 | Mathematics - 1801 - 658 pages
...sides of any spherical triangle is less than 360°-! * DEMONSTRATION. The shortest distance between any two points on the surface of a sphere is the arc of a great circle pissing through them. The sides of a spherical triangle then are the shortest distances betwcn the... | |
 | Samuel Webber - Mathematics - 1808 - 520 pages
...a spheric triangle is greater than the third.* • DEMONSTRATION. The shortest distance between any two points on the surface of a sphere is the arc of a yre.it circle passing through them. The sides of a spheric triiuic'.e theft 412 THEOREM II. The sum... | |
 | William Nicholson - 1809 - 722 pages
...ili'tant troin any of the polis of a great circle «ill be parallel tu the plane of that great circle. 7. The shortest distance between two points, on the surface of a sphere, is the arch of a great circle passing through these points. 8. If one great circle meets another, the angles... | |
 | William Nicholson - Natural history - 1821 - 384 pages
...distant from any of the poles of a great circle, will be parallel to the plane of that great circle. 7. The shortest distance between two points, on the surface of a sphere, is the arch of a great circle passing through these points. 8. If one great circle meets another, the angles... | |
 | William Nicholson - Natural history - 1821 - 382 pages
...distant from any of the poles of a great circle, will be parallel to the plane of that great circle. 7. The shortest distance between two points, on the surface of a sphere, is the arch of a great circle passing through these points. 8. If one great circle meets another, the" angles... | |
 | Adrien Marie Legendre - 1825 - 570 pages
...ABC is less than the sum of the other two. THEOREM. 460. The shortest way from one point to another on the surface of a sphere is the arc of a great circle which joins the two given points. Fij.223. Demonstration. Let ANB (fig. 223) be the arc of a great... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...ABC is less than the sum of the other two. THEOREM. 460. The shortest way from one point to another on the surface of a sphere is the arc of a great circle which joins the two given points. Fig. 223. Demonstration. Let ANB (fig. 223) be the arc of a great... | |
 | Adrien Marie Legendre - Geometry - 1825 - 276 pages
...triangle ABC is less than the sum of the other two. 460. The shortest way from one point to another on the surface of a sphere is the arc of a great circle which joins the two given points. Fig. 223. Demonstration. Let ANB (fig. 223) be the arc of a great... | |
 | Henry Raper - 1840 - 108 pages
...as the crow flies," except when the course is due north or south, or east and 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... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...ABC is less than the sum of the other two. THBOREM. 460. The shortest way from one point to another on the surface of a sphere is the arc of a great circle which joins the two given points. Fis. 223. Demonstration. Let ANB (fig. 223) be the arc of a great... | |
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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. 
