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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... "
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... - Σελίδα 263
των William Chauvenet - 1872 - 368 σελίδες
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - 1871 - 192 σελίδες
...and the angle E, are respectively supplements of each other. 446. Corollary. If therefore we denote the angles of a spherical triangle by A, B, C ; and the sides respecf'Voly opposite by a, b, c ; the angles of the polar triangle must be 180° — a, 180° —...

Treatise on Plane and Solid Geometry for Colleges, Schools, and Private Students

Eli Todd Tappan - 1873 - 288 σελίδες
...subtracting one of the isosceles triangles from the sum of the other two. *794i. It has been shown that the sum of the angles of a spherical triangle is greater than the sum of the angles of a plane triangle (771). Since any spherical polygon can be divided into triangles...

Harvard Examination Papers

1873 - 192 σελίδες
...triangular pyramid is a third part of a triangular prism of the same base and altitude. 5. Prove that the sum of the angles of a spherical triangle is greater than two right angles. 6. Given the radius of a sphere = 2 inches. Compute the volume and convex surface. III....

Catalogue - Harvard University

Harvard University - 1876 - 554 σελίδες
...circles is measured by an arc drawn from the vertex as a pole, and included between its sides. Prove. 9. The sum of the angles of a spherical triangle is greater than two right angles ; and either angle is greater than the difference between the turn of the other two and...

An Elementary Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - 1877 - 262 σελίδες
...theorem AC <^ AB, which is also contrary to the hypothesis. Hence the angle ABC>C. THEOREM XV. 37 1 The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. The sum of the arcs which measure the angles of a spherical triangle together with the three sides...

Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 436 σελίδες
...relations polar triangles are often called supplemental triangles. PROPOSITION XVIII. ТНЕOДЕМ. 732. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. Let ABC be a spherical triangle. We are to prove ZA + ZB + ZC greater than 2, and less than 6, right...

Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1877 - 458 σελίδες
...is greater than the angle ABC. Therefore, in a spherical triangle, etc. PROPOSITION XVII. THEOREM. The sum of the angles of a spherical triangle is greater than two, and less than six right angles. Let A, B, and C be the angles of a spherical triangle. The arcs which measure the angles A, B, and...

An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - 1880 - 260 σελίδες
...theorem AC <^ AB, which is also contrary to the hypothesis. Hence the angle ABC>C. THEOREM XV. 37i The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. The sum of the arcs which measure the angles of a spherical triangle together with the three sides...

The Elements of Plane and Spherical Trigonometry: With the Construction and ...

John Charles Snowball - 1880 - 256 σελίδες
...В) < \тг. .... COR. 4. a', V, c', being the sides of the polar triangle, . + BC; o?,A + BC<v. 21. The sum of the angles of a spherical triangle is greater than two right angles, and less than six, Let А, Б, О be the, angles, and а, Ъ, с the sides, of a triangle;...

The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - 1882 - 286 σελίδες
...any number of sides, is less than the circumference of a great circle. Proposition 16. Theorem. — The sum of the angles of a spherical triangle is greater than two, and less than six right angles. For an angle of a triangle, together with the opposite side of the polar triangle, is equal to 180° (IX....




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