 | Perry Fairfax Nursey - Industrial arts - 1852 - 550 pages
...between two points on any surface will take the shortest line on that surface. Now, the Dividing- line is the shortest line that can be drawn on the surface of a vessel from any point on the sternpost to the stern." Now, what fair analogy can be drawn between a... | |
 | Industrial arts - 1852 - 568 pages
...between two points on any surface will take the shortest line on that surface. Now, the Dividing-line is the shortest line that can be drawn on the surface of a vessel from any point on the stempost to the stern." Now, what fair analogy can be drawn between a... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...that can be drawn on the surface of a sphere between two points is the arc of a great circle, less than a semi-circumference, joining the two points....sphere ; and let C be any arbitrary point taken in that arc. Then we say that the shortest line from A to B, on the surface of the sphere, must pass through... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...sphere. SHORTEST LINE ON THE SURFACE OF A SPHERE BETWEEN TWO POINTS. PROPOSITION XXXIV.— THEOREM. 105. The shortest line that can be drawn on the surface....between two points is the arc of a great circle, less than a semi-circumference, joining the two points. Let AB be an arc of a great circle, less than... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...point. 9. The shortest distance on the surface of a sphere from one point of the surface to another is the arc of a great circle, not greater than a semi-circumference, whose extremities are these points. II. SPHERICAL ANGLES AND TRIANGLES. 451. Definitions and Remarks.... | |
 | Eugene Lamb Richards - Measurement - 1880 - 108 pages
...on the earth, the latitude and longitude of each jjoint being given. We have to find the length of the arc of a great circle not greater than a semi-circumference joining the two points (Ch. Art. 105, VIII.). Suppose A and C to represent the two points. If P represents the pole of the... | |
 | Isaac Sharpless - Geometry - 1882 - 286 pages
...sphere, are measured in degrees, minutes and seconds. Proposition 6. Theorem. — The shortest line on the surface of a sphere between two points is the arc of the great circle which joins them. Let A and B be two points on the surface of a sphere. The shortest... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...proposition. PROPOSITION XXIII. THEOREM. 683. The shortest line on the surface of a sphere between two given points is the arc of a great circle, not greater than a semi-circumference, which joins the points. Let AB be an arc of a great circle, not greater than a semi-circumfereuce,... | |
 | William Chauvenet - Geometry - 1887 - 336 pages
...question. SHORTEST LINE ON THE SURFACE OF A SPHERE BETWEEN TWO POINTS. PROPOSITION XXIII.— THEOREM. 76. The shortest line that can be drawn on the surface...sphere ; and let C be any arbitrary point taken in that arc. Then we say that the shortest line from A to B, on the surface of the sphere, must pass through... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 332 pages
...triaugle is equal to the excess of the sum of its angles over two right angles. PROPOSITION XXIII. The shortest line that can be drawn on the surface...than a semi-circumference, joining the two points. BOOK IX. THEOREMS. PROPOSITION I. If a prism whose base is a regular polygon be inscribed in or circumscribed... | |
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The shortest line that can be drawn on the surface of a sphere between two points is the arc of a great circle, not greater than a semicircumference, joining the two points. 
