| Timothy Walker - Geometry - 1829 - 156 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
...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... | |
| Adrien Marie Legendre - Geometry - 1836 - 394 pages
...general 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 the angles A and D be equal... | |
| 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 it in the other... | |
| 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 the other triangle... | |
| William Grier - Mechanical engineering - 1836 - 384 pages
...angle C equal to the angle F ; then will the two triangles be identical, or equal in all respects. 2. Let the two triangles ABC, DEF, have the angle A equal to the angle D, the angle B equal to the angle E,and the side AB equal to the side DE; then these two triangle!) will... | |
| William Grier - Mechanical engineering - 1836 - 380 pages
...angle C equal to the angle F; then will the two triangles be identical, or equal iu all respects. 2. Let the two triangles ABC, DEF, have the angle A equal to the angle D, the angle B equal to the angle E,an(l the side AB equal to the side DE; then these two triangles will... | |
| 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 the other triangle... | |
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