 | Pierce Morton - 1830 - 584 Seiten
...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 Seiten
...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 Seiten
...is equal (9. 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 of the other have their sides about the equal angles reciprocally proportional: Jind triangles which have one angle in the... | |
 | 1834 - 578 Seiten
...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... | |
 | 1835 - 684 Seiten
...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 Seiten
...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 Seiten
...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... | |
 | 1836 - 488 Seiten
...of the other, have their sides about the equal 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. XV. Equal... | |
 | John Playfair - 1836 - 148 Seiten
...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,... | |
 | Andrew Bell - 1837 - 290 Seiten
...therefore the triangle ABC is equiangular to the triangle DEP. PROPOSITION VI. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides ahout the equal angles proportionals, the triangles shall be equiangular, and shall have... | |
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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. 
