 | Charles Davies - Geometry - 1854 - 436 pages
...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 - 270 pages
...reciprocally proportional, they are equiangular. PROP. XV. ТНЕORЕМ. Equal triangles which have an angle of the one equal to an angle of the other, have their sides about the equal angles reciprocally proportional; and conversely, triangles which... | |
 | Euclides - 1855 - 230 pages
...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... | |
 | Peter Nicholson - Cabinetwork - 1856 - 518 pages
...hypothesis AB : DE :: AC : DF; therefore AH is equal to DF. The two triangles AGH, DEF, have therefore an angle of the one equal to an angle of the other, and the sides containing these angles equal ; therefore they are equal (53) ; but the triangle AGH... | |
 | 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.... | |
 | Euclid - 1859 - 150 pages
...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... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...(T. VI.) : BC : B'C' : : AC : A'C' : : AB : A'B'. GEOMETRY. THEOREM T1ll. Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing these angles proportional, are similar. In the two triangles ABC, A'B'C',... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...by implication, those of all figures. PROPOSITION XXIV . — THEOREM. 264. Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing these angles proportional, are similar. Let the two triangles ABC, DEF have... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...by implication, those of all figures. PROPOSITION XXIV. — THEOREM. 264. Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing. these angles proportional, are similar. Let the two triangles ABC, DEF have... | |
 | Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...construction similar to DGE : hence, it is also similar to DFE. Therefore, two triangles, etc. THEOREM V. Two triangles having an angle of the one equal to an angle of the other, and the sides about those angles proportional, are similar. Let the two triangles ABC, DEF, have the... | |
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Two parallelograms are similar when they have an angle of the one equal to an angle of the other, and the including sides proportional. 
