 | 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... | |
 | 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... | |
 | Euclid - 1835 - 540 pages
...parallelogram BC. Therefore, " equal parallelograms," &C. QED Book VI. PROP. XV. THEOR. v-~ ^ 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 : And triangles which have one angle... | |
 | Mathematics - 1835 - 684 pages
...about the equal angles reciprocally proportional, are equal to one another ; and, conversely, 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. For, if the triangles be completed... | |
 | Mathematics - 1836 - 488 pages
...and their sides about the equal angles reciprocally proportional, are equal to one another. XV. 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 : And triangles which have one angle... | |
 | John Playfair - Geometry - 1836 - 148 pages
...equal (14. 4.) 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 ; and triangles which have one angle... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...Wherefore the parallelogram AB is equal to the parallelogram BC (V. 9). PROPOSITION XT. THEOREM. 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 ; and triangles which have one angle... | |
 | 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.... | |
 | Charles Reiner - Geometry - 1837 - 246 pages
...angles of the one are equal to the angles of the other, each to each. M. — Draw two triangles having one angle of the one equal to one angle of the other. P. — Let the angle bac be equal to the angle e df. ? M. — If the angle bac be equal to the angle... | |
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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. 
