 | Mathematics - 1801 - 658 pages
...necessary, to the circumference, and the intercepted arc AB is the measure of the angle required. 2. When * A spherical angle is measured by the arc of a great circle, intercepted between the two sides, that form the angle, at the distance of 90° from the angular point.... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...the angle of the lune is to four right angles. It has already been shown that the angle of the lune is measured by the arc of a great circle whose pole is at the vertex. Thus, if AB is the axis of the arc DE, then DE measures the angle DAE, which is equal... | |
 | Eli Todd Tappan - Geometry - 1868 - 432 pages
...the angle of the lune is lo four right angles. It has already been shown that the angle of the lunc is measured by the arc of a great circle whose pole is at the vertex. Thus, if AB is the axis of the arc DE, then DE measures the angle DAE, which is equal... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...spherical angle PAB, which is equal to the measure of the diedral, is also right. 5ffO. COR. 2. — A spherical angle is measured by the arc of a great circle, interceptetl between its sides, and at a quadrant's distance from itts vertex. Thus, the spherical... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...the angle of the lune is to four right angles. It has already been shown that the angle of the lune is measured by the arc of a great circle whose pole is at the vertex. Thus, if AB is the axis of the arc DE, then DE measures the angle DAE, which is equal... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...spherical angle PAB, which is equal to the measure of the diedral, is also right. 560. COR. 2. — A spherical angle is measured by the arc of a great circle intercepted FIG. 323. between its sides, and at a quadrant's distance from its ver lex. Thus, the spherical... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...sphmcal polygon respectively measure the dihedral angles of the corresponding spherical pyramid. (?) 2. A spherical angle is measured by the arc of a great circle described about its vertex as a pole, and intercepted by its sides produced, if necessary. For, if... | |
 | William Guy Peck - Conic sections - 1876 - 376 pages
...sphere with the same facilitj that a circle can be drawn on a plane surface. PROPOSITION II. THEOREM. A spherical angle is measured by the arc of a great circle described from the vertex as a pole, and limited by the sides of the angle. Let FAG be a spherical... | |
 | George Albert Wentworth - Geometry - 1877 - 436 pages
...; §710 .'. spherical Z. BP С is equal to the measure of dihedral Z. C-PP'-B. QED 714. COROLLARY. A spherical angle is measured by the arc. of a great circle described about its vertex as a pole and intercepted by its sides (produced if necessary). For, if... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...PAB, which is equal to the measure of the diedral, is also right. QED Fig. 303. 680. COROLLARY 1. — A spherical angle is measured by the arc of a great circle intercepted between its sides, and at a quadrant's distance from its vertex. Thus, the spherical angle... | |
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A spherical angle is measured by the arc of a great circle described from its vertex as a pole, and included between its sides, produced if necessary. 
