 | George Salmon - Geometry, Analytic - 1862 - 490 pages
...by the base, we have o> = A, 6' = B, 6" = CT - (7, and the total curvature is A + B+C— TT. Hence the excess over 180° of the sum of the angles of a geodesic triangle is measured by the area of that portion of a unit sphere which corresponds to the... | |
 | George Salmon - Geometry, Analytic - 1862 - 506 pages
...and by the base, we have ai = A, 0' = B, 0" = CT - (7, and the total curvature is A + B+C—tr. Hence the excess over 180° of the sum of the angles of a geodesic triangle is measured by the area of that portion of a unit sphere which corresponds to the... | |
 | Carl Friedrich Gauss - Surfaces - 1902 - 142 pages
...former, will be demonstrated both analytically and by simple geometrical considerations. The excess of the sum of the angles of a triangle formed by shortest lines over two right angles is equal to the total curvature of the triangle. It will be assumed here that... | |
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The excess over 180° of the sum of the angles of a triangle formed by shortest lines on a concavo-concave... 