 | John Playfair - Euclid's Elements - 1833 - 346 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... | |
 | Euclides - 1834 - 518 pages
...the triangle DEF. Wherefore, if the sides, &c. <?. /.•./,. ' n. . 'PROPOSITION VI. THEOR. — If two triangles have one angle of the one, equal to...have those angles equal which are opposite to the funuologous sides. Let the triangles ABC, DEF have the angle BAC in the one, equal to the angle EDF... | |
 | 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...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
...the angle at D. Therefore the triangle ABC is equiangular to the triangle DEF. PROP. VI. THEOR. If two triangles have one angle of the one equal to one...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 - Euclid's Elements - 1836 - 488 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 one...sides. Let the triangles ABC, DEF have the angle BAC in 1C Book VI. the one equal to the angle EDF in the other, and the v— ~i~— ' sides about those angles... | |
 | 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... | |
 | 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... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...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...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... | |
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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. 
