 | Euclides - 1863 - 122 pages
...angle EDF (H,,p.') Therefore the remaining angle at B is equal to the remaining angle at E (I. 32); and the triangle ABC is equiangular to the triangle DEF. Wherefore, if two triangles, &c. QED (V. 11); and ED is equal to DG (V. 9). PEOP. VII. (THEonEM.)—If two triangles (ABC and DEF) have... | |
 | Euclides - 1864 - 448 pages
...same reason, the angle A CB is equal to the angle DFE, and the angle at A equal to the angle at D : therefore the triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROPOSITION VI. THEOREM. If two triangles have one angle of the one equal to one... | |
 | Euclides - 1865 - 402 pages
...equiangular, and shall have those angles equal which are opposite to the homologous sides. Prop. 7. If two triangles have one angle of the one equal to one angle of tha other, and the sides about two other angles proportionals ; then, if each of the remaining angles... | |
 | Robert Potts - 1865 - 528 pages
...same reason, the angle A CB is equal to the angle DFE, and the angle at A equal to the angle at D : therefore the triangle ABC is equiangular to the triangle DEF. "Wherefore, if the sides, &c. QED PROPOSITION VL THEOREM. If two triangles hare one angle of the one equal to one... | |
 | James Robert Christie - Mathematics - 1866 - 428 pages
...the other have their sides about the equal angles reciprocally proportional: and parallelograms that have one angle of the one equal to one angle of the other and their sides about the equal angles reciprocally proportional are equal to one another. CO-ORDINATE... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...same reason, the angle ACB is equal to the angle DFE, and the angle at A is equal to the angle at D. Therefore the triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides &c. QED PROPOSITION C. THEOREM. If two triangles have one angle of the one equal to one angle... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...same reason, the angle ACB is equal to the angle DFE, and the angle at A is equal to the angle at D. Therefore the triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides &c. QED PROPOSITION a. THEOREM. If two triangles have one angle of the one equal to one angle... | |
 | Edinburgh univ - 1868 - 336 pages
...by the segments of the other. 4. To inscribe a circle in a given triangle. 5- 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. 6. Find the continued product of... | |
 | Mathematics - 1868 - 272 pages
...joining the point P to the points A and B cut a line in the points a, /3. The areas of triangles which have one angle of the one equal to one angle of the other, have to one another the ratio which is compounded of the ratios of the sides. Applying this to the... | |
 | E. M. Reynolds - Geometry - 1868 - 172 pages
...; Therefore ABC is equiangular to A'B'C'. Relation of Areas of Figures. THEOREM VI. Triangles which have one angle of the one equal to one angle of the other, are to each other as the products of the sides containing the equal angle. Let the triangles ABC, A'BC'... | |
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If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides. 
