 | 1843 - 582 pagina’s
...equal angles reciprocally proportional: and triangles which have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal. 5. A common tangent is drawn to two circles which touch externally : if a circle be described... | |
 | Nicholas Tillinghast - 1844 - 108 pagina’s
...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,... | |
 | Euclides - 1845 - 546 pagina’s
...reciprocally proportional : and conversely, parallelograms that have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another. Let AB, BC be equal parallelograms, which have the angles at B equal. The... | |
 | Euclid, James Thomson - 1845 - 382 pagina’s
...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... | |
 | Euclid - 1845 - 218 pagina’s
...equal angles reciprocally proportional: and parallelograms that have one angle of the one, equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another. Let AB, BC be equal parallelograms which have the angles at B equal, and... | |
 | Euclides - 1846 - 272 pagina’s
...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... | |
 | Euclides - 1846 - 292 pagina’s
...angles reciprocally proportional : and parallelograms, which have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another. First, let AB, BC be equal parallelograms, which have the angles at B equal... | |
 | George Roberts Perkins - 1847 - 326 pagina’s
...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... | |
 | Euclides - 1848 - 52 pagina’s
...reciprocally proportional : and conversely, parallelograms that have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another. PROP. XV. THEOREM. Equal triangles which have one angle of the one equal... | |
 | George Clinton Whitlock - 1848 - 338 pagina’s
...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,... | |
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... have an angle of the one equal to an angle of the other, and the sides about those angles reciprocally proportional, are equal to une another. 
