 | 1834 - 578 σελίδες
...: 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 σελίδες
...are subtended by the equal sides (1. 1.). Wherefore the angle DFE is equal to the angle GFE, and EOF to EGF : and because the angle DEF is equal to the...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 - 1837 - 290 σελίδες
...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... | |
 | Charles Reiner - 1837 - 246 σελίδες
...angles of the one are equal to the angles of the other, each to each. M. — Draw two triangles having one angle of the one equal to one angle of the other. P. — Let the angle bac be equal to the angle e df. ? M. — If the angle bac be equal to the angle... | |
 | Robert Simson - 1838 - 434 σελίδες
...the triangle ABC is equiangular to the triangle DEF. Wherefore, if two triangles, &c, (JED PROP. VII. THEOR. 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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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. 
