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" ... 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 353
by John Frederick William Herschel - 1833 - 422 pages
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Institutes of Natural Philosophy: Theoretical and Practical

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

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...
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The complete measurer: or, The whole art of measuring, containing the ...

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

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...
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Dictionary of the Mathematical and Physical Sciences, According to the ...

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...
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A Grammar of Natural and Experimental Philosophy ...: With One Hundred ...

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...
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Elements of geometry: Being chiefly a selection from Playfair's geometry

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...
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Encyclopędia Americana: A Popular Dictionary of Arts, Sciences ..., Volume 10

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...
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Encyclopaedia Americana: A Popular Dictionary of Arts, Sciences ..., Volume 10

Francis Lieber, Edward Wigglesworth, Thomas Gamaliel Bradford - 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 each oiher as their altitudes; and when their...
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Astronomy

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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