 6.) to the whole angle FGH... | |
 | Euclides - 1842 - 316 σελίδες
...equal to the angle GFL ( 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...wherefore the angle ABE is equal to the angle FGL ; and, because the polygons are similar, the whole angle ABC is equal (1. Def. 6.) to the whole angle FGH;... | |
 | Joseph Gwilt - 1842 - 1114 σελίδες
...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.... | |
 | Euclid - 1845 - 218 σελίδες
...angle BAE is equal to the angle GFL*, and BA is to AE, as GF to FLf : * J £*•£. Wherefore, because the triangles ABE, FGL have an angle in one equal...angles proportionals, the triangle ABE is equiangular J, and therefore similar, to the triangle FGL|| ; j *;£; wherefore the angle ABE is equal to the angle... | |
 | Euclides - 1845 - 546 σελίδες
...equal to the angle GFL, (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...the other, and their sides about these equal angles p oportionals, the triangle ABE is equiangular to the triangle FGL ; (vi. 6.) and therefore similar... | |
 | Euclid, James Thomson - 1845 - 382 σελίδες
...the polygons are 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. 0) equiangular, ana therefore... | |
 | Euclid, John Playfair - 1846 - 334 σελίδες
...BAE is equal to the angle GFL (def. 1. 6.), and BA : AE : : GF : FL (def. 1.6.): wherefore, because the triangles ABE, FGL have an angle in one equal...wherefore the angle ABE is equal to the angle FGL : and, because the polygons are similar, the whole angle ABC is equal (def. 1. 6.) to the whole angle FGH... | |
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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. 
