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" COROLLARY. The measure of the surface of a spherical triangle is the difference between the sum of its three angles and two right angles. For if s =-J- of the surface of the sphere, 180xm=s X(A + B + C— 180). "
Sir Isaac Newton's Two Treatises: Of the Quadrature of Curves and Analysis ... - Page 288
by Sir Isaac Newton - 1745 - 479 pages
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An Introduction to the Theory and Practice of Plane and Spherical ...

Thomas Keith - Navigation - 1810 - 420 pages
...s=r^ of the surface of the sphere, 180x 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...
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A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ...

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...
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An Introduction to the Theory and Practice of Plain and Spherical ...

Thomas Keith - Navigation - 1826 - 442 pages
...surface of the sphere, 180xm=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,...
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Mathematical Treatise: Containing I. The Theory of Analytical Functions, II ...

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'...
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An introduction to the theory ... of plane and spherical trigonometry ...

Thomas Keith - 1839
...right angles. For if si= | of the surface of the sphere, 180xm=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...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich, Thomas Stephens Davies, Stephen Fenwick, William Rutherford - Mathematics - 1853
...cones are in the ratio compounded of the ratio of their bases and the ratio of their altitudes. (f) The surface of the sphere is equal to four times the area of its great circle. (j?) Every sphere is in volume equal to two-thirds of its circumscribing cylinder....
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Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

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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