| Thomas Keith - Navigation - 1810 - 420 pages
...s=r^ of the surface of the sphere, 180°x wi=sx (A + B+C- 180°). SX(A + B4 c-180") S But the whole **surface of the sphere is equal to four times the area of** one of its great • cird es *, and the area of a great circle = •i- circumference x radius = 1 80°... | |
| John Bonnycastle - Trigonometry - 1818 - 438 pages
...360° : the part, or arc, am : : surface of the sphere : the area of the lune AB c AQED COR. Since **the surface of the sphere is equal to four times the area of** one of its great circles, if d be put = diameter, c = circumference, and a — length of the arc B... | |
| Thomas Keith - Navigation - 1826 - 442 pages
...surface of the sphere, 180°xm=s X(A + B + C— 180°). SX(A + B + C-180°) S '* -- -- But the whole **surface of the sphere is equal to four times the area of** one of its great circles*, and the area of a great circle=£ circumference x radius =1 80° x radius,... | |
| John West, Sir John Leslie - Analytic functions - 1838 - 574 pages
...circumference of the generating circle multiplied by the altitude of the segment. Hence, the whole **surface of the sphere is equal to four times the area of a great circle.** EXAMPLE 5. To find the curve surface of the parabolic conoid. From the equation of the parabola, y'... | |
| Thomas Keith - 1839
...right angles. For if si= | of the surface of the sphere, 180°xm=sx (A + B + C — 180°) But the whole **surface of the sphere is equal to four times the area of** one of its great circles *, and the area of a great circles | circumference x radius = 180° x radius... | |
| Paolo Mancosu - Drama - 1999 - 275 pages
...Archimedean demonstrations clear and evident ones." 38 Guldin expressed his admiration for the theorem **that the surface of the sphere is equal to four times the** great circle, a theorem proved apagogically by Archimedes. However, the proof provided by Archimedes... | |
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