 | Elias Loomis - 1849 - 252 σελίδες
...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 σελίδες
...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 σελίδες
...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... | |
 | Euclid - 1853 - 176 σελίδες
...(a) Hypoth. (41 I.29. (c) I. 26. fa) I. 29. (6) Hypoth. (c) I. 34. COROLLARY 2. If two parallelograms have an angle of the one equal to an angle of the other, the remaining angles shall be respectively equal. For the angles opposite the equal angles are equal... | |
 | Charles Davies - 1854 - 436 σελίδες
...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 - 532 σελίδες
...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 σελίδες
...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 - 262 σελίδες
...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... | |
 | George Roberts Perkins - 1856 - 460 σελίδες
...other, and the sides containing the equal angles proportional. Two rhombuses are similar, when they have an angle of the one equal to an angle of the other. All squares are similar figures. All regular polygons of the same number of sides are similar figures.... | |
 | Peter Nicholson - 1856 - 482 σελίδες
...equal to the sum of the two lines AD, DB, therefore AB'=AC*+BC9. THEOREM 54,. 125. Two triangles, which have an angle of the one equal to an angle of the other, are to each other as the rectangle of the sides about the equal angles. Suppose the two triangles joined,... | |
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The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C'... 
