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. A Shorter Geometry - Page xviLimited preview - About this book
| Euclides - 1845
...AB, BC, a mean proportional -DB is found. QEF ^ PROPOSITION XIV. THEOREM. 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 conversely, parallelograms... | |
| John Playfair - Euclid's Elements - 1846 - 317 pages
...the parallelogram AB is equal (9. 5.) to the parallelogram BC. PROP. XV. THEOR. 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 triangles which have one angle... | |
| Euclides - 1846
...parallelogram BC. Wherefore, Equal parallelograms *rc. QED PROP. XV. THEOR. 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 triangles, which have one angle... | |
| Euclides - 1846
...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.... | |
| Dennis M'Curdy - Geometry - 1846 - 138 pages
...of two triangles, &c. QED Kecite (a) p. 23, 1; Wp.9,5; (4) 32, 1 ; (Op.8,1: p. 4, 6; ax. 1,1. 6 Th. **If two triangles have one angle of the one equal to one** of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular,... | |
| Harvey Goodwin (bp. of Carlisle.) - Mathematics - 1847 - 80 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 council of educ - 1848
...definition will satisfy one 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, and the sides about** two other angles proportionals ; then, if each of the remaining angles be either less, or not less... | |
| Bengal (India) - 1848
...definition will satisfy one 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, and the sides about** two other angles proportionals ; then, if each of the remaining angles be either less, or not less... | |
| Euclides - 1848
...mean proportional between two given straight lines. PROP. XIV. THEOREM. 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 conversely, parallelograms... | |
| 1852
...to one another. 2. About a given circle, to describe i triangle equiangular to a given triangle. 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, and shall have those angles equal... | |
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