 | 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 the sides... | |
 | 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
...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 pages
...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 - Geometry - 1836 - 242 pages
...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... | |
 | Mathematics - 1836 - 488 pages
...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 - Geometry - 1836 - 148 pages
...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,... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...triangles ABC, DEF are equiangular : wherefore, if the sides, &c. PROP. VI. THEOR. 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 remaining angles are equal, each to each,... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...of the other, have their sides about the equal angles reciprocally proportional : And pa allelograms which have one angle of the one equal to one angle of the ot/ier, and their sides about the equal angles reciprocally proportional, are equal to one another.... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...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. 
