 | Arthur Schultze, Frank Louis Sevenoak - 1901 - 396 σελίδες
...are ends of a diameter, any number of great circles can be passed through these points. 686. DBF. The distance between two points on the surface of a sphere is the length of the minor arc of a great circle between them. Ex. 1169. What is the radius of a small circle,... | |
 | Arthur Schultze, Frank Louis Sevenoak - 1901 - 394 σελίδες
...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... | |
 | George Albert Wentworth - 1902 - 248 σελίδες
...points are the ends cf a diameter, the position of the circle is not determined. § 494 757. 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 in the... | |
 | Alan Sanders - 1903 - 396 σελίδες
...circle on the surface of a material sphere. PROPOSITION IV. THEOREM 1082. The shortest line joining two points on the surface of a sphere is the arc of a great circle, less than a semicircwmference, that joins them. Let A and B be any two points on the surface of a sphere... | |
 | American School (Chicago, Ill.) - 1903 - 390 σελίδες
...the sphere is the common center of all great circles. The shortest distance between any two points on a sphere is the arc of a great circle passing through those points. A small circle is any circle whose plane does not pass through the center of the sphere. A spherical... | |
 | George Albert Wentworth - 1904 - 496 σελίδες
...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 in the... | |
 | Fletcher Durell - 1911 - 553 σελίδες
...triangle is greater than the difference between the other two sides. 111. COR. 2. The shortest path between two points on the surface of a sphere is the arc of the great circle joining those points. For any other path between "the two points may be made the limit... | |
 | Daniel Coit Gilman, Harry Thurston Peck, Frank Moore Colby - 1904 - 1176 σελίδες
...passing through the points of departure and arrival. ¡Since the shortest lino between any two points of a sphere is the arc of a great circle passing through the points, it follows that a ship which moves from one point to another on the earth's surface will... | |
 | Fletcher Durell - 1904 - 232 σελίδες
...not in the same plane with the center, one small circle, and only one, can ~be passed. 746. DEF. The distance between two points on the surface of a sphere is the length of the minor arc of a great circle joining the points. Ex. 1. If the radius of a sphere is 13... | |
 | Charles Davison - 1905 - 140 σελίδες
...is equal to the projection of the chord on the diameter. SPHERICAL TRIANGLES, ETC. 93. DBF. 71. The distance between two points on the surface of a sphere is the minor arc of the great circle passing through them. 94. PROP. 63. All points on the circumference of... | |
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The shortest DISTANCE between two points on the surface of a sphere is the arc of a great circle passing through those points. 
