 | 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... | |
 | Physics - 1828 - 524 pages
...together equal to two right angles. 81. If two triangles have one angle in one equal to one angle in the other, and the sides about the equal angles proportionals,...equal which are opposite to the homologous sides. 82. Find the angles which the sides of a regular pentagon make with each other. 83. In any triangle... | |
 | 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 - 1832 - 356 pages
...triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROP. VI. THEOR. If two triangles have one angle of the one equal to...homologous sides. Let the triangles ABC, DEF have the angle BAG in the one equal to the angle EDF in the other, and the sides about those angles propdrtionals;... | |
 | John Playfair - Euclid's Elements - 1833 - 348 pages
...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... | |
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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. 
