| Euclides - 1826 - 226 pagina’s
...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 - 1827 - 546 pagina’s
...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... | |
| Pierce Morton - 1830 - 584 pagina’s
...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 - 1831 - 282 pagina’s
...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 the sides... | |
| John Playfair - 1832 - 358 pagina’s
...parallelogram AB is equal (9. 5.) to the parallelogram BC. Therefore equal parallelograms, &c. QED PROP. XV. THEOR. Equal triangles which have one angle...the one equal to one angle of the other have their sides about the equal angles reciprocally proportional: Jind triangles which have one angle in the... | |
| 1834 - 578 pagina’s
...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... | |
| Robert Simson - 1835 - 544 pagina’s
...the parallelogram AB is equal ° to the parallelogram BC. Therefore, " equal parallelograms" &c. QED Book VI. PROP. XV. THEOR. , — • — ' Equal triangles...the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : And triangles which have one angle in the... | |
| 1835 - 684 pagina’s
...the altitude of the first, the two triangles will be equal to one another (11. Cor. 2.). PROP. 40. Triangles which have one angle of the one equal to one angle of the other, are to one another in the ratio which is compounded of the ratios of the sides about the equal angles.... | |
| Euclid - 1835 - 540 pagina’s
...other, have their sides about the 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,... | |
| Eugenius Nulty - 1836 - 242 pagina’s
...Multiply these equal ratios, and there will result ABС:DEF::AС.BG: DF.EH(th.T). THEOREM XXIV. 69. Two triangles which have one angle of the one equal to one angle of the other, are proportional to the products of the sides which contain those angles. E в Let AB С, DEF be two... | |
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