 | Daniel Cresswell - Geometry - 1816 - 294 pages
...proposition, of the first Book of Euclid's Elements. (Art. 99.) PROP. XI. (99.) Theorem. If two spherical triangles have the three angles of the one equal to the three angles of the other, each to each, the three sides of the one shall, also, be equal to the three sides of the other, each... | |
 | Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...which has the greater surface shall have the 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... | |
 | Daniel Cresswell - Geometry - 1819 - 486 pages
...therefore, that DAB is the triangle which was to be 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 fall from the right angle... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...C, the angle В А С is likewise equal to the ande EDF. Therefore, &c. PROP. 16. If two spherical triangles have the three angles of the one equal to the three angles of the other, each to each, they shall likewise have the three sides of the one equal to the three sides of the othrr,... | |
 | Mathematics - 1835 - 684 pages
...А' С, the angle BAG is likewise equal to the angle ED F. Therefore, &c. PROP. 1C. If two spherical triangles have the three angles of the one equal to the three angles of the other, each to each, they shall likewise have the three sides of the one equal to the three sides of the other,... | |
 | James Hamblin Smith - Trigonometry - 1870 - 286 pages
...given, we cannot determine the sides, because an infinite number of triangles may be constructed with the three angles of the one equal to the three angles of the other, each to each. 173. "We shall denote the angles of a triangle by the letters A, Б, C ; the sides respectively... | |
 | David Mair - Mathematics - 1907 - 412 pages
...of the following forms : — 158 two sides in the same ratio. For example, in Fig. 7 AD/AB = AE/AC. If two triangles have the three angles of the one equal to the three angles of the other, corresponding sides of the two triangles have the same D B ratio. For example, in Fig. 8, in which... | |
 | Mathematics - 1915 - 830 pages
...translation. There is, however, one case presenting a striking difference. On S, if two triangles have three angles of the one equal to the three angles of the other, the triangles are either symmetric or congruent; in P they are merely similar. Corresponding to these several cases of congruence,... | |
 | Mabel Sykes, Clarence Elmer Comstock - Geometry, Modern - 1918 - 576 pages
...122. THEOREM 91 . If two spherical triangles on the same or on congruent spheres have three angles of one equal to the three angles of the other, the triangles are either congruent or symmetric. Analysis: To prove &ABC congruent or symmetric to AA'B'C', prove their polars congruent or symmetric.... | |
 | Mabel Sykes, Clarence Elmer Comstock - Geometry, Solid - 1922 - 236 pages
...122. THEOREM 91. If two spherical triangles on the same or on congruent spheres have three angles of one equal to the three angles of the other, the triangles are either congruent or symmetric. Analysis: To prove AABC congruent or symmetric to AA'B'C', prove their polars congruent or symmetric.... | |
| |
В А С is equal to the angle В А' С, the angle BAG is likewise equal to the angle ED F. Therefore, &c. PROP. 1C. If two spherical triangles have the three angles of the one equal to the three angles of the other, each to each... 