 | John Playfair - 1842 - 332 pagine
...straight linos AB, BC, a mean proportional DB is found. PROP. XIV. PROB. • 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 one... | |
 | 1843 - 582 pagine
...angle, and one of the other sides of a triangle are given ; construct it. 4. 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... | |
 | 1844 - 688 pagine
...this line makes with 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.... | |
 | Euclid, James Thomson - 1845 - 382 pagine
...Therefore the triangles 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... | |
 | Euclid - 1845 - 218 pagine
...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... | |
 | Euclides - 1845 - 546 pagine
...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... | |
 | Scottish school-book assoc - 1845 - 444 pagine
...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... | |
 | Euclides - 1846 - 272 pagine
...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.... | |
 | Euclid, John Playfair - 1846 - 334 pagine
...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 - 292 pagine
...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... | |
| |
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. 
