 | Henry Raper - Nautical astronomy - 1908 - 1018 pages
...than a semicircle or 180". In every spherical triangle the greater side is opposite the greater angle. The sum of the three sides of a spherical triangle is less than 360°. The sum of the three angles of a spherical triangle is greater than two right angles and less... | |
 | Arthur Graham Hall, Fred Goodrich Frink - Trigonometry - 1910 - 204 pages
...restated without proof : The sum of any two sides of a spherical triangle is greater than the third side. The sum of the three sides of a spherical triangle is less than 360°. The triangle may have one, two, or three sides greater than 90°. The sum of the three angles... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Solid - 1911 - 208 pages
...COROLLARY 1. The sum of two sides of a spherical triangle is greater than the third side. 229. COROLLARY 2. The sum of the three sides of a spherical triangle is less than a great circle. Proof: AC A' +ABA'= a great circle. But AC < ACA' and AB < ABA', and 'BC < liA' + CA'... | |
 | Carolyn Soward Armentrout - 1925 - 116 pages
...triangle, (see Figure 20)« bet а'Ъ'с' Ъе the sides of the polar triangle. Then, since we Know that the sum of the three sides of a spherical triangle is less than the circumference of a great circle, we Know that a' + b1 + 2 < 2 тт. But we also knew that a1 = IT- A , Ъ1 = ir- В , с' = ir- С.... | |
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The sum of the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle; produce the sides AB, AU, till they meet again in D. 
