 | 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 - 235 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 - 237 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 - 96 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 - 308 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 - 324 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 - 384 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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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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C'... 
