...proposition asserted. (B.) The greater angle of a spherical triangle is opposite, to the greater side, and the sum of the angles of a spherical triangle is greater than two and less than six right angles. Also the sum of any two angles is less than the, third increased...

...— c; and the sides of the polar triangle ISO° — ,4, 180° — B, 180° — C. \ 447. Theorem. The sum of the angles of a spherical triangle is greater than two right angles. Demonstration. Let A, B, C be the angles of the spherical triangle. The sides of...

...triangle, V+6'>c'; .-. (тг- А) + (тг-B)>(ж-С); .: тг>A + B-С. Or, A + B - С < тг. 21. The sum of the angles of a spherical triangle is greater than two, and less than six, right angles. Let A, B, С be the angles, and a, b, с the sides of a triangle;...

...Astronomy, which, as a science of observation, depends entirely on angular measurements. PROP. XIV. The sum of the angles of a spherical triangle is greater than two and less than six right angles, For each angle is less than two (note to Prop. 8), hence the sum...

...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...

...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...

...common surface of the two fluids. (6.) Describe Nicholson's Hydrometer and the mode in which it is used in practice. (7.) Describe the process of filling...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...

...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...

...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...

...equilateral, rectangular, bir ectangular, and trirectangular, according to their triedrals. 771. Corollary — The sum of the angles of a spherical triangle is greater than two, and less than six right angles (591). equal to its symmetrical, and has equal angles opposite...