 | 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
...Therefore 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... | |
 | Euclides - 1834 - 518 pages
...ABC is equiangular to the triangle DEF. Wherefore, if two triangles, &c. QED PROPOSITION VII. See N. THEOR.— If two triangles have one angle of the one,...of the other, and the sides about two other angles proportionals ; then, if each of the remaining angles be either less, or not less, than a right angle,... | |
 | 1834 - 578 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 one angle of the other, and the sides about the equal angles proportionals, the triangles are equiangular, and consequently similar ; we have seen... | |
 | Robert Simson - Trigonometry - 1835 - 544 pages
...equiangular to the triangle DEF. Wherefore, " if the sides," &c. QED Book VI. PROP. VI. THEOR. v— v—' 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... | |
 | Euclid - 1835 - 540 pages
...DB is found. Which was to be done. a 11. 1. b 31. 3. PROP. XIV. THEOR. 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... | |
 | Mathematics - 1835 - 684 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 (g) Two triangles are similar,... | |
 | John Playfair - Geometry - 1836 - 148 pages
...a 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, have their sides about the equal angles reciprocally proportional ; and parallelograms that have one... | |
 | Mathematics - 1836 - 488 pages
...about the equal angles reciprocally proportional, are equal to one another. XV. 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... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...and A to D. Therefore the triangles ABC, DEF are equiangular : wherefore, if the sides, &c. PROP. VI. THEOR. 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 remaining angles are equal, each to each, viz., those which are... | |
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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. 
