| James Atkinson - Navigation - 1765 - 504 pages
...Angle god. Note i. In every Spheric Triangle, each Side is Jefs than a Semi-circle, or 1 80 Degrees. 2. **The Sum of any two Sides is greater than the third Side.** 3. The three Sides added together, their Sum is lefs than 360 Degrees. 4. The Sum of the three Angles... | |
| James Atkinson - Navigation - 1770 - 514 pages
...Angle god. Nate i. In every Spheric Triangle, each Side is lefs than a Semi-circle, or 180 Degrees. 2. **The Sum of any two Sides is greater than the third Side.** 3. The three Sides added together, their fum is lefs than 360 Degrees. 4. The Sum of the three Angles... | |
| John Bonnycastle - Trigonometry - 1806 - 464 pages
...180°. 2. The greater side 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...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... | |
| John Bonnycastle - Trigonometry - 1818 - 488 pages
...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 - 666 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... | |
| Peter Nicholson - Mathematics - 1825 - 1046 pages
...one above, and the other below the center of the spheie. But we know that in any right-lined triangle **the sum of any two sides is greater than the third side.** Therefore in any spherical triangle ABC, the sum of any two arcs is also 'greater than the third arc... | |
| Charles Brooke - Mathematics - 1829 - 386 pages
...sum of the three sides is always < 360°. The sum of the three angles is always > 180°, and < 540°. **The sum of any two sides is greater than the third side.** The angles at the base of an isosceles spherical triangle aré equal ; and conversely. The greater... | |
| James Hann - Spherical trigonometry - 1849 - 82 pages
...will be accordingly all less than 90°, all equal to 90°, or all greater than 00°, and vice versa. **The sum of any two sides is greater than the third...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... | |
| Edward Olney - Geometry - 1872 - 472 pages
...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... | |
| Edward Olney - 1872 - 270 pages
...to plane triangles. PROPOSITION XL 569. Theorem.—The sum of any two sides of a spherieal triangle **is greater than the third side, and their difference is less than the third side.** DEM.—Let ABC be any spherical triangle; then is BC < BA + AC, and BC - AC < BA; and the same is true... | |
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