 | George Lees - 1826 - 266 pages
...DAE of the other, have their sides about the 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 equivalent. Let the triangles... | |
 | Euclid - 1826 - 236 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... | |
 | Euclides - 1826 - 226 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. And because... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROP. VI. THEOR. If tix>o triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have... | |
 | John Playfair - Geometry - 1829 - 210 pages
...triangles will be equiangular. Equal parallelograms, and also equal triangles, which have one angle of one equal to one angle of the other, have their sides...angles reciprocally proportional ; and parallelograms, and also • triangles, which have one angle of one equal to one angle of the other, and their sides... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...reciprocally proportional. Cor. 3. (Eue. vi. 14.) And, in the same manner, it may be shown, that any two 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 ; and conversely.... | |
 | John Martin Frederick Wright - Astronomy - 1831 - 282 pages
...a given triangle. 12. Ratios that are the same to the same ratio, are the same to one another. 13. Equal parallelograms, which have one angle of the...about the equal angles reciprocally proportional. M. In a plane triangle, of which the sides are a, b, c, and opposite angles A, B, C, prove that sin.A... | |
 | John Playfair - Euclid's Elements - 1832 - 358 pages
...5.) to the parallelogram BC. Therefore equal parallelograms, &c. QED PROP. XV. THEOR. Equal triangles which have one angle of the one equal to one angle...about the equal angles reciprocally proportional: Jind triangles which have one angle in the one equal to one angle in the other, and their sides about... | |
 | John Playfair - Euclid's Elements - 1833 - 346 pages
...to the parallelogram BC. Therefore equal parallelograms, &c. QED PROP. XV. THEOR. * Equal triangles which have one angle of the one equal to one angle...have their sides about the equal angles reciprocally proportiontil : And triangles which have one angle in the one equal to one angle in the other, and... | |
 | 1834 - 574 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... | |
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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. 
