 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...parallelogram AB is equal to the parallelogram BC. Therefore equal parallelograms, &c. PROP. XV. THEOR. EQUAL triangles which have an angle of the one equal to an angle of the other, have their sides about those angles reciprocally proportional : and (2.) triangles which have an angle... | |
 | Adrien Marie Legendre - Geometry - 1838 - 382 pages
...general properties of triangles include, by implication, those of all figures. PROPOSITION XX. THEOREM. Two triangles, which have an angle of the one equal to an angle of the oiher, and the sides containing those angles proportional, are similar. In the two triangles ABC, DEF,... | |
 | Euclides - 1840 - 192 pages
...an angle (BAD) of the other, have the sides about the equal angles reciprocally proportional : and, triangles which have an angle of the one equal to an angle of the other, and the sides about the equal angles reciprocally proportional, are equal. Let the triangles be so placed that the... | |
 | Euclides - 1840 - 82 pages
...other, and the sides about the equal angles reciprocally proportional, are equal. PROP. XV. THEOR. Equal triangles which have an angle of the one equal to an angle of the other, have the sides about the equal angles reciprocally proportional : and triangles which have an angle... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...right-angled triangles. Thus the general properties of triangles involve those of all figures. THEOREM. 208. Two triangles, which have an angle of the one equal to an angle of the other, and the sides about these angles proportional, are similar. fig. 122. Demonstration. Let the angle A = D (fig. 122),... | |
 | Euclides - Geometry - 1841 - 378 pages
...to the angle ACD; wherefore * I Ax. a i so BAC is equal* to CDE: and because the triangles ABC, DCE have the angle A equal to the angle D, and the sides about these equal angles proportionals, viz. BA to AC, as CD to DE, the triangle ABC is *6. 6 equiangular*... | |
 | William Grier - Mechanical engineering - 1842 - 320 pages
...angle C equal to the angle F; then will the two triangles be identical, or equal in all respects. 2. Let the two triangles ABC, DEF, have the angle A equal to the angle D, the angle B equal to the angle E, and the side AB equal to the side DE ; then these two triangles will... | |
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 110 pages
...equiangular with ABC ; and therefore (by the Corollary to the last Proposition) similar. PROP. XVII. THEOREM. Two triangles, which have an angle of the one equal to an angle of the other, and the sides about the equal angles proportional, are similar. In the triangles ABC, DEF, let the angles, C, F,be... | |
 | James Bates Thomson - Geometry - 1844 - 268 pages
...triangle AGH is similar to ABC ; therefore DEF is also similar to ABC. Hence, If any two triangles have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, those two triangles are similar. PROPOSITION XXI. THEOREM. Two triangles,... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...AB is equal to the parallelogram BC. Therefore equal parallelograms, &c. PROP. XV. THEOR. — Equal triangles which have an angle of the one equal to an angle of the other, have their sides about those angles reciprocally proportional : and (2) triangles which have an angle... | |
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Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing these angles proportional, are similar. 
