 | Eli Todd Tappan - 1868 - 432 σελίδες
...A GREAT CIRCLE. 751. Theorem — The shortest line which can extend from one point to another along the surface of a sphere, is the arc of a great circle, passing through the two points. Only one great circle can pass through two given points on the surface of a sphere... | |
 | Charles Davies, Adrien Marie Legendre - 1869 - 470 σελίδες
...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 - 1870 - 578 σελίδες
...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... | |
 | Eli Todd Tappan - 1873 - 288 σελίδες
...GEEAT CIRCLE. 751. Theorem. — The shortest line which can extend from one point to another along the surface of a sphere, is the arc of a great circle, passing through the two points. Only one great circle can pass through two given points on the surface of a sphere... | |
 | GEORGE H. COOK - 1874 - 52 σελίδες
...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 - 1877 - 262 σελίδες
...(VI. 7) ; and therefore the arcs of great circles PA, PB, PD are equal (III. 12). (». Scholium. The distance between two points on the surface of a sphere is the length of the arc of a great circle drawn between the points. . (See 1 7.) 1. Cor. 1. If G HI is a... | |
 | De Volson Wood - 1882 - 360 σελίδες
...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 what could very easily... | |
 | Borden Parker Bowne - 1879 - 464 σελίδες
...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... | |
 | Borden Parker Bowne - 1879 - 474 σελίδες
...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... | |
 | William Frothingham Bradbury - 1880 - 260 σελίδες
...(VI. 7); and therefore the arcs of great circles PA, PB, PD are equal (III. 12). (i. Scholium. The distance between two points on the surface of a sphere is the length of the arc of a great circle drawn between the points. (See 17.) 7. Cor. 1. If G HI is 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. 
