 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...is to O Jj?. V. 5. and .'. O AB=CJ BC. V. 8. QED Pnoposmoif 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. Let A BO, ADE be equal AS, having... | |
 | Euclides - 1874 - 342 pages
...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, and shall have... | |
 | Braithwaite Arnett - 1874 - 130 pages
...it shall cut the other sides, or these produced, proportionally. 7. 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. 8. Prove that the ratio of the diameter... | |
 | L J V. Gerard - 1874 - 428 pages
...other, the greater third side subtends a greater angle. (Eucl. I. 25.) THEOREM 20. If two triangles have one angle of the one equal to one angle of. the other, if the sides forming another angle lie equal, to each, and if the third angle be acute in both triangles,... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...QB as O QX : £J QH, \ .-. a QX : O Qffas O QX : O QK; (v. 3) THEOREM (»). Equal triangles having one angle of the one equal to one angle of the other, have tjte sides about those angles reciprocally proportional. -Af Let AQD, BQC be equal triangles,... | |
 | Richard Wormell - 1876 - 268 pages
...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 angles be either... | |
 | Sir George Greenhill - Mathematics - 1876 - 318 pages
...AC in points MN, such that and therefore DMEFN is a regular pentagon. v. Equal triangles which have one angle of the one equal to one angle of the other have their sides about the equal angles reciprqcally proportional ; and triangles which have one angle... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...BC, a mean proportional DB is found. QEF PROPOSITION XIV. THEOREM. Equal parallelograms, which hate one angle of the one equal to one angle of the other, have their tides about the equal angles reciprocally proportional: and com-erscly, parallelograms that... | |
 | D. Tierney - 1877 - 126 pages
...FB; but, since triangle BEC=2 triangle DEC, therefore1 AE:ED::2AF:FB. 10. 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... | |
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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. 
