 | Richard Wilson - Logarithms - 1831 - 372 pages
...the plane of one of them, is also perpendicular to the plane of the other. (Eue. XI. 14.) 4. PROP. A great circle may be drawn through any two points on the surface of a sphere, but not generally through more than two. For the plane of a great circle must also pass through... | |
 | 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... | |
 | George Biddell Airy - Trigonometry - 1855 - 121 pages
...is a radius of the sphere. Two circles are said to be parallel when their planes are parallel. (81.) A great circle may be drawn through any two points on the surface of a sphere, but not generally through more than two. For the plane of a great circle must also pass 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... | |
 | 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... | |
 | 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... | |
 | 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.... | |
 | 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.... | |
 | Nathaniel Bowditch - Nautical astronomy - 1906 - 670 pages
...small circle is a section by a plane which intersects the sphere without passing through the center. A great circle may be drawn through any two points on the surface of a sphere, and the arc of that circle lying between those points is shorter than any other distance... | |
 | John William Norie, J. W. Saul - Nautical astronomy - 1917 - 642 pages
...equal to each other, and bisect each other ; ie, divide each other into two equal parts or semicircles. A great circle may be drawn through any two points on the surface of a sphere, but not through more than two, taken at random. If through the centre of a circle, whether... | |
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A great circle may be drawn through any two points on the surface of a sphere, but not through more than two, taken at random. 