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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. "
British Encyclopedia: Or, Dictionary of Arts and Sciences, Comprising an ... - Page 15
by William Nicholson - 1821
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The British encyclopedia, or, Dictionary of arts and sciences, Volume 6

William Nicholson - 1809
...surface of the sphere, equally 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...8. If one great circle meets another, the angles on cither side are supplements to each otlier; and every spherical angle is less than 180". 9. If two...
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The practice of navigation and nautical astronomy. [With] Tables [and ...

Henry Raper - 1840
...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
...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
...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

Adrien Marie Legendre - Geometry - 1869 - 455 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
...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
...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 - 240 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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The Elements of Coordinate Geometry: In Three Parts: 1. Cartesian Geometry ...

De Volson Wood - Geometry, Analytic - 1882 - 333 pages
...The shortest distance between two points is a straight line ; The evolutc of a circle is a point ; The shortest distance between two points on the surface of a sphere is the arc of a great circle ; the student might infer that it was a cumbersome and tedious process of proving...
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Studies in Theism

Borden Parker Bowne - Theism - 1879 - 444 pages
...of a sphere, and the shortest distance between two points in such a space would be what we mean by the shortest distance between two points on the surface of a sphere. That the imaginary inhabitants should declare such shortest distance to be an arc need not surprise...
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