 | Benjamin Peirce - Geometry - 1847 - 204 pages
...180° — c; and the sides of the polar triangle 180° — .#, 180° — B, 180° — C. 447. Theorem. The sum of the angles of a spherical triangle is greater than two right angles. Proof. Let A, B, C be the angles of the spherical triangle. The sides of its polar triangle... | |
 | Thomas Grainger Hall - Trigonometry - 1848 - 192 pages
...the sign of the square root appears to be a negative quantity ; but it is really positive. For since the sum of the angles of a spherical triangle is greater than two right angles, but less than six, S is always greater than 90°, and less than 270° ; and therefore... | |
 | Bengal council of educ - 1852 - 348 pages
...circumstances ? What point in Reaumur's and in Centigrade scale correspond to 44° Fahrenheit. (8.) The sum of the angles of a spherical triangle is greater than two right angles, and less than six. Show that the angles at the base of an isosceles triangle are equal.... | |
 | Charles Astor Bristed - 1852 - 470 pages
...demonstration that it is true only when 6 lies between 0 and £ir. 8. Show that the sum of the angles of every spherical triangle is greater than two and less than six right angles. 9. In any spherical triangle prove that ii A i_ P\ cos i (a — 6) i ^ n tan i(A + £) 1- ( cot ij-... | |
 | Education - 1852 - 478 pages
...all circumstances ? What point in Reaumur's and in Centigrade scale correspond to 44° Fahrenheit. 8. The sum of the angles of a spherical triangle is greater than tno right angles, and less than six. Show that the angles at the base of an isosceles triangle are... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...the angle E ; and AB is the supplement of the arc which measures the nnjrle F. PROPOSITION X. 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 triangre. The arcs which measure the angles A, B, and... | |
 | Elias Loomis - Conic sections - 1861 - 244 pages
...the anglexE ; and AB is the supplement of the arc which measures the angle F. PROPOSITION X. 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... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...subtracting one of the isosceles triangles from the sum of the other two. 794. 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... | |
 | William Rossiter - 1868 - 186 pages
...spherical and plane triangles are alike : in the following wo find them differ. The sum of the three angles of a spherical triangle is greater than two and less than six right anales. The sum of the three sides is less than 360°. The sum of two sides is 180° if the sum of... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 pages
...subtracting one of the isosceles triangles from the sum of the other two. 794.. 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 divtded into triangles... | |
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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... 
