 | Education - 1911 - 1334 pages
...Find tan 75° by means of tan 45° and tan 30°. so JOURNAL OF EDUCATION. 5. Prove the proposition: The shortest line that can be drawn on the surface of a sphere between two given points is the arc of a great circle, not greater than a semicircle, which joins the points. 6.... | |
 | William Herschel Bruce, Claude Carr Cody - Geometry, Solid - 1912 - 134 pages
...sum of the sides of a spherical polygon- is less than a great circle. PROPOSITION X. THEOREM. 764. The shortest line that can be drawn on the surface of a sphere between two points on the surface is the arc of a great circIe not greater than a semicircle. To prove AB is the shortest... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...to, less than, or greater than the ZB ItZ.C = ZB, ihenAB = AC; §680 PROPOSITION XXII. THEOREM 682. The shortest line that can be drawn on the surface...sphere between two points is the arc of a great circle joining the two points, not greater than a semicircle. Given AB, the arc of a great circle, not greater... | |
 | Sophia Foster Richardson - Geometry, Solid - 1914 - 236 pages
...is covered by a spherical triangle whose angles are respectively 65^*, 75°, and 85°? 431. THEOREM. The shortest line that can be drawn on the surface...circle not greater than a semicircumference joining the points. Given AB the arc of a great circle not greater than a semicircumference joining the points... | |
 | William Garnett - Map projection - 1914 - 128 pages
...straight line. On a sphere it lies on a great circle. We therefore infer that — The great circle is the shortest line that can be drawn on the surface of a sphere between any two points. This is why sailors like to sail on the great circle between two ocean ports. Generally... | |
 | John H. Williams, Kenneth P. Williams - Geometry, Solid - 1916 - 184 pages
...AB<AC+CD+DB. Draw a great circle arc AD. Then AD<AC+CD, and AB<AD+DB. Hence, AB<AC+CD+DB. 744. THEOREM. The shortest line that can be drawn on the surface of a sphere between two points is the arc of the great circle that joins them. Let A and B be the points, AB the arc of a great circle, and ACB... | |
 | William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 pages
...the ends of a diameter of a sphere an indefinite number of great circles will pass. 741. ASSUMPTION. The shortest line that can be drawn on the surface of a sphere, joining two given points, is the minor arc of the great circle passed through the two given points.... | |
 | William Betz - Geometry - 1916 - 536 pages
...the ends of a diameter of a sphere an indefinite number of great circles will pass. 741. ASSUMPTION. The shortest line that can be drawn on the surface of a sphere, joining two given points, is the minor arc of the great circle passed through the two given points.... | |
 | Webster Wells, Walter Wilson Hart - Geometry - 1916 - 490 pages
...triangle. PROPOSITION XXX. THEOREM 715. The shortest line on the surface of a sphere between two given points is the arc of a great circle, not greater than a semicircle which joins the two points. Hypothesis. Points A and B are on the surface of a sphere, and... | |
 | Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Solid - 1917 - 220 pages
...< AB + BC. 1. Post. 1. 2. § 507. 3. § 677. Q.ED. 689. COR. The shortest line that can be drawn on a sphere between .two points is the arc of a great...than a semicircumference, joining the two points. PROPOSITION XV. THEOREM 690. The sum of the sides of a convex spherical polygon is less than the circumference... | |
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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. 
