 | Euclides - 1834 - 518 σελίδες
...is equiangular to the triangle DEF. Wherefore, if the sides, &c. <?. /.•./,. ' n. . 'PROPOSITION VI. THEOR. — If two triangles have one angle of...be equiangular, and shall have those angles equal which are opposite to the funuologous sides. Let the triangles ABC, DEF have the angle BAC in the one,... | |
 | 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... | |
 | Robert Simson - 1835 - 544 σελίδες
...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...be equiangular, and shall have those angles equal which are opposite to the homologous sides. Let the triangles ABC, DEF have the angle BAC in the one... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | John Playfair - 1837 - 332 σελίδες
...other, have their sides about the equal angles reciprocally proportional : And pa allelograms which have one angle of the one equal to one angle of the ot/ier, and their sides about the equal angles reciprocally proportional, are equal to one another.... | |
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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. 
