 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...proportional DB is found : which was to be done.* PROP. XIV. THEOR. — Equal parallelograms which have an angle of the one equal to an angle of the other, have their sides about those angles reciprocally proportional : and (2) parallelograms which have an... | |
 | 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
...Therefore, by equality of ratios, we have AC : GK : : CD : KL. Hence the two triangles ACD and GKL have an angle of the one equal to an angle of the other, and the sides about those angles proportional, and consequently the triangles are similar. In the same... | |
 | George Clinton Whitlock - Mathematics - 1848 - 338 pages
...90 2. 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,... | |
 | George Clinton Whitlock - Mathematics - 1848 - 340 pages
...90 2. Trapezoid — consequences, measures, parallelogram, triangle, comparisons, equalities 92 3. Triangles having an angle of the one equal to an angle of the otherconsequence 93 4. Exercises 94 BOOK THIRD. PLANE GEOMETRY DEPENDING ON THE CIRCLE, ELLIPSE, HYPERBOLA,... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...similar. Wherefore, two triangles, &c. PROPOSITION XX. THEOREM. Two triangles are similar, when they have an angle of the one equal to an angle of the other, and the sides containing those angles proportional. Let the triangles ABC, DEF have the angle A of... | |
 | 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... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...Therefore by equality of ratios, we have AC : GK : : CD : KL. Hence the two triangles ACD and GKL have an angle of the one equal to an angle of the other, and the sides about those angles proportional, and consequently the triangles are similar. In the same... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...implication, those of all figures. B 109 D DF., PROPOSITION XX. THEOEEM. 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... | |
 | Euclid - Geometry - 1853 - 176 pages
...Hypoth. (41 I.29. (c) I. 26. fa) I. 29. (6) Hypoth. (c) I. 34. COROLLARY 2. If two parallelograms have an angle of the one equal to an angle of the other, the remaining angles shall be respectively equal. For the angles opposite the equal angles are equal... | |
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Two triangles having 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. 
