| John Bonnycastle - Trigonometry - 1806 - 419 pages
...is opposite to the greater angle, and the less side to the less angle. 3. The sum of any two sides **is greater than the third side ; and their difference is less than the third side.** 4. The difference of any two sides is less than 180°; and the sum of the three sides is less than... | |
| Francis Nichols - Plane trigonometry - 1811 - 128 pages
...is opposite to the greater angle, and the less side to the less angle. 27. The sum of any two sides **is greater than the third side, and their difference is less than the third side.** 28. The difference of any two sides is less than 180°, or a semicircle; and the sum of the three sides... | |
| John Bonnycastle - Trigonometry - 1818 - 438 pages
...the greater angle, and the less side to the less angle. 3. The sum of any two sides of a spherical **triangle, is greater than the third side ; and their difference is less than the third side.** 4. The difference of any two sides of a spherical triangle is less than a semicircle, or 180°; and... | |
| James Mitchell - Mathematics - 1823 - 576 pages
...spherical triangle is less than a semicircle, or 180°. 3. The sum of any two sides of a spherical **triangle is greater than the third side; and their difference is less than the third side.** 4. The dilference of any two Aides of a spherical triangle is less than a semicircle, or ISO9 ; and... | |
| James Hann - Spherical trigonometry - 1849 - 68 pages
...less than 90°, all equal to 90°, or all greater than 90°, and vice versa. The sum of any two sides **is greater than the third side, and their difference is less than the third side.** The sum of any two angles is greater than the supplement of the third angle. The sum of the three sides... | |
| Industrial arts - 1849
...to the notice of the reader, tne author remarks, that " Euclid has demonstrated that tho sum of any **two sides of a triangle is greater than the third side ; and** from this proposition Mr. Simpson has solved the very useful problem of finding a point in a line given... | |
| Perry Fairfax Nursey - Industrial arts - 1849
...to the notice of the reader, the author remarks, that " Euclid has demonstrated that the sum of any **two sides of a triangle is greater than the third side ; and** from this proposition Mr. Simpson has solved the very useful problem of finding a point in a line given... | |
| Euclides - 1860
...triangles AGC, PGB, are equal; that is, angle A = BPG (I. 32, Cor. 3) = FPE (I. 15). EXERCISE XXII. — **THEOREM. The sum of two sides of a triangle is greater than** twice the line joining the vertex and the middle of the base. Let ABC be a triangle, and CO the line... | |
| Archibald Sandeman - Algebra - 1868 - 464 pages
...EF whereof no adjoining two are in one straight line and AC AD AE AFbe joined the line ABC made up **of two sides of a triangle is greater than the third side** AC therefore to each putting CD ABCD>ACD but A CD either is AD to wit if AC CD be in one straight line... | |
| Edward Olney - Geometry - 1872 - 239 pages
...manner as to plane triangles. PROPOSITION XI. 569. Theorem.— The sum of any two sides of a spherical **triangle is greater than the third side, and their difference is less than the third side.** DEM.— Let ABC be any spherical triangle; then l3 BO' < BA + AC, and BC - AC < BA ; and the same is... | |
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