 ... solid thus generated is equal to the product of the revolving area and the path described by the center of gravity of the plane area during the revolution.  Applied Mechanics - Page 125de Charles Edward Fuller, William Atkinson Johnston - 1913Affichage du livre entier - À propos de ce livre
 | Bartholomew Price - 1856 - 664 pages
...generates a solid of revolution, the volume of the solid thus generated is equal to the (geometrical) product of the revolving area, and of the path described by its centre of gravity during the revolution. As (42) is true for the whole revolution, a similar theorem... | |
 | George Bruce Halsted - 1881 - 258 pages
...a plane figure, lying wholly on the same side of a line in its own plane, revolves about that line, the volume of the solid thus generated is equal to the product of the revolving area by the length of the path described by its center of mass. /Scholium. As for 66, so we give under 94,... | |
 | Gaetano Lanza - 1889 - 770 pages
...centre of gravity in one revolution. Hence follows the proposition. THEOREM II. — If a plane area lying wholly on the same side of a straight line in...of the revolving area, and of the path described by the centre of gravity of the plane area during the revolution. Proof. — Let the area lie in the xy... | |
 | Calvin Frank Allen - 1894 - 232 pages
...Draw OKP parallel to AB. By the "Theorem of Pappus" (see Lanza, Applied Mechanics), "If a plane area lying wholly on the same side of a straight line in...of the revolving area and of the path described by the center of gravity of the plane area during the revolution." The correction for curvature, or the... | |
 | Calvin Frank Allen - 1894 - 236 pages
...Draw OKP parallel to AB. By the " Theorem of Pappus" (see Lanza, Applied Mechanics), "If a plane area lying wholly on the same side of a straight line in...generated is equal to the product of the revolving FIG. 1. area and of the path described by the center of gravity of the plane area during the revolution."... | |
 | Gaetano Lanza - 1905 - 974 pages
...centre of gravity in one revolution. Hence follows the proposition. THEOREM II. — If a plane area lying wholly on the same side of a straight line in...thereby generates a solid of revolution, the volume of th solid thus generated is equal to the product of the revolvin area, and of the path described by... | |
 | Mansfield Merriman - 1911 - 1404 pages
...may be found by an application of Pappus1 Theorem. **lf i plane area lying wholly on the same aide of a straight line in its own plane revolves about that line and thereby generates a solid ot revolution, the volume of that solid tbus generated is equal to the product of the revolving area... | |
 | Mansfield Merriman - 1912 - 1506 pages
...must be applied. This correction may be found by an application of Pappus' Theorem, '" If a plane area lying wholly on the same side of a straight line in its own plane revolve? about that line and thereby generates a solid ot revolution, the volume of that solid thus... | |
 | Mansfield Merriman - 1916 - 1622 pages
...must be applied. This correction may be found by an application of Pappus' Theorem, *" If a plane area lying wholly on the same side of a straight line in...revolves about that line and thereby generates a solid ot revolution, the volume of that solid thus generated is equal to the product of the revolving area... | |
 | Mansfield Merriman - 1920 - 2038 pages
...must be applied. This correction may be found by an application of Pappus1 Theorem, ** If a plane area lying wholly on the same side of a straight line in its own plane revolves aboul that line and thereby generates a solid oi revolution, the volume of that solid thus generated... | |
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