 | Pierce Morton - 1830 - 584 páginas
...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 - 1831 - 282 páginas
...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 - 1833 - 346 páginas
...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 páginas
...: 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 - 1835 - 336 páginas
...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 the one equal to...equal angles proportionals, the triangles shall be eo/uiangulart and shall have those angles equal which are opposite to the homologous sides. Let the... | |
 | 1835 - 684 páginas
...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,... | |
 | Euclid - 1835 - 540 páginas
...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... | |
 | 1836 - 488 páginas
...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 - 1836 - 148 páginas
...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 - 1837 - 410 páginas
...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...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. 
