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" The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC... "
An Elementary Treatise on Plane and Solid Geometry - Page 138
by Benjamin Peirce - 1871 - 150 pages
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A Treatise on Plane and Spherical Trigonometry

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...
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Elements of Geometry: Plane and Solid

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 :...
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Plane and Solid Geometry

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...
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Plane and Solid Geometry

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...
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Elements of Geometry

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...
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Elementary Solid Geometry and Mensuration

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...
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Elements of Geometry

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...
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New Plane and Spherical Trigonometry

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...
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Syllabus of Geometry

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...
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Elements of Geometry

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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