| 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... | |
| 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,... | |
| Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...and in (fig. 8.) 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... | |
| Benjamin Peirce - Spherical trigonometry - 1836 - 92 pages
...EFR, and in (fig. 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... | |
| Adrien Marie Legendre - Geometry - 1836 - 394 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... | |
| Benjamin Peirce - Geometry - 1837 - 216 pages
...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 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, James Thomson - 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 - 382 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 - 192 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... | |
| Euclides - 1840 - 82 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. PROP. XVI. THEOR. If four... | |
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