 | Charles Hutton - Mathematics - 1812
...their like linear dimensions, since they are composed of pyramids every way similar. THEOREM CXVI. If a Sphere be cut by a Plane, the Section will be...then will the section ADB be a circle. Draw the chord AB, or diameter of the section ; perpendicular to which, or to the section ADB, draw the axis of the... | |
 | Charles Hutton - Mathematics - 1818 - 646 pages
...their like linear dimensions, since they are composed of pyramids every way similar. THEOREM CXY1. lf a Sphere be cut by a Plane, the Section will be a...then will the section ADB be a circle. Draw the chord AB, or diameter of the section ; perpendicular to which, or to the section ADB, draw the axis of the... | |
 | Charles Hutton - Mathematics - 1822 - 618 pages
...their like linear dimensions, since they are composed of pyramids every way similar, THEOREM CXVI. If a Sphere be cut by a Plane, the Section will be...a Circle.. LET the sphere AEBF be cut by the plane ADR ; then will the section ADB be a circle. Draw the chord AB, or diameter of the section ; perpendicular... | |
 | Charles Hutton - Mathematics - 1825
...linear dimensions, since they are composed of pyramids every way similar. THEOREM CXVI. If a Sphere b« cut by a Plane, the Section will be a Circle. LET...then will the section ADB be a circle. Draw the chord AB. or diameter of the section ; perpendicular to which, or to the section ADB, draw the axis of the... | |
 | Peter Nicholson - 1826 - 382 pages
...walls from whence they spring, are dependant on the following principles. 158. It is well known that, if a sphere be cut by a plane, the section will be a circle; and, if a hemisphere be cut by a plane perpendicular to its base, the section will be a semi-circle.... | |
 | Charles Hutton - Mathematics - 1831 - 634 pages
...their like linear dimensions, since they are composed of pyramids every way similar. THEOREM cxvr. IF a sphere be cut by a plane, the section will be a circle. Let the sphere AEBF be cut by the plane .ми; ; then will the section ADB be a circle. If the section pass through the centre of the sphere,... | |
 | Charles Hutton - Mathematics - 1831 - 670 pages
...their like linear dimensions, since they are composed of pyramids every way similar. THEOREM CXVI. IP a sphere be cut by a plane, the section will be a circle. Let the sphere AEBF be cut by the plane _K_ ADB ; then will the section ADB be a circle. If the section pass through the centre of the sphere,... | |
 | William Galbraith - Astronomy - 1834 - 428 pages
...revolving semicircle. 5. The axis of the sphere is the straight line about which the semicircle relolves. PROPOSITION I. 6. If a sphere be cut by a plane, the...perpendicular to the section ADB, and through the centre C draw the axis of the sphere ECGF, which will (Euc. III. 3.) bisect the chord AB in the point G. Also... | |
 | Olinthus Gregory - Mathematics - 1834 - 472 pages
...equal to one another. 11. Every pyramid is a third part of a prism of the same base and altitude. 12. If a sphere be cut by a plane, the section will be a circle. 13. Every sphere is two-thirds of its circumscribing cylinder. 14. A cone hemisphere, and cylinder... | |
 | Luke Hebert - Industrial arts - 1835 - 938 pages
...a perfectly flat surface in whatever position, as horizontal plane, vertical plane, inclined plane. If a sphere be cut by a plane, the section will be a circle. If a prism or cylinder be cut by a plane, either through or parallel to its axis, the section will... | |
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... pyramids or cones are as the cubes of their like linear sides, or diameters, or altitudes, &c. And the same for all similar solids whatever, viz. that they are in proportion to each other, as the cubes of their like linear dimensions, since they are... 
