| Elias Loomis - Conic sections - 1849 - 252 pages
...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 one, equal... | |
| George Roberts Perkins - Geometry - 1850 - 332 pages
...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 similar, we... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...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 the angle... | |
| Euclid - Geometry - 1853 - 176 pages
...(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 - Geometry - 1854 - 436 pages
...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 the angle... | |
| William Somerville Orr - Science - 1854 - 532 pages
...the other, have their sides about the equal angles reciprocally proportional ; and triangles which **have an angle of the one equal to an angle of the other, and** their sides about those angles reciprocally proportional, are equal to one another. Let the triangles... | |
| Euclides - 1855 - 230 pages
...equal to an angle of the other. If triangles are equiangular . If triangles are similar . . If equal **triangles have an angle of the one equal to an angle of the other.** If triangles have an angle in the one equal to an angle in the other, and their sides about the equal... | |
| Euclides - 1855 - 262 pages
...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 - Geometry - 1856 - 460 pages
...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 - Cabinetwork - 1856 - 482 pages
...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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