 | 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
...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... | |
 | 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...about the equal angles proportionals, the triangles are equiangular, and consequently similar ; we have seen that the two triangles A bc, A" F'E" are so... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...and the angle at A to the angle at D. Therefore the triangle ABC is equiangular to the triangle DEF. PROP. VI. THEOR. If two triangles have one angle of...equal angles proportionals, the triangles shall be eo/uiangulart and shall have those angles equal which are opposite to the homologous sides. Let the... | |
 | 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
...to DFE, 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 sides about the equal angles proportionals ; the remaining angles are equal, each to each, viz., those which are opposite to the homologous sides. Let... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...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... | |
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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. 
