| John Bonnycastle - Trigonometry - 1806 - 464 pages
...common section of all the great circles which pass through its two extremities. 3. A great circle can **be drawn through any two points on the surface of a sphere** ; and a small circle can be drawn through any three points on its surface. 4. All parallel circles... | |
| Francis Nichols - Plane trigonometry - 1811 - 162 pages
...common section of all the great circles which pass through its two extremities. 17. A great circle can **be drawn through any two points on the surface of a sphere,** and a small circle can be drawn through any three points on its surface. 18. All parallel circles of... | |
| John Radford Young - Astronomy - 1833 - 286 pages
...great circle of the sphere, and every other a small circle. It is obvious that the circumference of **a great circle may be drawn through any two points on the surface of a sphere,** because a plane may be drawn through these two points and through the centre also, but a great circle... | |
| Richard Abbatt - Spherical astronomy - 1841 - 234 pages
...pole, however, in the case of the small circle, is usually restricted to the nearer point P. (73.) **A great circle may be drawn through any two points on the surface of** the sphere, but not generally through more than two : for the plane of the circle passes likewise through... | |
| Sir Edward James Reed, Joseph Woolley - Naval art and science - 1872 - 570 pages
...things for granted induces a very unscientific frame of mind, we shall here introduce proofs of them. **A great circle may be drawn through any two points on the surface of a sphere.** For if these two points be joined by a straight line, and a plane in which this line lies be made to... | |
| Nathaniel Bowditch - Nautical astronomy - 1888 - 704 pages
...pass through its poles are called its »econdaries. ЛИ secondaric . cut the primary at right angles. **A great circle may be drawn through any two points on the surface of a sphere.** The .shortest distance between any two points measured on the surface of a sphere is the arc of the... | |
| Arthur Latham Baker - Geometry, Solid - 1893 - 154 pages
...through the centre of the sphere, and is therefore a diameter of each circle. 231. COR. C. An arc of **a great circle may be drawn through any two points on the surface of a sphere.** For the two given points and the centre of the sphere determine the plane of a great circle passing... | |
| William James Milne - Geometry - 1899 - 396 pages
...points on its surface. What kind of a circle is the section thus formed ? What kind of an arc, then, **may be drawn through any two points on the surface of a sphere** ? 8. Form a sphere and pass a plane through any three points on its surface. What plane figure is the... | |
| Isaac Newton Failor - Geometry - 1906 - 440 pages
...points determine a plane (§ 515) which cuts the sphere in a circle. § 749 762 COROLLARY 6. An arc of **a great circle may be drawn through any two points on the surface of a sphere.** For the two points on the surface and the center of the sphere determine a great circle. § 515 The... | |
| Isaac Newton Failor - Geometry - 1906 - 431 pages
...points determine a plane (§ 515) which cuts the sphere in a circle. § 749 762 COROLLARY 6. An arc of **a great circle may be drawn through any two points on the surface of a sphere.** For the two points on the surface and the center of the sphere determine a great circle. § 515 The... | |
| |