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" Each side of a spherical triangle is less than the sum of the other two sides. "
Chauvenet's Treatise on Elementary Geometry - Page 280
by William Chauvenet, William Elwood Byerly - 1887 - 322 pages
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Elements of Plane and Spherical Trigonometry: With Its Applications to the ...

John Radford Young - Astronomy - 1833 - 308 pages
...circles are perpendicular to each other, or the spherical angle at Q is a right angle. (38.) Any one side of a spherical triangle is less than the sum of the other two. Let ABC be any spherical triangle, and О the centre of die sphere; draw the radii OA, OB, ОС, then there will...
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Elements of Plane and Spherical Trigonometry: With Its Applications to the ...

John Radford Young - Astronomy - 1833 - 286 pages
...Every great circle passing through the poles of another is at right.angles to it . . . . . ib. 38. Any side of a spherical triangle is less than the sum of the other two . . . . . .69 39. The three sides are together less than a whole circumference . ib. 40. Characteristic...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...spherical sector. The base of the sector is the zone generated by the arc DP, or FH. 438. Theorem, Either side of a spherical triangle is less than the sum of the other two. Demonstration. From the centre O (fig. 179) of the sphere draw the radii OA, OB, OC to the vertices...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 204 pages
...spherical sector. The base of the sector is the zone generated by the arc DF, or FH. 438. Theorem. Either side of a spherical triangle is less than the sum of the other two. Proof. From the centre O (fig. 179) of the sphere draw the radii OA, OB, OCto the vertices .5, B, C...
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Elementary Course of Geometry ...

Charles William Hackley - Geometry - 1847 - 248 pages
...called Polar triangles, or Supplemental triangles. PROP. VII. In any spherical triangle any one side is less than the sum of the other two. Let ABC be a sphercal triangle, O the center of the sphere. Draw the radii OA, OB, OC. Then the three plane angles...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...angles forming a polyedral angle is less than the sum of the two other angles (B. vL, P. 19); hence, any side of a spherical triangle is less than the sum of the two other sides. PROPOSITION II. THEOEEM. The sum of all the sides of any spherical polygon is less...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...which bound a polyedral angle is less than the sum of the two other angles (B. v1., P. 19) ; hence, any side of a spherical triangle is less than the sum of the two other sides. PROPOSITION II. THEOREM. The sum of all the sides of any spherical polygon is less...
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre ...

Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...which bound a polyedral angle is less than the sum of the two other angles (B. VL, p. 19) ; hence, any side of a spherical triangle is less than the sum of the two other sides. PROPOSITION II. THEOREM. The sum of all the sides of any spherical polygon is less...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 638 pages
...angles forming a triedral angle is less than the sum of the other two (Prop. XIX. Bk. VIL). Hence, any side of a spherical triangle is less than the sum of the other two. PBOPOSTTIOS IIL — THEOREM. 523. The shortest path from one point to another, on the surface of a...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 518 pages
...following propositions, of which the first four have been demonstrated in Book IX. of the Geometry. I. Any side of a spherical triangle is less than the sum of the other two. II. The sum of the sides is less than 360°. III. The sum of the angles is greater than 180°. IV....
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