| Adrien Marie Legendre - Geometry - 1825 - 280 pages
...line AD from the vertex A to the point D the middle of the base BC ; the two triangles ABD, ADC, will **have the three sides of the one, equal to the three sides of the** qther, each to each, namely, AD common to both, AB — AC, by hypothesis, and BD = DC, by construction... | |
| Pierce Morton - Geometry - 1830 - 584 pages
...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, each to each, viz. those which are opposite to the equal angles.* Let the spherical triangles... | |
| Mathematics - 1835
...and С с ; draw P О perpendicular to Ce; and join OQ. Then, because the triangles С P с, С Q с **have the three sides of the one equal to the three sides** scribe two circles, and kt them cut one another in P; and from P draw PM perpendicular to А В : then... | |
| Benjamin Peirce - Geometry - 1837 - 216 pages
...and, by transposition, A> B+ C— 360° + 180°, or A > (B + C) — 180°, as we wished to prove. 449. **Theorem. If two spherical triangles on the same sphere, or on equal** sphere?, are equilateral with respect to each other, they are also equiangular with respect to each... | |
| Benjamin Peirce - Geometry - 1841 - 186 pages
...and, by transposition, A>^-B1C — 360° + 180°, or *9>(5+ C) — 180°, as we wished to prove. 449. **Theorem. If two spherical triangles on the same sphere, or on equal spheres,** are equilateral with respect to each other, they are also equiangular with respect to each other. Proof.... | |
| Benjamin Peirce - Geometry - 1847 - 150 pages
...by transposition, A > -f- BC — 360° + 180°, or A>(B + C)— 180°, as we wished to prove. 449. **Theorem. If two spherical triangles on the same sphere, or on equal spheres,** are equilateral with respect to each other, they are also equiangular with respect to each other. Proof.... | |
| Charles Davies - Geometry - 1850 - 236 pages
...chord, and the arc AE equal to EB. First. Draw the two radii CA, CB. Then the two triangles A CD, DCS, **have the three sides of the one equal to the three sides of the** Of the Circle. B other, each to each : viz. AC equal to CB, being radii, AD equal to DB, by hypothesis,... | |
| Charles Davies - Geometry - 1850 - 218 pages
...chord, and the arc AE equal to EB. First. Draw the two radii CA, CB. Then the two triangles A CD, DCB, **have the three sides of the one equal to the three sides of the** *Note. When reference is made from one theorem to another, in the same Book, the number of the theorem... | |
| Charles Davies - Geometry - 1855 - 336 pages
...chord, and the arc AE equal to EB- ^ First- Draw the two radii CA, CBThen the two triangles A CD, DCB, **have the three sides of the one equal to the three sides of the** *Note- When reference is made from one theorem to another, in the same Book, the number of the theorem... | |
| 1873 - 164 pages
...that similar prisms, or pyramids, are to each other as the cubes of their altitudes. 5. Prove that **if two spherical triangles on the same sphere, or on equal spheres,** are equilateral with respect to each other, they are also equiangular with respect to each other. LOGARITHMS... | |
| |