 | John Radford Young - 1833 - 286 σελίδες
...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... | |
 | John Radford Young - 1833 - 308 σελίδες
...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... | |
 | Benjamin Peirce - 1837 - 216 σελίδες
...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... | |
 | Benjamin Peirce - 1847 - 204 σελίδες
...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... | |
 | Adrien Marie Legendre - 1852 - 436 σελίδες
...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... | |
 | Charles Davies - 1854 - 436 σελίδες
...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... | |
 | Adrien Marie Legendre, Charles Davies - 1857 - 442 σελίδες
...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... | |
 | Benjamin Greenleaf - 1862 - 518 σελίδες
...4', to find the angle opposite to the quadrantal side. Ans. 104° 24' 21". SOLUTION OF OBLIQUE-ANGLED SPHERICAL TRIANGLES. 179. In the solution of oblique-angled...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.... | |
 | Benjamin Greenleaf - 1862 - 532 σελίδες
...4', to find the angle opposite to the quadrantal side. Ans. 104° 24' 21". SOLUTION OF OBLIQUE-ANGLED SPHERICAL TRIANGLES. 179. In the solution of oblique-angled...Geometry. I. Any side of a spherical triangle is less títan the sum of tía other two. II. Tlie sum of the sides is less than 300°. III. Tlte sum of the... | |
 | Benjamin Greenleaf - 1861 - 638 σελίδες
...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... | |
| |
Each side of a spherical triangle is less than the sum of the other two sides. 
