| 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° —... | |
| 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... | |
| 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.... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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;... | |
| 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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