| 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 : : AC : AF,... | |
| James Hayward - Geometry - 1829 - 218 pages
...order, and 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... | |
| Pierce Morton - Geometry - 1830 - 584 pages
...side (r). 3. The three sides (/). 4. Two angles, and a side opposite to one of them . »r. 14 5. Au **angle of the one equal to an angle of the other, and the sides** about two other angles, each to each, and the remaining an;;!« of the same affection, or one of them... | |
| Mathematics - 1835 - 684 pages
...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, or one of them... | |
| Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...three partial triangles DER, DFR, and EFR, and in (fig. 8.) is the difference between DER and the surn **of the other two triangles. 86. Lemma. If two triangles...sides which include the angle in one triangle are** supplements of those which include it in the other triangle ; the sum of the surfaces of the two triangles... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...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 the angles A and... | |
| Benjamin Peirce - Geometry - 1837 - 216 pages
...all triangles, which are equilateral or equiangular with respect to each other, are equivalent. 467. **Lemma. If two triangles have an angle of the one equal...sides which include the angle in one triangle are** supplements of those which include it in the other triangle ; the sum of the surfaces of the two triangles... | |
| Euclid - Geometry - 1837 - 410 pages
...which exhibits the subject in a different, and in some respects, a preferable light. Triangles which **have an angle of the one equal to an angle of the other,** are proportional to the rectangles contained by the sides about those angles : and (2.) equiangular... | |
| Adrien Marie Legendre - Geometry - 1838 - 386 pages
...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,... | |
| Euclides - 1840 - 194 pages
...of the other, have the sides about the equal angles reciprocally proportional : and, triangles which **have an angle of the one equal to an angle of the other, and the sides** about the equal angles reciprocally proportional, are equal. Let the triangles be so placed that the... | |
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