| 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.... | |
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