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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...
Mathematical and Astronomical Tables: For the Use of Students of Mathematics ... - Page 40
by William Galbraith - 1827 - 322 pages

## A Course of Mathematics: For the Use of Academies as Well as ..., Volume 1

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...

## A Course of Mathematics: In Two Volumes. For the Use of Academies ..., Volume 1

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...

## A Course of Mathematics: For the Use of Academies, as Well as Private ...

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...

## A Course of Mathematics for the Use of Academies: As Well as ..., Volume 1

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...

## Practical carpentry, joinery, and cabinet-making [by P. Nicholson

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....

## A Course of Mathematics: For the Use of Academies as Well as ..., Volume 1

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,...

## A Course of Mathematics: For the Use of Academies as Well as ..., Volume 1

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,...

## Mathematical and Astronomical Tables: For the Use of Students in Mathematics ...

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...