 | 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
...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... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 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 - 246 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... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...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.... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides, &e. Q,. ED PROP. VI. THEOR. IF two triangles have one angle of the one equal to...equal which are opposite to the homologous sides. Let the triangles ABC, DEF have the angle BAC in the one equal to the angle EDF in the other, and the... | |
 | Euclides - 1838 - 264 pages
...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, ham their sides about the equal angles reciprocally proportional : and parallelograms that have one... | |
 | Great Britain. Committee on Education - School buildings - 1853 - 1218 pages
...to one another. 2. About a given circle, to describe a triangle equiangular to a given triangle. 3. If two triangles have one angle of the one equal to...equal which are opposite to the homologous sides. 4. Show that straight lines, which are perpendicular to parallel straight lines, are themselves also... | |
 | Euclides - 1840 - 82 pages
...equiangular, and shall have those angles equal which are opposite to the homologous sides, 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 proportional; then, if the remaining angles be each either less or not less than a... | |
 | Euclides - 1840 - 192 pages
...the one, equal to one angle (DFE) of the other, and the sides about the equal angles proportional, the triangles shall be equiangular, and shall have...equal which are opposite to the homologous sides. From the extremities of EF, one of the sides of the triangle DEF, about the angle DFE, draw EG and... | |
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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. 
