| Euclides - 1840 - 82 pages
...a mean proportional between two given straight lines. PROP. XIV. THEOR. Equal parallelograms which **have an angle of the one equal to an angle of the other,** have the sides about the equal angles reciprocally proportional : and parallelograms which have an... | |
| Benjamin Peirce - Geometry - 1841 - 186 pages
...equilateral or equiangular with respect to each other, are equivalent. /'468. Lemma. If two spherical **triangles have an angle of the one equal to an angle...sides which include the angle in one triangle are** supplements of those which include it in the other triangle ; the sum of the surfaces of the two triangles... | |
| Adrien Marie Legendre - Geometry - 1841 - 288 pages
...the general properties of triangles involve those of all figures. THEOREM. 208. Two triangles, which **have an angle of the one equal to an angle of the other, and the sides** about these angles proportional, are similar. fig. 122. Demonstration. Let the angle A = D (fig. 122),... | |
| James Bates Thomson - Geometry - 1844 - 268 pages
...equal. But the triangle AGH is similar to ABC ; therefore DEF is also similar to ABC. Hence, If any **two triangles have an angle of the one equal to an angle of the other, and the sides** containing those angles proportional, those two triangles are similar. PROPOSITION XXI. THEOREM. Two... | |
| Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...therefore (by the Corollary to the last Proposition) similar. PROP. XVII. THEOREM. Two triangles, which **have an angle of the one equal to an angle of the other, and the sides** about the equal angles proportional, are similar. In the triangles ABC, DEF, let the angles, C, F,be... | |
| Euclid, James Thomson - Geometry - 1845 - 380 pages
...the parallelogram BC. Therefore equal parallelograms, &c. PROP. XV. THEOR. — Equal triangles which **have an angle of the one equal to an angle of the other,** have their sides about those angles reciprocally proportional : and (2) triangles which have an angle... | |
| Euclides - 1846 - 272 pages
...right, since they are equal to these right angles (by Prop. 34.) CoR. 2. — If two parallelograms **have an angle of the one equal to an angle of the other,** the remaining angles will be also equal ; for the angles which are opposite to these equal angles are... | |
| George Roberts Perkins - Geometry - 1847 - 326 pages
...must also be proportional to the sides GH, HK ,( B. IV, Def. 3). 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,... | |
| George Clinton Whitlock - Mathematics - 1848 - 338 pages
...Trapezoid— -consequences, measures, parallelogram, triangle, comparisons, equalities 92 3. Triangles having **an angle of the one equal to an angle of the other** — consequence • 93 4. Exercises.... 94 BOOK THIRD. PLANE GEOMETRY DEPENDING ON THE CIRCLE, ELLIPSE,... | |
| Charles Davies - Trigonometry - 1849 - 372 pages
...triangles include, by implication, those of all figures. 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. In the two triangles ABC, DEF, let the angles A... | |
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