According to his view, all mountain ranges parallel to the same great circle of the earth are of strictly contemporaneous origin, and between the great circles a relation of symmetry exists in the form of a pentagonal reseau.

He showed that the surface of a segment is equal to the area of the circle whose radius equals the distance from the vertex to the base of the segment; that the surface of the entire sphere is equal to the curved surface of the circumscribing cylinder, and to four times the area of a great circle of the sphere; and that the volume is twothirds that of the circumscribing cylinder.

This result created a great sensation, and proved that Transatlantic electric wave telegraphy was quite feasible and not inhibited by distance, or by the earth's curvature even over an arc of a great circle 3000 m.

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In like manner a great circle drawn through East Cape and the extremity of the Malay peninsula, passes nearly over the coasts of Manchuria, China and Cochin-China, and departs comparatively little from the eastern boundary.

To the former he owes his appreciation of exact investigation and a complete knowledge of the aims of science, to the latter an equal admiration for the great circle of ideas which had been diffused by the teaching of Fichte, Schelling and Hegel.

Proposition 30 describes the construction of a curve of double curvature called by Pappus the helix on a sphere; it is described by a point moving uniformly along the arc of a great circle, which itself turns about its diameter uniformly, the point describing a quadrant and the great circle a complete revolution in the same time.

The ecliptic itself is the great circle in which this plane meets the celestial sphere.