 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 - Page 64by John Playfair - 1836 - 114 pagesFull view - About this book
 | John Playfair - 1819 - 354 pages
...Therefore the triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides, &c. Q, ED PROP. VI. THEOR. If two triangles have one angle of the one equal to one angle of the oiker, and the sides about the equal angles proportionals, the triangles shall be equiangular, and... | |
 | John Playfair - Circle-squaring - 1819 - 348 pages
...oiher, have their sides about the equal angles reciprocally proportional : And parallelograms which 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. Let AB, BC... | |
 | Euclid, Robert Simson - Geometry - 1821 - 514 pages
...triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides, &e. QED D PROP. VI. THEOR. IP two triangles have one angle of the one equal to one...of the other, and the sides about the equal angles Eroportionals, the triangles shall be equiangular, and shall ave those angles equal which are opposite... | |
 | Peter Nicholson - Mathematics - 1825 - 1058 pages
...parallelogram BC. Therefore equal ograms, Лес. Q. E, D. PROP. XV. THEOR. Equal triangles nhich have have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : And triangles nhich have one angle... | |
 | Euclid - 1826 - 234 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... | |
 | 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... | |
 | George Lees - 1826 - 276 pages
...the other, have their sides about the equal angles reciprocally proportional ; and triangles which have one angle of the one equal to- one angle of the other, and their sides about the equal angles reciprocally proportional, are equivalent. Let the triangles be... | |
 | 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... | |
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