...less than 360°. Q^ ED [See the figure on next pige.] THEOREM III. The sum of the three angles-of any spherical triangle is greater than two right angles, and less than six.* CQR. i. Hence a spherical triangle may have its three angles either right or obtuse ; and therefore,...

...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 by...

...semicircumference, which is the measure of two right angles ; hence, in the second place, the sum of all the angles of a spherical triangle is greater than two right angles. Cor. 1 . The sum of all the angles of a spherical triangle is not constant, like that of all the angles...

...— 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 its polar triangle...

...polar 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;...

...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 are 180°...

...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 of...

...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 cos. S is negative....

...BС=180°— D; AС=180°— E; A=180— FE; B = 180° — FD; С = 180° — DE. The sum of the three angles of a spherical triangle is greater than two right angles, and less than six right angles. For if a' + b' + c' be the sides of the supplemental or polar triangle, A=180°— a';...

...semicircumference. which is the measure of two right angles; hence, in the second place, the sum of all the angles of a spherical triangle is greater than two right angles. Cor. 1. The sum of all the angles of a spherical triangle is not constant, like that of all the angles...