| Ephraim Miller - Plane trigonometry - 1894 - 220 pages
...90°. REMARK II. The functions of Ła, $b, and $c, in [57] and [59], are real quantities. For since **the sum of the angles of a spherical triangle is greater than** 180°, and less than six right angles, then S, or $(A + В + C)- in [57] and [59], is greater than... | |
| John Macnie - Geometry - 1895 - 388 pages
...the side of A'B'C' that is opposite ZA, etc., we have the relations : PROPOSITION XV. THEOREM. 633. **The sum, of the angles of a spherical triangle* is greater than two,** and less than six, right angles. Given: A, B, C, the angles of a spherical triangle ABC; To Prove :... | |
| Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 320 pages
...Geometry. EXERCISES. 736. Show that a trirectangular triangle is its own polar. 737. From step 7 show that **the sum of the angles of a spherical triangle is greater than** a straight angle*. 738. A spherical triangle is to the surface of the sphere as the spherical excess... | |
| Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 320 pages
...Geometry. EXERCISES. 736. Show that a trirectangular triangle is its own polar. 737. From step 7 show that **the sum of the angles of a spherical triangle is greater than** a straight angle. 738. A spherical triangle is to the surface of the sphere as the spherical excess... | |
| George Cunningham Edwards - Geometry - 1895 - 332 pages
...the area of any spherical polygon, the angles of which are given. NOTE. — It has been shown that **the sum of the angles of a spherical triangle is greater than** 180°: The amount, in degrees, by which the sum of the angles exceeds 180°, is called the spherical... | |
| Henry Dallas Thompson - Geometry, Solid - 1896 - 224 pages
...with the measure of the opposite angle of the polar equals two quadrants. 241. THEOREM. The measure of **the sum of the angles of a spherical triangle is greater than two** and less than six quadrants. For the measures of the three angles together with the three si'des of... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 556 pages
...AB and AC. In a similar manner the remaining relations are proved. QED PROPOSITION XXX. THEOREM 878. **The sum of the angles of a spherical triangle is greater than two,** and less than six', right angles. GIVEN the spherical triangle ABC. Denote its angles by A, B, C, and... | |
| Webster Wells - Trigonometry - 1896 - 236 pages
...opposite the greater side. 3. The sum of the sides of a spherical triangle is less than 360°. 80 4. **The sum of the angles of a spherical triangle is greater than** 180°, and less than 540°. 5. If A'B'C' is the polar triangle of ABC, that is, if A, B, and С are... | |
| George Albert Wentworth - Geometry - 1896 - 50 pages
...two polar triangles each angle of the one is the supplement of the opposite side in the other. 737. **The sum of the angles of a spherical triangle is greater than** 180° and less than 540°. 741. In a bi-rectangular spherical triangle the sides opposite the right... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 562 pages
...AB and AC. In a similar manner the remaining relations are proved. QED PROPOSITION XXX. THEOREM 8Y8. **The sum of the angles of a spherical triangle is greater than two,** and less than six, right angles. GIVEN the spherical triangle ABC. Denote its angles by A, B, C, and... | |
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