 | Euclid, Isaac Todhunter - 1867 - 426 σελίδες
...proportional, but not their angles equal. VI. 7. In VI. 7 the enunciation is imperfect ; it should be, "if two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportionals, so that the sides subtending... | |
 | Robert Potts - 1868 - 434 σελίδες
...triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROPOSITION VI. 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,... | |
 | James Maurice Wilson - 1868 - 150 σελίδες
...additional equality of a pair of corresponding sides involves the identity of the triangles. THEOREM 7. If two triangles have one angle of the one equal to one angle of the other; and the sides about the equal angles proportionals, then will the triangles be... | |
 | Civil service - 1871 - 264 σελίδες
...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,... | |
 | Henry William Watson - 1871 - 320 σελίδες
...polygon on AB + the area of the polygon on AC is equal to the area of the polygon on BC. EXAMPLES. 1. If two triangles have one angle of the one equal to one angle of the other, and likewise one angle of the one supplementary to one angle of the other, the... | |
 | Euclides, James Hamblin Smith - 1872 - 376 σελίδες
...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... | |
 | Euclides - 1874 - 342 σελίδες
...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,... | |
 | Francis Cuthbertson - 1874 - 400 σελίδες
...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... | |
 | L J V. Gerard - 1874 - 428 σελίδες
...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... | |
 | Braithwaite Arnett - 1874 - 130 σελίδες
...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... | |
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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, and shall have those angles equal which are opposite to the homologous sides. 
