 | David Munn - Measurement - 1874 - 374 pages
...AB ; .-. whole volume = f ir , AP2 . CP • = — , where s denotes the length of side. 4 ii. Since the volume generated is equal to the product of the area of the parallelogram by the circumference described by its centre, we have volume generated round AB = area... | |
 | Benjamin Williamson - Calculus - 1877 - 372 pages
...revolution is 2ir (y + y') ds = qirbds. Consequently the surface generated by the entire curve is 2irbS, where S denotes the whole length of the curve. A similar...volume of this solid is plainly represented by or by *• J (y - y'} (y But the area of the curve is represented by J (y - y) dx •. consequently, denoting... | |
 | Benjamin Williamson - Calculus of variations - 1880 - 398 pages
...is represented by им g- 43Consequently the surface generated by the entire curve is 2irbS, where 8 denotes the whole length of the curve. A similar theorem...the revolving curve into the circumference of the san^e circle as before. For the volume of this solid is plainly represented by or by я- 1 (yy')(y... | |
 | Benjamin Williamson - Calculus of variations - 1884 - 424 pages
...complete revolution is represented by 43Consequently the surface generated by the entire curve is 2irbS, where S denotes the whole length of the curve. A similar...volume of this solid is plainly represented by or by ir\(y- У') (У + У') dx = 2-nb \(y - y") dx. But the area of the curve is represented Ly \(yy'}<lc:... | |
 | Oxford univ, local exams - 1885 - 358 pages
...right line, be made to revolve round a parallel line which does not intersect the curve, prove that the volume generated is equal to the product of the...the revolving curve into the circumference of the circle whose radius is the distance between the parallel lines. Discuss the theorem when the axis of... | |
 | 1902 - 786 pages
...y1 " Shew that if the trapezium is rotated about the square end so as to generate a truncated cone, the volume generated is equal to the product of the area of the trapezium and the length of the path described by its cm 8. State and prove Archimedes' Theorem of... | |
 | Encyclopedias and dictionaries - 1907 - 936 pages
...length of the path described by the centre of gravity of that perimeter ; ('.Hi the volume of the solid is equal to the product of the area of the revolving curve and the length of the path described by the centre of gravity of the revolving area. We content ourselves... | |
 | Edwin Bidwell Wilson - Calculus - 1912 - 586 pages
...orders. 27. A theorem of Pappus. If a closed plane curve be revolved about an axis which does not cut it, the volume generated is equal to the product of the area of the curve by the distance traversed by the center of gravity of the area. Prove either analytically or... | |
 | Ernst Rudolph Breslich - Logarithms - 1917 - 408 pages
...completely around a straight line in its plane, not crossing it, but parallel to one of its sides, the volume generated is equal to the product of the area of the square and the length of the circumference traced by its center. (Harvard.) 14. A glass vessel made... | |
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P'Q' in a complete revolution is represented by 43Consequently the surface generated by the entire curve is 2irbS, where S denotes the whole length of the curve. A similar theorem holds for the volume of the solid generated : viz., the volume generated... 