| John Playfair - Euclid's Elements - 1833 - 333 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
...: 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 - 316 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 - 513 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
...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 - 114 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 - 472 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 - 390 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 - 240 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... | |
| Charles Reiner - Geometry - 1837 - 215 pages
...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... | |
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