| Euclides - 1840 - 192 pages
...an angle (BAD) of the other, have the sides about the equal angles reciprocally proportional : and, **triangles which have an angle of the one equal to an angle of the other,** and the sides about the equal angles reciprocally proportional, are equal. Let the triangles be so... | |
| Adrien Marie Legendre - Geometry - 1841 - 288 pages
...right-angled triangles. Thus 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... | |
| Nicholas Tillinghast - Geometry, Plane - 1844 - 110 pages
...equiangular with ABC ; and 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... | |
| Euclides, James Thomson - Geometry - 1845 - 382 pages
...AB is equal to 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... | |
| Nathan Scholfield - 1845 - 894 pages
...properties of triangles include, by implication, those of all figures. FROPOSITION XIX. THEOREM.Two **triangles, which have an angle of the one equal to an angle of** tlie other, and the sides containing those angles proportional, are similar, In the two triangles ABC,... | |
| 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... | |
| George Clinton Whitlock - Mathematics - 1848 - 340 pages
...(147) with (148).] Of PROPOSITION III. Two triangles, having an angle of the one equal to an (159) **angle of the other, are to each other as the products of the sides** about the equal angles. Let the equal apgles of the triangles A, B, be made vertical, and join the... | |
| 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
...general properties of 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... | |
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