Musschenbroek, Petrus van
,
Physicae experimentales, et geometricae de magnete, tuborum capillarium vitreorumque speculorum attractione, magnitudine terrae, cohaerentia corporum firmorum dissertationes: ut et ephemerides meteorologicae ultraiectinae
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INTRODUCTIO AD COHÆRENTIAM
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ſoliditas hemisphærii A B C erit = {crr:</
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xml:space
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rio centrum gravitatis {3/8} r ab A C. </
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momentum = {cr
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/8}. </
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<
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lindri.</
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<
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">Determinare Cohærentiam hemisphærii
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A B C & </
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">ſegmenti ejus F B E, cujus baſis parallela baſi A D C. </
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<
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ſitis his baſibus parieti affixis.</
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<
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">Sunt hæ Cohærentiæ inter ſe, uti Cubi diametrorum in baſibus
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A C, F E. </
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">ut autem magnitudines horum cuborum noſcantur, vo-
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cetur A D aut D B, r. </
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<
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">B G ſit = x. </
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<
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">eritque F G
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= 2rx-xx, unde
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Cubus F G = 2rx-xx X 2rx - xx. </
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">& </
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<
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. </
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<
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re Cohærentia baſeos A D C eſt ad eam baſeos F G E uti r
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ad
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2rx - xx X 2rx - xx.</
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">Dati Hemispbærii ABC, & </
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FBE invenire momenta ex gravitate oriunda, poſitis baſibus
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A C, F E parieti ad horizontem perpendiculari affixis.</
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<
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<
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">circumferentia circuli c. </
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">erit mo.
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</
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<
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">mentum Hemisphærii = {cr
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/8} per Propoſitionem XC: </
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<
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B G = x. </
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<
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<
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">ſumatur Gg pars infinite parva, erit
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hæc = dx, ut proinde habeatur peripheria circuli deſcripti â
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puncto F. </
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xml:space
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">{cy/r} = peripheriæ, quæ ductain {1/2}y, dabit
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{cyy/2r} = circulo; </
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<
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">hic multiplicatus per d x, dabit {cyvdx/2r} differentiale
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ſolidum; </
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<
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">verum ex natura ſphæræ eſt yy = 2rx - xx unde pro yy
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ſubſtituendo hunc valorem, fit{cyydx/2r} = cxdx - {cxxdx/2r}, </
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