 | 1868 - 276 Seiten
...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 Seiten
...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 Seiten
...(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... | |
 | Simon Somerville Laurie - 1865 - 432 Seiten
...ft. To inscribe an equilateral and equiangular pentagon in a given circle. 0. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proper tionals, the triangles shall be equiangular. 7. Similar polygons may be divided... | |
 | Robert Potts - 1865 - 528 Seiten
...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 Seiten
...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 - 1866 - 428 Seiten
...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 Seiten
...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 Seiten
...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 - 1883 - 428 Seiten
...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. 
