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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

## Bulletin of the American Mathematical Society

Mathematics - 1900
...by side. In one respect; at least, the spherical geometry is the simpler, for it may be shown that the sum of the angles of a spherical triangle is greater than jr. In the plane geometry one must content himself with the theorems that the sum of the angles of...

## Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 370 pages
...triangle are 20°, 90°, 80°. Find the sides of the polar triangle. PROPOSITION XVl. THEOREM 731. The sum of the angles of a spherical triangle is greater than two and less than six right angles. Hyp. ABC is a spherical triangle. To prove ZA+ZB+ZC> 180°, and ZA+ZB+ZC<...

## Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...20°, 90°, 80°. Find the sides of the polar triangle. POLAR TRIANGLES PROPOSITION XVI. THEOREM 731. The sum of the angles of a spherical triangle is greater than two and less than six right angks. (729) Hyp. ABC is a spherical triangle. To prove ZA + ZB + ZO 180°,...

## Plane and Spherical Trigonometry

George Albert Wentworth - Trigonometry - 1902 - 256 pages
...conversely. 2. The sum of the sides of a spherical triangle is less than 360°. FIO. 79 FIo. 80 3. The sum of the angles of a spherical triangle is greater than 180° and less than 540°. 4. If, from the vertices of a spherical triangle as poles, arcs of great...

## Executive Documents, Minnesota ..., Volume 1

Minnesota - 1903
...are unequal, the opposite sides are unequal, and the greater side is opposite the greater angle. 7. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. ENGLISH LITERATURE. 1. Why does the study of English literature have...

## Five-place Logarithmic and Trigonometric Tables

George Albert Wentworth, George Anthony Hill - Logarithms - 1903 - 348 pages
...conversely. 2. The sum of the sides of a spherical triangle is less than 360°. Fio. 79 FIG. 80 3. The sum of the angles of a spherical triangle is greater than 180° and less than 540°. 4. If, from the vertices of a spherical triangle as poles, arcs of great...

## Plane and Solid Geometry

Fletcher Durell - Geometry - 1911 - 553 pages
...spherical triangles each of which is the polar triangle of the other. PROPOSITION XIV. THEOREM 783. The sum of the angles of a spherical triangle is greater than 180°, and less than 540°. \b <*] ^0 ' a' Given the spherical triangle ABO. To prove A + B + 0 > 180°...

## Solid Geometry

Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...spherical triangles each of which is the polar triangle of the other. PROPOSITION XIV. THEOREM 783. The sum -of the angles of a spherical triangle is greater than 180°, and less than 540°. Given the spherical triangle ABO. To prove A + B + C > 180° and < 540°....