 | Mathematics - 1868 - 276 pages
...the point P to the points A and B cut a line in the points a, /3. The areas of triangles which have one angle of the one equal to one angle of the other, have to one another the ratio which is compounded of the ratios of the sides. Applying this to the... | |
 | Robert Potts - 1863 - 482 pages
...produced. Also describe a circle touching three sides of a parallelogram. 6. 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, triangle shall be equiangular, and shall have those angles equal... | |
 | Euclides - 1864 - 448 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 reciprocallg proportional : and converselg, triangles which... | |
 | Robert Potts - 1865 - 528 pages
...BC, & mean proportional DB is iound. QBF PROPOSITION XIV. THEOREM. Equal parallelograms which have one angle of the one equal to one angle of the other, hate their sides about the equal angles reciprocally proportional: and conversely, parallelograms that... | |
 | Euclides - 1865 - 402 pages
...BO. (v. 9.) Therefore equal parallelograms, &c. QED PROP. 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... | |
 | James Robert Christie - Mathematics - 1866 - 428 pages
...described about a circle are together equal to the other two opposite sides. 5. 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 &c. 6. If two planes which... | |
 | Mathematical association - 1883 - 86 pages
...those sides which are opposite to the equal angles are homologous. THEOR. 3. If two triangles have one angle of the one equal to one angle of the other and the sides about these angles proportional, they are similar, and those angles which are opposite to the homologous... | |
 | University of Glasgow - 1883 - 438 pages
...together make up a right angle. 4. Inscribe u circle in a given triangle. 5. Parallelograms that have one angle of the one equal to one angle of the other, and their, sides about the equal angles reciprocally proportional, are equal to one another. 6. Simplify... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...AB, BC, a mean proportional DB is found. QEF PROPOSITION 14. 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 parallelograms which have one... | |
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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. 
