 | Euclid - 1826 - 234 pages
...angle of the other, the sides about the equal angles are reciprocally proportional ; and if triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles reciprocally proportional, these triangles are equal. BAC equal... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...to the parallelogram BC. Therefore equal pa- * 9' 5rallelograms, &c. QED PROP. XV. THEOR. • Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : and triangles whichhave one angle... | |
 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...subduplicates will also be equal. PROPOSITION XXIII. THEOREM. (640) Equiangular parallelograms (AD and CG) are to each other in a ratio compounded of the ratios of their sides. Let two of the sides AB and BC about the equal angles be placed so that they may form... | |
 | John Playfair - Geometry - 1829 - 210 pages
...ratios of their sides about the equal angles. ED. CoR. 2. Two parallelograms, which have one angle of one equal to one angle of the other, are to each other in a ratio compounded of the ratios of the sides of one to the sides of the other, each to each, about their equal angles. For two parals. having one... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...of the ratios of the sides about the equal angles, or as the rectangles under those sides . G6 (/) Triangles which have one angle of the one equal to one angle of the other, and the sides about the equal angles reciprocally proportional, are equal to one another; and, conversely,... | |
 | John Martin Frederick Wright - Astronomy - 1831 - 282 pages
...Ratios that are the same to the same ratio, are the same to one another. 13. Equal parallelograms, which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. M. In a plane triangle, of which... | |
 | Euclid - Euclid's Elements - 1833 - 216 pages
...compounded of the ratios of the sides containing the equal angles. Cor. 3. Any parallelograms or triangles are to each other in a ratio compounded of the ratios of their bases and altitudes ; for they are equal to rectangles, or to right-angled triangles, on the... | |
 | 1834 - 578 pages
...A c : A 6 : : A" E": A" F". Now it is demonstrated in treatises on geometry,* that if two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles are equiangular, and consequently... | |
 | Mathematics - 1835 - 684 pages
...about the equal angles reciprocally proportional, are equal to one another ; and, conversely, equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. For, if the triangles be completed... | |
 | Euclid - 1835 - 540 pages
...parallelogram BC. Therefore, " equal parallelograms," &C. QED Book VI. PROP. XV. THEOR. v-~ ^ Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : And triangles which have one angle... | |
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If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar. 
