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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. "
Chauvenet's Treatise on Elementary Geometry - Page 285
by William Chauvenet - 1889 - 322 pages
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Iron: An Illustrated Weekly Journal for Iron and Steel ..., Volume 56

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...
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The Mechanics' Magazine, Museum, Register, Journal, and Gazette, Volume 56

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...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 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...two points is the arc of a great circle, not greater tlian a semicircumference, joining the two points. Let AB be an arc of a great circle, less than a...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Mathematics - 1872 - 382 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...sphere 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...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1875 - 466 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...points A and B of the surface of a 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...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1875 - 390 pages
...SHOBTEST LINE ON ItflE SURFACE OF A SPHERE BETWEEN TWO POINTS. PROPOSITION XXXIV.— THEOREM. 105. The shortest line that can be drawn on the surface...points is the arc of a great circle, not greater than a semitnrcumference, joining the two points. Let AB be an arc of a great circle, less than a semi-circumference,...
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Elements of Geometry with Exercises for Students: An an Introduction to ...

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....
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A Treatise on Elementary Geometry, with Appendices Containing a Collection ...

William Chauvenet - Geometry - 1879 - 380 pages
...sphere. SHORTEST LINE ON THE SURFACE OF A SPHERE BETWEEN TWO POINTS. PROPOSITION XXXTV.—THEOREM. 105. The shortest line that can be drawn on the surface of a sphere between two points is the are of a great circle, not greater than a semicircumference, joining the two points. Let AB be an arc...
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Applications of Plane and Spherical Trigonometry

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...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

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...
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