...... , . — 4T, and conCOR. 1. Making T = 1, we have ABC =A + B + C— 2. Hence we sometimes say the spherical triangle is measured by the excess of the sum of its angles abtwi two right angles. As many right angles as there are in this measure, just so many tri-rectangular...

...to eomput' the area. This problem is solved in geometry, -where it is proved that the surface of a spherical triangle is measured by the excess of the sum of its three angles over two right angles, by which is meant, that the area is as many times the area of the tri-rectangular...

...928). 882. Taking the tri-rectangular spherical triangle and the right triangle as units (881): 1st. A spherical triangle is measured by the excess of the sum of its angles over two right angles. 2d. Any spherical polygon is measured by the excess of the sum of its...

...sin x. cos x 11. Find the value of 13. Prove that the area of a spherical triangle is proportional to the excess of the sum of its three angles above two right angles. 14. In a spherical triangle sin C cot A=Cot a gin b-cosb cos C. 15. Prove sin a = a - ^ + f^j+ etc...

...with respect to each other, they are also equilateral with respect to each other. 6. The surface of a spherical triangle is measured by the excess of the sum of its three angles over two right angles. Prove. 7. Given that the area of the surface, generated by a straight line revolving...

...what is the ratio of the volume above to that below the cutting plane ? 9. Prove that the surface of a spherical triangle is measured by the excess of the sum of its angles over 180°. EXAMINATIONS FOR ADMISSION. 321 TRIGONOMETRY. 1. Find the sine of 1° 13' 52". 2....

...enunciations: "A dihedral angle is measured by the plane angle included between its sides;" "The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles," etc. ; enunciations which have no meaning in themselves, and from which every trace of homogeneity...

...terms. Take for examples, 5 + VIO-.V6-V15 and 15-2V§-2Vl5 + 3V2"-2 N/6+2 Vs"-2 V30. 2. Prove that the surface of any spherical triangle is measured by the excess of the sum of its angles above two right angles. 3. Spatia quae corpus urgente quacunque vi finita describit, sive vis...

...sides are very small in relation to the radius of the sphere, if from each of its angles one third of the excess of the sum of its three angles above two right angles, be subtracted, the angles so diminished, may be taken for the angles of a rectilineal triangle., the...