 | Charles Davies - 1849 - 372 pagina’s
...triangles include, by implication, those of all figures. PROPOSITION XX. THEOREM. Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar. In the two triangles ABC, DEF, let the... | |
 | Elias Loomis - 1849 - 252 pagina’s
...similar. Wherefore, two triangles, &c. PROPOSITION XX. THEOREM. Two triangles are similar, when they have an angle of the one equal to an angle of the other, and the sides containing those angles proportional. Let the triangles ABC, DEF have the angle A of the... | |
 | George Roberts Perkins - 1850 - 332 pagina’s
...also be proportional to the sides GH, HK, (B. IV, Def. III.) Therefore, the two triangles ABC, GHK have an angle of the one equal to an angle of the other, and the sides about those angles proportional, and consequently these triangles are similar; and being... | |
 | Adrien Marie Legendre - 1852 - 436 pagina’s
...include, by implication, those of all figures. B 109 D DF., PROPOSITION XX. THEOEEM. Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar. Let ABC, DEF, be two triangles, having... | |
 | Euclides - 1853 - 176 pagina’s
...equal angles reciprocally proportional ; and parallelograms that have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another. LET ab, b С be equal parallelograms, which have the angles at b equal, and... | |
 | Royal Military Academy, Woolwich - 1853 - 400 pagina’s
...equal angles reciprocally proportional : and parallelograms that have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another. Let AB, BC be equal parallelograms which have the angles at B equal, and... | |
 | Charles Davies - 1854 - 436 pagina’s
...by implication, those of all f1gures. BOOK IY. 109 D PROPOSITION XX. THEOREM. Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar. Let ABC, DEF, be two triangles, having... | |
 | William Somerville Orr - 1854 - 534 pagina’s
...other, have their sides about the equal angles reciprocally proportional : and parallelograms that have an angle of the one equal to an angle of the other, and the sides about those angles reciprocally proportional, are equal to une another. Let the sides DI5,... | |
 | Euclides - 1855 - 230 pagina’s
...proportioned, between AB BC the segments of the base (c). PROPOSITION XIV. THEOREM [1.]—If equal parallelograms (AB and BC) have an angle of the one equal to an angle of the other, their sides about the equal angles are reciprocally proportional (DB is to BE, as GB is to BF). [3.]... | |
 | Euclides - 1855 - 270 pagina’s
...compounded of the ratios which are the game with the ratios of the sides. Corollary 1. — Triangles which have an angle of the one equal to an angle of the other, are to one another as the rectangles contained by the sides about those angles. Corollary 2. — Equiangular... | |
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... have an angle of the one equal to an angle of the other, and the sides about those angles reciprocally proportional, are equal to une another. 
