Assuming that 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... SYLLABUS OF PLANE GEOMETRY - Side 171876Uten tilgangsbegrensning - Om denne boken
| Euclides - 1855
...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
...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... | |
| 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.... | |
| Peter Nicholson - 1856 - 216 sider
...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... | |
| Euclides - 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... | |
| George Roberts Perkins - 1860 - 443 sider
...(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 - 1862 - 490 sider
...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 - 1862 - 490 sider
...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 - 1863 - 320 sider
...by implication, those of all f1gures. 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 - 1862 - 98 sider
...: 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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