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 shall have those angles equal which are opposite to the homologous sides. A Shorter Geometry - Page xviLimited preview - About this book
| Robert Simson - Trigonometry - 1775 - 520 pages
...is found. Which was to be done. - *' ' PROP. Book VI. PROP. XIV. THEO R. EQUAL parallelograms which **have one angle of the one equal to one angle of the other,** have their fides about the equal angles reciprocally proportional: And parallelograms that have one... | |
| Euclid - Geometry - 1776 - 264 pages
...BC : Which was to be done. PROP. XIV. and XV. THEO R. EQJJ . AL parallelograms and triangles, having **one angle of the one equal to one angle of the other,** have the ftdes about 5 the equal angles reciprocally proportional ; and thefe parallelograms and triangles... | |
| Euclid - 1781 - 520 pages
...parallelograms, &c. Q^ED PROP. Book VI. 14. r. • ..• J PRO P. XV. THEO R. QtJAL triangles which **have one angle of the one equal to one angle of the other,** have their fides >ut the equal angles reciprocally proportional : And Jangles which have one angle... | |
| John Keill - Logarithms - 1782 - 399 pages
...Angle of the other, have the Sides *ibout the equal Angles reciprocal; and tbofe Parallelograms that **have one Angle of the one equal to one Angle of the other, and the Sides** that are about the equal Angles reciprO' tal, are equal. TETAB, BC, be equal Parallelograms, having... | |
| Euclid - Euclid's Elements - 1789 - 272 pages
...DEF will be equiangular with the triangle AGH (I. 7.) or ABC, as was to be fhewn. PROP. VI. THEOREM. **If two triangles have one angle of the one equal to one angle of the other, and the** fides about the equal angles proportional, the triangles will be equiangular. Let ABC, DEF be two triangles,... | |
| John Playfair - Euclid's Elements - 1795 - 400 pages
...parallelograms, &c. a 14. i. b 7-. $• c i. 6. a ii. 5. PROP. XV. THE OR. s. .•»-*• " triangles which **have- one angle of the one equal to one angle of the other,** have their iides about the equal angles reciprocally proportional : And triangles which have one angle... | |
| Alexander Ingram - Trigonometry - 1799 - 351 pages
...parallelogram BC. Therefore equal parallelograms, Sec. Q^ ED PROP. XV. THEOR. EQUAL triangles which **have one angle of the one equal to one angle of the other,** have their fides about the equal angles reciprocally proportional : And triangles which have one angle... | |
| Robert Simson - Trigonometry - 1804
..."parallelogram BC. Therefore equal parallelograms, &c. D. Book VI. PROP. XV. THEOR. EQUAL triangles which **have one angle of the one equal to one angle of the other,** have their fides about the equal angles reciprocally proportional. and triangles which have one angle... | |
| John Playfair - Euclid's Elements - 1804 - 440 pages
...triangle DEF. Wherefore, if two triangles, fitc. Q^ ED PROP. PROP. VII. THE OR. IF two triangles have ow **angle of the one equal to one angle of the other, and the** fides about two other angles proportionals, then, if each of the remaining angles be either lefs, or... | |
| Robert Simson - Trigonometry - 1806 - 518 pages
...is equiangular to the triangle DEF. Wherefore, if two triangles, &c. QE D, PROP. VII. THEOR. See N. **IF two triangles have one angle of the one 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,... | |
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