... of the spherical shell, which form the bases of both the cones, or pyramids, be similar and equally inclined to their axes. Therefore their areas will be to each other as the squares of their distances from the common apex. Therefore their attractions... Astronomy - Page 353by John Frederick William Herschel - 1833 - 422 pagesFull view - About this book
| William Enfield - Astronomy - 1811 - 428 pages
...candle through a square orifice, will diverge as it pro ' ceeds, and will illuminate surfaces which **will be to each other as the squares of their distances from the** candle. Thus at the distance AF the candle will illuminate the square BF, at the distance AO it will... | |
| Charles Hutton - Mathematics - 1812
...BCD be a cone, and GUI a section parallel, to the base BCD ; then will GHI be a circle, and BCD, GUI, **will be to each other, as the squares of their distances from the** vertex. For, draw ALP perpendicular to the two parallel planes ; and let the planes ACE, ADB, pass... | |
| Thomas Keith - 1817
...plane parallel to its base, the section will be similar to the base ; and the section and the base **will be to each other, as the squares of their distances from the** vertex •f the pyramid or cone. (Kdib'i Geometry, 12 and 13 of X.) 11. A wedge is a solid, having... | |
| Charles Hutton - Mathematics - 1822
...ABCD be a cone, and GHI a section parallel to the base BCD ; then will GHI be acircle,and BCD, CHI, **will be to each other, as the squares of their distances from the** vertex. For, draw ALF perpendicular to the two parallel planes ; and let the planes ACE, ADB, pass... | |
| James Mitchell - Mathematics - 1823 - 576 pages
...dissimilar. 3. Any section of a pyramid parallel to its base will be similar to the base, and these **areas will be to each other as the squares of their distances from the** vertex. 4. Pyramids, when their bases are equal, are to each other as their altitudes, and when their... | |
| Sir Richard Phillips - Physics - 1826 - 214 pages
...candle or any luminous bodj>, will diverge as it proceeds, and will illuminate surfaces, which surfaces **will be to each other as the squares of their distances from the** candle. Thus, if at the distance of one foot, the candle illuminates any surface, at double the distance... | |
| John Playfair - Mathematics - 1829 - 186 pages
...plane parallel to its base, the section will be similar to the base ; and the section and the base **will be to each other as the squares of their distances from the** vertex of the pyramid. 1. Let ABCD be a pyramid, and EFG a section parallel to the base ABC. From the... | |
| Francis Lieber - Encyclopedias and dictionaries - 1832
...dissimilar. 3. Any section of a pyramid parallel to its base will be similar to the base, and these **areas will be to each other as the squares of their distances from the** vertex. 4. Pyramids, when their bases are equal, are to euch other as their altitudes ; and when their... | |
| sir John Frederick W. Herschel (1st bart.) - 1833
...well to demonstrate it ; which may be done very simply, and without the aid of any calculus. Conceive **a spherical shell, and a point within it : every line...in opposite directions, and, therefore, counteract** each other. Therefore, the point is in equilibrium between them ; and as the same is true of every... | |
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