| George Roberts Perkins - Geometry - 1850 - 320 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... | |
| A. M. LEGENDRE - 1852
...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 - Geometry - 1853 - 136 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... | |
| William Somerville Orr - Science - 1854
...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,... | |
| Charles Davies, Adrien Marie Legendre - Geometry - 1854 - 432 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... | |
| Euclides - 1855
...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
...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... | |
| Peter Nicholson - 1856
...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,... | |
| GEORGE R. PERKINS - 1856
...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.... | |
| Joseph Allen Galbraith - 1859
...àvriirtirèvQaaiv at ir\tvpai, ai irepi ràç; îffaç ywviaç, laa iariv iKtlva. Equal triangles which **have an angle of the one equal to an angle of the other** have their sides about the equal angle* reciprocally proportional ; and triangles which have an angle... | |
| |