| 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 triangles... | |
| 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... | |
| Robert Mudie - Mathematics - 1836 - 524 pages
...ratio of their bases. Therefore, again — Triangles or parallelograms which have different bases, are to each other in a ratio compounded of the ratios of their bases and altitudes. Thus, for instance, if the base of the triangle or parallelogram A is 12,... | |
| Robert Mudie - Mathematics - 1836 - 542 pages
...of their bases. Therefore, again — ••Triangles or parallelograms which have different bases, are to each other in a ratio compounded of the ratios of their bases and altitudes. Thus, for instance, if the base of the triangle or parallelogram A is 12,... | |
| 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... | |
| 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.... | |
| 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,... | |
| 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... | |
| Euclides - 1838 - 264 pages
...BC, a mean proportional DB is found. Which was to be done. PROP. XIV. THEOR. Equal parallelograms, which have one angle of the one equal to one angle of the other, ham their sides about the equal angles reciprocally proportional : and parallelograms that have one... | |
| |