 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...two similar figures. 203. CoroUary. In order to be similar, it is sufficient that two triangles have two angles of the one respectively equal to two angles of the other ; for then the third angles will be equal and the two triangles will be equiangular. 5204. Scholium.... | |
 | Euclides - 1821 - 294 pages
...the adjacent internal atig Z= to two right angles, (by the 13th.) .-. &c. •jy two triangles have two angles of the one respectively equal to two angles of the other, and a side of the one equal to a side of the other, whether it be adjacent or opposite to these equal angles,... | |
 | John Farrar - Logarithms - 1822 - 270 pages
...the angle OT'S' is equal to OT*, and consequently equal to OEF. Therefore the triangles EX&, T'xF, having two angles of the one respectively equal to two angles of the other, are similar ; whence Ex : xT' :: S'x : xF, and S'xx xT' = Ex x xF. "BvAEx, xF, xy, being radii of the... | |
 | Adrien Marie Legendre - Geometry - 1825 - 276 pages
...two similar figures. 203. Corollary. In order to be similar, it is sufficient that two triangles have two angles of the one respectively equal to two angles of the other ; for then the third angles will be equal ahd the two triangles will be equiangular. 204. Scholium.... | |
 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...includes the twentieth proposition. PROPOSITION XXVI. THEOREM. (105) If two triangles (BAC, DEF) have two angles of the one respectively equal to two angles of the other (B to D and C to F), and a side ot the one equal to a side of the other similarly placed with respect... | |
 | John Farrar - Trigonometry - 1833 - 274 pages
...OTS' is equal to i . K*fi ^: OTS, and consequently equal to OEF. Therefore the triangles ExS', TxF, having two angles of the one respectively equal to two angles of the other are similar ; whence Ex : xT : : S'x : xF, and S'x X xT = Ex X xF, t Suppose a straight line Ff drawn... | |
 | John Farrar - Trigonometry - 1833 - 276 pages
...the angle OT'S' is equal to OTS, and consequently equal to OEF. Therefore the triangles ExS', T'xF, having two angles of the one respectively equal to two angles of^ the other are similar ; whence Ex : xT : : S'x : xF, and S'x X xT = Ex X xF, But Ex, xF, xy, being radii of the... | |
 | Benjamin Peirce - Geometry - 1837 - 216 pages
...173. Corollary. Hence, and from art. 66, it follows that two triangles are similar, when they have two angles of the one respectively equal to two angles of the other. 174. Corollary. Two right triangles are similar, when they tiave an acute angle of the one equal to... | |
 | Euclides - 1840 - 82 pages
...greater than the angle subtended by the less base of the other. PROP. XXVI. THEOR. If two triangles have two angles of the one respectively equal to two angles of the other, and also a side in the one equal to a side similarly situated in the other, that is to say, either lying... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...two similar figures. 203. Corollary. In order to be similar, it is sufficient that two triangles have two angles of the one respectively equal to two angles of the other ; for then the third angles will be equal, and the two triangles will be equiangular. 204. Scholium.... | |
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If two triangles have two angles of the one respectively equal to two angles of the other, the third angles are equal. 
