| Euclides - 1826 - 226 pages
...to FE so is вс to FE, therefore the parallelogram AB is equal to PROPOSITION XV. THEOREM. If equal **triangles have one angle of the one equal to one angle of the other,** the sides about the equal angles are reciprocally proportional; and if triangles have one angle of... | |
| Euclid - 1826 - 236 pages
...the parallelogram ac.d Therefore if equal parallelograms, &C. QED PROPOSITION XV. THEOREM. If equal **triangles have one angle of the one equal to one angle of the other,** the sides about the equal angles are reciprocally proportional ; and if triangles have one angle of... | |
| John Playfair - Circle-squaring - 1826 - 326 pages
...a mean proportional DB is found. Whieh was to be done. PROP. XIV. THEOR. Equal parallelograms whieh **have one angle of the one equal to one angle of the** pther, have their sides about the equal angles reeiproeally proportional : And parallelograms whieh... | |
| Robert Simson - Trigonometry - 1827 - 546 pages
...parallelogram BC. Therefore equal pa- * 9' 5rallelograms, &c. 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 whichhave one angle... | |
| John Playfair - Geometry - 1829 - 210 pages
...Wherefore, if the sides &c. QED PROPOSITION VI. THEOREM. If two triangles have one angle of one triangle **equal to one angle of the other, and the sides about the equal angles** proportional, the triangles will he equiangular, and will have those angles equal which are opposite... | |
| Pierce Morton - Geometry - 1830 - 584 pages
...angles reciprocally proportional, are equal to one another; and, conversely, equal triangles, which **have one angle of the one equal to one angle of the other,** have the sides about the equal angles reciprocally proportional . 66 (j) Two triangles are similar,... | |
| John Martin Frederick Wright - Astronomy - 1831 - 282 pages
...Ratios that are the same to the same ratio, are the same to one another. 13. 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. M. In a plane triangle, of which... | |
| John Playfair - Euclid's Elements - 1833 - 346 pages
...the triangle ABC is equiangular to the triangle DEF. Wherefore, if two triangles, &c. QED PROP. VII. **THEOR. If two triangles have one angle of the one equal to one angle of** tJie other, and the sides about two other angles proportionals, then, if each of the remaining angles... | |
| 1834 - 574 pages
...: A b, that is, A c : A 6 : : A" E": A" F". Now it is demonstrated in treatises on geometry,* that **if two triangles have one angle of the one equal to...about the equal angles proportionals, the triangles** are equiangular, and consequently similar ; we have seen that the two triangles A bc, A" F'E" are so... | |
| John Playfair - Euclid's Elements - 1835 - 336 pages
...and the angle at A to the angle at D. Therefore the triangle ABC is equiangular to the triangle DEF. **PROP. VI. THEOR. If two triangles have one angle of...equal angles proportionals, the triangles shall be** eo/uiangulart and shall have those angles equal which are opposite to the homologous sides. Let the... | |
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