...(2) is Girard•s Theorem, and shows that the area of a spherical triangle may be represented by e, the excess of the sum of its three angles above two right angles. e is technically termed the Spherical Excess. 1),A1 + B1+C,-ir=%, (3.) (3) expresses the spherical...

...triangle ABC is equivalent to (A + B + C — 2) X T. Hence the area of a spherical triangle is equal to the excess of the sum of its three angles above two right angles multiplied by the quadrantal triangle. 564. Cor. If the sum of the three angles of a spherical triangle...

...Bis obtuse. SURFACE OP THE SFHERICAL TRIANGLE. 191. The surface of a spherical triangle is equal to the excess of the sum of its three angles above two right angles. This excess, which is also called the spherical excess, may be found from the sides, by the aid of...

...many spherical triangles as it has sides less two. But the area of each of these triangles is equal to the excess of the sum of its three angles above two right angles multiplied by the quadrantal triangle (Prop. XX.) ; and the sum of the angles in all the triangles...

...right angles, and greater than two." P. XIV. B. IX. 4. "The surface of a spherical triangle is equal to the excess of the sum of its three angles above two right angles multiplied by the tri-rectaugular triangle. P. XVIII. B. IX. Many other questions and Propositions...

...THEOREM. The surface of any spherical triangle is to the surface of the tr {-rectangular triangle, as the excess of the sum of its three angles above two right angles is to one right angle. Let ABC be the proposed triangle ; produce its sides until they meet the great...

...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...

...proposed, of which the 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 so diminished, may be taken for the angles of a rectilineal triangle., the sides of which are equal in length to those of the proposed spherical triangle."...

...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...