| William Nicholson - 1809 - 722 pages
...surface of the sphere, equally 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...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... | |
| 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... | |
| Bengal council of educ - 1852 - 348 pages
...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... | |
| Charles Knight - Encyclopedias and dictionaries - 1868 - 528 pages
...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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| De Volson Wood - Geometry, Analytic - 1882 - 360 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... | |
| Borden Parker Bowne - Theism - 1879 - 474 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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