 | Daniel Cresswell - Geometry - 1816 - 352 pages
...spheres. (226.) COR. If the three angles of the one, of two spherical triangles, on different spheres, be equal to the three angles of the other, each to each, and if the sides of the triangles be also similarly posited, the triangles are proportional to the squares... | |
 | Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...greater perimeter. PROP. XXVI. (xiv.) If two right-angled triangles have the three angles of the one equal to the three angles of the other, each to each, and if a side of the one be equal to the perpendicular let fall from the right angle upon the hypotenuse... | |
 | Daniel Cresswell - Geometry - 1819 - 446 pages
...constructed. PROP. XVI. 24. THEOREM. If two right-angled triangles have the three angles of the one equal to the three angles of the other, each to each, and if a side of the one be equal to the perpendicular let fail from the right angle upon the hypotenuse... | |
 | Charles William Hackley - Geometry - 1847 - 248 pages
...spherical triangles (unlike two plane triangles in this respect) are equal when the three angles of the one are equal to the three angles of the other, each to each. For the polar triangles of the two given triangles \vill have equal sides (Prop. 6), and, consequently,... | |
 | W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...triangles having two angles of the one equal to two angles of the other, are similar triangles, because the three angles of the one triangle are equal to the three angles of the other ; therefore two rectangular triangles, having, besides the two right angles, two other equal angles,... | |
 | 1880 - 594 pages
...AD in K. Then AH, HD are parallelograms. Now in the triangles AFB, DFC, the three angles of the one are equal to the three angles of the other, each to each, and the side AB to DC ; therefore BF is equal to FD and AF to FC (I. 26). Then in the two triangles FBH,... | |
 | Euclid - Geometry - 1892 - 460 pages
...this statement two obvious exceptions must be made. (i) When in two triangles the three angles of one are equal to the three angles of the other, each to each, it does twt necessarily follow that the triangles are equal in all respects. (ii) When in two triangles... | |
 | William James Milne - Geometry, Modern - 1899 - 258 pages
...angle D, angle C = angle F, and AC = DF. Ex. 43. Are two triangles equal, if the three angles of one are equal to the three angles of the other, each to each ? Ex. 44. Can two triangles, having two sides and an angle of one respective^ equal to two sides and... | |
 | William James Milne - Geometry - 1899 - 404 pages
...angle D, angle C = angle F, and AC = DF. Ex. 43. Are two triangles equal, if the three angles of one are equal to the three angles of the other, each to each ? Proposition XX 103. 1. Draw a straight line and a perpendicular to that line at its middle point... | |
 | William James Milne - Geometry - 1899 - 326 pages
...their parts. Hence, § 36, Д ABC = Д DEF. Ex. 43. Are two triangles equal, if the three angles of one are equal to the three angles of the other, each to each ? No, not necessarily. The accompanying figure represents two triangles whose angles are equal, each... | |
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When the three angles of one are equal to the three angles of the other, each to each, the adjoining diagram shews that the triangles need not be equal in all respects. 
