 | Education - 1844 - 688 pages
...the touching line, shall be equal to the angles in the alternate segments. 12. 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. MECHANICS AND HYDROSTATICS. MONDAY,... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...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, viz. those which are... | |
 | Euclid - Geometry - 1845 - 218 pages
...proportional DB is found. Which was to be done. PROPOSITION XIV. THEOR. — Equal parallelograms which have one angle of the one, equal to one angle of the other, have their sides about the equal angles reciprocally proportional: and parallelograms that have one... | |
 | Scottish school-book assoc - 1845 - 444 pages
...and second terms AABD, we have AABC : ADBE=AB'BC : DB-BE, (Alg. 116) Cor. Parallelograms which have one angle of the one equal to one angle of the other, are to one another in the ratio which is compounded of the ratios of the sides about the equal angles.... | |
 | Euclides - 1845 - 546 pages
...(v.9-) Therefore equal parallelograms, &c. QED PROPOSITION XV. 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 conversely, triangles which... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...Therefore the triangle ABC is equiangular to the triangle DEF. PROP. VII. THEOR. If two triangles have one angle of the one equal to one angle of the other,...angles be either less, or not less, than a right angle, the triangles shall be equiangular, and have those angles equal about which the sides are proportionals.... | |
 | Euclides - 1846 - 292 pages
...a mean proportional DB has been found. O..E. p. PROP. XIV. THEOR. Equal parallelograms, which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : and parallelograms, which have... | |
 | Euclides - 1846 - 272 pages
...therefore ex oequali, BD will be to CG, as I to L (by Prop. 33, B. 5). COR. 2. — Triangles which have one angle of the one equal to one angle of the other, are to each other in a ratio compounded of the ratios of the sides about the equal angles. COR. 3.... | |
 | Harvey Goodwin (bp. of Carlisle.) - Mathematics - 1847 - 136 pages
...than the sum of the two sides by the diameter of the inscribed circle. 23. If two triangles have an angle of the one equal to one angle of the other, and also another angle of the one equal to the supplement of another angle of the other, the sides about... | |
 | Bengal (India) - 1848 - 520 pages
...of the tests of the former. 2. Give a proof of the following proposition : " If two triangles have one angle of the one equal to one angle of the other,...not less than a right angle, or if one of them be a right angle, the triangles shall be equiangular." And show clearly by a diagram the necessity for... | |
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If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar. 
