| Timothy Walker - Geometry - 1829 - 158 pages
...vertices by the space of a quadrant, the sides will become parallel each to each. 3. — When they **have an angle of the one equal to an angle of the other,** and the sides including these angles proportional. Thus if the angle A = A (fig. 45), and if AB : AD... | |
| James Hayward - Geometry - 1829 - 218 pages
...suppress , BD . ... ABC ABXAC the common factor =-, we snail have —AE~V~AF' That is — If two triangles **have an angle of the one equal to an angle of the other,** their areas will be as the products of the sides containing the equal angles. Fig. 94. 17o if we take... | |
| John Playfair - Geometry - 1829 - 186 pages
...the ratio which is compounded of the ratios of their sides about the equal angles ; " that is, they **are to one another as the rectangles contained by the sides about** the equal angles.." Let AC, CF be two equiangular parallelograms, having the angle BCD equal to ECG;... | |
| Mathematics - 1835
...interjacent side (c). 3. The three sides (/). 4. Two angles, and a side opposite to one of them . cor. 14 5. **An angle of the one equal to an angle of the other,** and the sides about two other angles, each to each, and the remaining angles of the same affection,... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...properties of triangles include, by implication, those of all figures. PROPOSITION XX. THEOREM. Two **triangles, which have an angle of the one equal to an angle of the other,** and the sides containing those angles proportional are similar, In the two triangles ABC, DEF, let... | |
| Benjamin Peirce - Spherical trigonometry - 1836 - 92 pages
...8.) is the difference between DER and the sum of the other two triangles. 86. Lemma. If two triangles **have an angle of the one equal to an angle of the other** ; and the sides which include the angle in one triangle are supple- 1887) ments of those which include... | |
| Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...is the difference between DER and the surn of the other two triangles. 86. Lemma. If two triangles **have an angle of the one equal to an angle of the other** ; and the sides which include the angle in one triangle are supplements of those which include it in... | |
| Euclid - Geometry - 1837 - 410 pages
...parallelogram AB is equal to the parallelogram BC. Therefore equal parallelograms, &c. PROP. XV. THEOR. EQUAL **triangles which have an angle of the one equal to an angle of the other,** have their sides about those angles reciprocally proportional : and (2.) triangles which have an angle... | |
| Benjamin Peirce - Geometry - 1837 - 216 pages
...equilateral or equiangular with respect to each other, are equivalent. 467. Lemma. If two triangles **have an angle of the one equal to an angle of the other** ; and the sides which include the angle in one triangle are supplements of those which include it in... | |
| Adrien Marie Legendre - Geometry - 1838 - 386 pages
...properties of triangles include, by implication, those of all figures. PROPOSITION XX. THEOREM. Two **triangles, which have an angle of the one equal to an angle of the** oiher, and the sides containing those angles proportional, are similar. In the two triangles ABC, DEF,... | |
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