Page:General Investigations of Curved Surfaces, by Carl Friedrich Gauss, translated into English by Adam Miller Hiltebeitel and James Caddall Morehead.djvu/58

It is easily verified that, with the same precision, the following formula may be taken instead of the above:

$$\sigma =\sigma ^{*}{\sqrt {\frac {\sin A.\sin B.\sin C}{\sin A^{*}.\sin B^{*}.\sin C^{*}}}}$$

If this formula is applied to triangles on non-spherical curved surfaces, the error, generally speaking, will be of the fifth order, but will be insensible in all triangles such as may be measured on the earth’s surface.