| Adrien Marie Legendre - Geometry - 1874 - 455 pages
...to be proved. PROPOSITION IX. THEOREM. If two spherical triangles on the same, or on equal spheres, **have two angles and the included side of the one equal...the included side of the other, each to each, the** remaining parts will be equal, each to each Let the spherical triangles ABC and EFG, have the angle... | |
| B. Marks - 1875
...a parallelogram, the interior alternate angles r and m are equal. Then the two triangles adb, bdc, **have two angles and the included side of the one equal...and the included side of the other, each to each,** and are therefore equal; And the side ab opposite the angle m is equal to the side cd opposite the... | |
| Aaron Schuyler - Measurement - 1875 - 184 pages
...angle COR is equal to the angle COR', since each is a right angle. Hence, the two triangles COR and COR **have two angles, and the included side of the one...and the included side of the other, each to each,** and are therefore equal in all their parts. Hence, OR, opposite the angle OCR, is equal to OR'. opposite... | |
| William Guy Peck - Conic sections - 1876 - 366 pages
...GEOMETRY. PROPOSITION VIII. THEOREM. If two spherical triangles have two angles and the included side of **one, equal to two angles and the included side of the other, each to each,** their remaining parts are equal, each to each. Let FGH and ACD be two spherical triangles, in which... | |
| Edward Olney - Geometry - 1876 - 239 pages
...on equal spheres, two sphev'cal triangles having two angles and the included side of the one eqval **to two angles and the included side of the other, each to each,** areequal, or symmetrical and equivalent. DEM.—Using the same triangles as in the preceding proposition,... | |
| Elias Loomis - Geometry - 1877 - 443 pages
...the included angle of the one equal to two sides and the included angle of the other each to each, or **two angles and the included side of the one equal to two angles and the included side of the other.** PROPOSITION XV. TIIEOREM. In an isosceles spherical triangle, the angles opposite the equal sides are... | |
| Thomas Hunter - 1878
...sides. If perpendiculars be let fall from any point, two right-angled triangles will be formed having **two angles and the included side of the one equal...and the included side of the other, each to each.** 5. The circle ABD is described upon the radius AB of the circle AEC: it is required to prove that the... | |
| Isaac Sharpless - Geometry - 1879 - 266 pages
...&ABC= &DEF ABG=DEF Proposition 8. Theorem.—If two triangles have two angles and the included side of **one, equal to two angles and the included side of...each, the triangles will be equal in all their parts.** DEF, DFE, and the side EF. The triangles will be equal in all their parts. Apply the triangle ABC to... | |
| Edward Olney - Geometry - 1879 - 440 pages
...angle E, and that the areas are equaL Fio. 204. PROPOSITION VH. 286. Theorem. — Two triangles which **have two angles and the included side of the one equal to two angles and** tlie included side of the other, each to each, are equal. ^ Pro. 805. DEM.— Let ABC and DEF be two... | |
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