| Euclides - 1826
...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... | |
| Euclid - 1826 - 180 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 - 513 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 - 186 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 - 272 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
...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 - 333 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 - 333 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
...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... | |
| Euclides - 1834
...was to be done. PROPOSITION XIV. THEOR. — Equal parallelogram* n.hirh hare one angle of tie oaf, **equal to one angle of the other, have their sides about the** eyual angles reciprocally proportional ; and parallelograms that have one angle of the one, equal to... | |
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