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. The Element of Geometry - Seite 64von John Playfair - 1836 - 114 SeitenVollansicht - Über dieses Buch
| Andrew Bell - 1837 - 290 Seiten
...lines AB, BC, a mean proportional DB is found. 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 parallelograms that have one... | |
| Charles Reiner - 1837 - 246 Seiten
...angles of the one are equal to the angles of the other, each to each. M. — Draw two triangles having one angle of the one equal to one angle of the other. P. — Let the angle bac be equal to the angle e df. ? M. — If the angle bac be equal to the angle... | |
| John Playfair - 1837 - 332 Seiten
...other, have their sides about the equal angles reciprocally proportional : And pa allelograms which have one angle of the one equal to one angle of the ot/ier, and their sides about the equal angles reciprocally proportional, are equal to one another.... | |
| Robert Simson - 1838 - 434 Seiten
...Therefore the triangle ABC is equiangular to the triangle DEF. Wherefore, if two triangles, &c, (JED PROP. VII. THEOR. IF two triangles have one angle...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,... | |
| Euclides - 1838 - 264 Seiten
...mean proportional DB is found. Which was to be done. PROP. XIV. THEOR. Equal parallelograms, which have one angle of the one equal to one angle of the other, ham their sides about the equal angles reciprocally proportional : and parallelograms that have one... | |
| Euclides - 1840 - 82 Seiten
...shall be equiangular, and shall have those angles equal which are opposite to the homologous sides, PROP. VII. THEOR. If two triangles have one angle...equal to one angle of the other, and the sides about two other angles proportional; then, if the remaining angles be each either less or not less than a... | |
| Euclides - 1841 - 378 Seiten
...the parallelogram BC. Therefore equal parallelograms, &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 triangle* which have one angle... | |
| Euclides - 1842 - 316 Seiten
...parallelogram в c. Therefore equivalent parallelograms, &c. QED PROP. XV. THEOR. EQUIVALENT 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... | |
| John Playfair - 1842 - 332 Seiten
...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 Seiten
...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... | |
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