 | 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
...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
...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
...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
...proportional DB is found : which was to be done.* PROP. XIV. THEOR. EQUAL parallelograms which have an angle of the one equal to an angle of the other, have their sides about those angles reciprocally proportional : and (2.) parallelograms which have... | |
 | Euclides - 1840 - 82 pages
...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... | |
 | Euclides - 1840 - 192 pages
...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... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...proportional to the sides FG, GH, so that AB:FG::BC:GH. It follows from this, that the triangles AB C, FGH, having an angle of the one equal to an angle of the other, and the sides about the equal angles proportional, are similar (208) ; consequently the angle BCA=... | |
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...(by -the Corollary to the last Proposition) similar. PROP. XVII. THEOREM. Two triangles, which have an angle of the one. equal to an angle of the other, and the sides about the equal angles proportional, are similar. In the triangles ABC, DEF, let the... | |
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Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. 
