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" The sum of any two sides is greater than the third side, and their difference is less than the third side. "
A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ... - Page 74
by Francis Nichols - 1811 - 128 pages
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Epitome of the Art of Navigation; Or, a Short, Easy, and Methodical Way to ...

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...
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Epitome of the Art of Navigation: Or, A Short, Easy and Methodical Way to ...

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...
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A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ...

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...
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A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ...

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...
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Dictionary of the Mathematical and Physical Sciences, According to the ...

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...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

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...
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A Synopsis of the Principal Formulae and Results of Pure Mathematics

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...
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The Elements of Spherical Trigonometry

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...
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A Treatise on Special, Or Elementary Geometry

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...
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A Treatise on Special Or Elementary Geometry

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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