 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...ABC is equiangular to the triangle DEF. Wherefore, if two triangles &c. QED PROPOSITION 7. THEOREM. 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... | |
 | Simon Newcomb - Geometry - 1881 - 418 pages
...produced portion of such sides is equal to the rectangle of the sides of the parallelogram. THEOREM 8. If two triangles have one angle of the one equal to one angle of the other, and the perpendiculars from the other two angles upon the opposite sides proportional,... | |
 | George Bruce Halsted - Measurement - 1881 - 266 pages
...rectangle from their ratio m:n, and its area E. f^jj l^g « = •»/ ; 0=-\l — . Ans. \ n \ m 521. 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 the third angles will be... | |
 | Isaac Sharpless - Geometry - 1882 - 286 pages
...Therefore ABC, DEF are also equiangular, and therefore (V. 4) similar. 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 proportional, the triangles will be similar.... | |
 | Euclides, James Hamblin Smith - 1883 - 376 pages
...shew that the lines BC, be divide each other in reciprocal proportion. And Conversely, Trianyks, which have one angle of the one equal to one of the other, and their sides about the equal angles reciprocally proportional, are eqiud to one another. Let the sides... | |
 | Mathematical association - 1883 - 86 pages
...they are similar, and those angles which are opposite to the homologous sides are equal. THEOR. 5. 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... | |
 | University of Glasgow - 1883 - 438 pages
...square. What is the ratio of the radins of the circle to the side of the second square ? 12. Prove that if two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportional, the triangles are similar. 14.... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...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, to that the sides subtending... | |
 | Woolwich roy. military acad - 1884 - 148 pages
...produced, such that the angle ECD is equal to CED, CD will touch the circle described about ACB. ro. 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 - 1884 - 434 pages
...construction : From AB cut off AO = HE, and through G draw OH || SC, meeting ACiAH. PROPOSITION 6. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides about these angles proportional, they shall be similar, those angles... | |
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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. 
