| Civil service - 1871
...drawn at right angles to the diameter of a circle from the extremity of it, touches the circle. 3. **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 shall be equiangular,... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 349 pages
...by Euclid) of another case in which two triangles are equal in all respects. PROPOSITION E. THEOEEM. **If two triangles have one angle of the one equal to one** angle of the other, and the sides about a second angle in each equal; then, if the third angles in... | |
| Braithwaite Arnett - 1874
...two sides produced, prove that the points B and C lie upon the circle of which PQ is the diameter. 9. **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 shall be equiangular... | |
| Francis Cuthbertson - Euclid's Elements - 1874 - 349 pages
...ratio of FB to GB\ and .-. cuts FG in B; ie iBPF= LAPP; .-. AP : PB as AF : FB; (vi. 2) THEOREM (</). **If two triangles have one angle of the one equal to one** angle of the other and the sides about two other angles proportional, then shall the triangles be equiangular... | |
| Euclides - 1874 - 342 pages
...ABC is equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROPOSITION 6. — Theorem. **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 shall be equiangular,... | |
| L J V. Gerard - 1874
...each other. Scholium. Equilateral triangles are similar to one another. THEOREM 26. (Eucl. VI. 7.) **If two triangles have one angle of the one equal to one** angle of the other, if the sides forming another angle be proportional, and if the third angle be acute... | |
| Robert Potts - Geometry - 1876 - 446 pages
...is equiangular to the triangle DEF. \Vherefore, if two triangles, &c. QED PROPOSITION VII. THEOREM. **If two triangles have one angle of the one equal to one** angle of the other, and the tides abnut two other angles proportionals; then, if each of the remaining... | |
| Richard Wormell - 1876
...D : F . ,(and D :E = A :B j 5- {andB = mF } then A - В = m (D _ F) EUCLID.-BOOK VI. Prop. Page 7. **If two triangles have one angle of the one equal to one** angle of the other, and the sides about two other angles proportionals, then if each of the remaining... | |
| Association for the improvement of geometrical teaching - Geometry, Plane - 1876 - 58 pages
...they are similar, and those sides which are opposite to the equal angles are homologous. THEOR. 3. **If two triangles have one angle of the one equal to one** angle of the other and the sides about these angles proportional, they are similar, and those angles... | |
| J. G - 1878 - 408 pages
...on the one are to one another in the same ratio as the corresponding intercepts on the other. " 7." **If two triangles have one angle of the one equal to one** angle of the other, and the sides about one other angle in each proportional, so that the sides opposite... | |
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