| James Thomson - 1845 - 358 sider
...to DFE, and A to D. Therefore the triangles ABC, DEF are equiangular : wherefore, if the sides, &c. **PROP. VI. THEOR. — If two triangles have one angle...the sides about the equal angles proportionals; the** remaining angles are equal, each to each, viz. those which are opposite to the homologous sides. Let... | |
| Robert Simson - 1845 - 199 sider
...ABC is equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROPOSITION VI. THEOB. — **If two triangles have one angle of the one equal to one angle of the** oiher, and the sides about the equal angles proportionals, the triangles shall be equiangular, and... | |
| 1845
...halves of parallelograms, upon the same base, and having the same altitude, equal triangles, which **have one angle of the one equal to one angle of the other,** have the sides about these angles reciprocally proportional ; and if two triangles have one angle of... | |
| Robert Potts - 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 - 1846 - 317 sider
...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
...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.... | |
| 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... | |
| Dennis M'Curdy - 1846 - 138 sider
...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.) - 1847 - 80 sider
...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
...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... | |
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