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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. "
Solid Geometry - Page 85
by Mabel Sykes, Clarence Elmer Comstock - 1922 - 218 pages
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The British encyclopedia, or, Dictionary of arts and sciences, Volume 6

William Nicholson - 1809 - 722 pages
...ili'tant troin any of the polis of a great circle Ģill 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...
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British Encyclopedia: Or, Dictionary of Arts and Sciences ..., Volume 11

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...
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American Edition of the British Encyclopedia: Or, Dictionary of ..., Volume 11

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...
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The practice of navigation and nautical astronomy. [With] Tables [and ...

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...
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Scholarship examinations of 1846/47 (-1853/54).

Bengal council of educ - 1852 - 348 pages
...expressions are real, and state why these data—insufficient in plane trigonometry—suffice here. 9. Prove that the shortest distance between two points on the surface of a sphere is the arc of a great circle passing through them. 10. Apply this to find the direction in which a ship must...
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Arts and Sciences: Or, Fourth Division of "The English Encyclopedia", Volume 7

Charles Knight - Encyclopedias and dictionaries - 1868 - 528 pages
...instead of its chord, although at first sight the reverse appears to bo the case. It is however certain, that the shortest distance between two points on the surface of a sphere is the arc of a great circle, the plane of which passes through the earth's centre. Now, if in the following...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1869 - 470 pages
...corresponding arcs of the small circle, and their sum is equal to the entire arc of the small circle. Cor. 3. The shortest distance between two points on the surface of a sphere, is measured on the arc of a great circle joining them. -(jV PROPOSITION H. THEOREM. The sum of the sides...
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Annual Report of the State Geologist of New Jersey for ...

Geological Survey of New Jersey - Geology - 1870 - 578 pages
...line we have just run is a straight line ; in other words, it is an arc of a great circle, which is the shortest distance between two points on the surface of a sphere. The present boundary, which was run in 1774, was run with the compass, and therefore would be approximately...
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REPORT ON A SURVEY OF THE BOUNDARY LINE BETWEEN NEW JERSEY AND NEW YORK ...

GEORGE H. COOK - 1874 - 52 pages
...line we have just run is a straight line ; in other words it is an arc of a great circle, which is the shortest distance between two points on the surface of a sphere* The present Boundary which was run in 1774 was run with the compass, and therefore would be approximately...
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An Elementary Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - Geometry - 1877 - 262 pages
...and C is any point in the arc For SPHERICAL GEOMETRY. 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. 181 Definition. If from the vertices of a spherical triangle...
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