 | 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. 296.) the angle A be... | |
 | John Playfair - 1842 - 332 σελίδες
...(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 σελίδες
...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... | |
 | Euclid, James Thomson - 1845 - 382 σελίδες
...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 (VI. 4 and def.... | |
 | Euclides - 1845 - 546 σελίδες
...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... | |
 | Euclid - 1845 - 218 σελίδες
...GFL*, and BA is to AE, as GF to FLf : * J £*•£. 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 J, and therefore... | |
 | Euclides - 1846 - 272 σελίδες
...reciprocally proportional (ABtoBCas BG to BD). And if two parallelograms (AD and GC) have an angle in the one equal to an angle in the other, and the sides about the equal angles reciprocally proportional ; they (hall be equal to each other. PART 1. — Let the... | |
 | Euclid, John Playfair - 1846 - 334 σελίδες
...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... | |
 | Charles William Hackley - 1847 - 248 σελίδες
...DEC, which is absurd, the angles being different. THEOREM LXV. Triangles which have an angle in the one equal to an angle in the other, and the sides about these angles proportional, are equiangular. Let ABC, DEF be two triangles, having the angle A = the angle... | |
 | George Roberts Perkins - 1847 - 326 σελίδες
...the parallelogram mentioned in Cor. 1. PROPOSITION X. THEOREM. Triangles, which have an angle in the one equal to an angle in the other, and the sides about these angles proportional, are equiangular. ,C ABDI i F Let ABC, DFG be two triangles, having the angle A... | |
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FGL ; (vi. 6.) and therefore similar to it ; (vi. 4.) wherefore the angle ABE is equal to the angle FGL: and, because the polygons are similar, the whole angle ABC is equal to the whole angle FGH ; (vi. 
