| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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