 | Borden Parker Bowne - Theism - 1879 - 464 pages
...of a sphere, and the shortest distance between two points in such a space would be what we mean by the shortest distance between two points on the surface of a sphere. That the imaginary inhabitants should declare such shortest distance to be an arc need not surprise... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...B must pass through C; and C is any point in the arc of a great circle drawn from A to B. Therefore the shortest distance between two points on the surface of a sphere is the arc of a great circle joining the points. 18i Definition. If from the vertices of a spherical triangle... | |
 | Henry Raper - Nautical astronomy - 1882 - 952 pages
..." as the crow flies," except when the course is due north or south, or east or west on the equator. The shortest distance between two points on the surface of a sphere is the portion or arc which they include of the circle passing through both the points and the centre of the... | |
 | De Volson Wood - Geometry, Analytic - 1890 - 372 pages
...The shortest distance between two points is a straight line ; The evolute of a circle is a point ; The shortest distance between two points on the surface of a sphere is the arc of a great circle ; the student might infer that it was a cumbersome and tedious process of proving... | |
 | John Thornton (M.A.) - Astronomy - 1890 - 372 pages
...does not pass through the centre cuts the surface of a sphere in what is called a small circle. The distance between two points on the surface of a sphere is the length of the arc of the great circle passing through them, and is usually measured by the angle which... | |
 | Webster Wells - Geometry - 1894 - 394 pages
...them ; for an indefinitely great number of planes can be drawn through the diameter. 588. DEF. The distance between two points on the surface of a sphere is the arc of a great circle, less than a semi-circumference, drawn between them. Thus, the distance between... | |
 | George Clinton Shutts - Geometry - 1894 - 412 pages
...compare with the one preceding it ? 8. Then, how must ACMDB compare with AB? Therefore — 641. The distance between two points on the surface of a sphere is the distance measured on the arc of a great circle. PROPOSITION XII. 642. Theorem. A II points in the circumference... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
...ends of a diameter, the position of the circle is not determined. § 494 THE SPHERE. 757. DEF. The distance between two points on the surface of a sphere is the arc of the great circle that joins them. PROPOSITION II. THEOREM. 758. The distances of all points... | |
 | George Albert Wentworth - Geometry - 1899 - 498 pages
...ends of a diameter, the position of the circle is not determined. § 494 THE SPHERE. 757. DBF. The distance between two points on the surface of a sphere is the arc of the great circle that joins them. PROPOSITION II. THEOREM. 758. The distances of all points... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...are ends of a diameter, any number of great circles can be passed through these points. 686. DEF. The distance between two points on the surface of a sphere is the length of the minor arc of a great circle between them. PROPOSITION II. THEOREM 687. All points in... | |
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The distance between two points on the surface of a sphere is the length of the minor arc of a great circle between them. 
