 | John Playfair - Euclid's Elements - 1836 - 488 pages
...HCF is equal to KCF, and the right angle FHC equal to the right angle FKC, in the triangles FHC, FKC two angles of the one are equal to two angles of the other, and the side FC, which is opposite to one of the equal angles in each, is common to both ; therefore,... | |
 | Thomas Lund - Geometry - 1854 - 520 pages
...restricted to the ' Circle '. to BD, and BC meets them, i ACE = i DBC; .-. in the two triangles ABC, BCD, two angles of the one are equal to two angles of the other, each to each, and one side BC, viz. the side common to those angles, the same in both, .'. the triangles are equal... | |
 | Euclides - 1855 - 270 pages
...FHC and FICC are also equal, being right angles (Const.). Therefore in the two triangles FHC, FKC, two angles of the one are equal to two angles of the other, and the side FC is common to both. Wherefore, the two triangles are equal (I. 26), and FH is equal... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...are equal to two sides of the other, each to each, and the included angles are equal ; — 4th, when two angles of the one are equal to two angles of the other, each to each, and the included sides are equal. PROPOSITION XIV. If two arcs of great circles intersect each other... | |
 | Euclides - 1862 - 172 pages
...the right angle BED is equal to the right angle BFD ; (ax. 11) then, in the triangles EBD, FBD, the two angles of the one are equal to two angles of the other, each to each ; and the side BD, which is opposite to one of the equal angles in each, IM THE SCHOOL EUCLID. therefore... | |
 | Euclides - 1863 - 122 pages
...angles FHC and FKC are also equal, being right angles (Cmst.); therefore in the two triangles FHC, FKC, two angles of the one are equal to two angles of the other, and the side FC is common to both. Wherefore, the two triangles are equal (I. 26), and FH is equal... | |
 | Euclides - 1865 - 402 pages
...the right angle BED is equal to the right angle BFD ; (ax. ") then, in the triangles EBD, FBD, the two angles of the one are equal to two angles of the other, each to each ; and the side BD, which is opposite to one of the equal angles in each, U common to both ; therefore... | |
 | Richard Wormell - Geometry, Modern - 1868 - 286 pages
...ratio of similitude, and homologous sides. 2. Prove that two triangles are similar when two angles of one are equal to two angles of the other, each to each. 3. Two triangles which have their sides perpendicular or parallel, each to each, are similar. 4. Two... | |
 | Richard Wormell - Geometry, Plane - 1870 - 304 pages
...ratio of similitude, and homologous sides. 2. Prove that two triangles are similar when two angles of one are equal to two angles of the other, each to each. 3. Two triangles which have their sides perpendicular or parallel, each to each, are similar. 4. Two... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...triangle formed by joining the extremities of one non-parallel side to the middle point of the other. 57. Two triangles are similar if two angles of the one are equal respectively to two angles of the other. 58. Two triangles are similar if their homologous sides are... | |
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Similarly, by placing A A'B'C' on A AB C, so that Z B' shall coincide with its equal, ^the ZB, we may prove that AB:A'B' = BC:B'C'. QED 355. COR. 1. Two triangles are similar if two angles of the one are equal, respectively, to two angles of the other. 
