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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vitate = {aacr/12}. </
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<
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xml:space
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">momentum ponderis = ap. </
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<
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xml:space
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">Cohærentia = 8r
<
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.
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</
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<
s
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xml:space
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">ſed Conoidis quæſitæ ſoliditas erit = {bbcx/4r}. </
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<
s
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echoid-s14590
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xml:space
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">ejuſque momentum
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lb
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= {bbcxx/12r}. </
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<
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xml:space
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">& </
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<
s
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xml:space
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">Cohærentia = 8b
<
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>
. </
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<
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">ponitur in Propoſitione
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{aacr/12} + ap, 8r
<
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:</
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>
<
s
xml:id
="
echoid-s14594
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xml:space
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">: {bbcxx/12r}. </
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<
s
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xml:space
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">8b
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<
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unde eruitur x = 8aab
<
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cr + 96b
<
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>
ap - 8bbcrr.</
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>
<
s
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</
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<
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<
s
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">Cognita longitudine parabolæ x, dataque ejus ordinata = b. </
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<
s
xml:id
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xml:space
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">fa-
<
lb
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cile invenitur parameter = {bb/x}. </
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>
<
s
xml:id
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echoid-s14599
"
xml:space
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preserve
">quâ erutâ deſcribetur parabola per
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Prop. </
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<
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">VII. </
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<
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">vel VIII. </
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">Hoſpitalii Lib. </
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">I. </
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<
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">Coniq. </
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<
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">deſcriptâ Para-
<
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bolâ circa axin circumvolutâ, generabitur Conois parabolica quæ-
<
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ſita.</
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<
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</
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</
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<
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">PROPOSITIO LXVII.</
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<
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<
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">XXVI. </
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<
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<
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">2. </
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<
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xml:space
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">Data Conoide parabolica gravi A B C dato-
<
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que pondere P, cujus momentum ſimul cum momento ponderis dati
<
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/>
ſolidi ſit in quacunque ratione data, invenire aliam Conoidem pa-
<
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/>
rabolicam, quæ datam quamlibet babeat longitudinem, & </
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<
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">cujus
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momentum ex gravitate ad Cohærentiam ſuam ſit in eadem ratione.</
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<
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</
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<
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<
s
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xml:space
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">Quantitatibus Conoidis A B C vocatis ut in præcedenti Propoſi-
<
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tione, erit Conoidis momentum = {aacr/12}. </
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>
<
s
xml:id
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xml:space
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">momentum ponderis
<
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/>
= ap. </
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>
<
s
xml:id
="
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xml:space
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">Cohærentia = 8r
<
emph
style
="
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emph
>
.</
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<
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</
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<
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<
s
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xml:space
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">Sit longitudo Conoidis quæſitæ data G F = d. </
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<
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xml:space
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">radius baſeos quæ-
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ſitus G D = x. </
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<
s
xml:id
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xml:space
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">erit ejus peri pheria = {cx/r}, ſolidum = {cdxx/4r}. </
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<
s
xml:id
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xml:space
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">cujus mo-
<
lb
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mentum = {cddxx/12r}. </
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<
s
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xml:space
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">Cohærentia = 8x
<
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>
. </
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>
<
s
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xml:space
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">quare ordinanda hæcpro-
<
lb
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portio, cum momenta gravitatis ad Cohærentias ſuas debent habe-
<
lb
/>
re eandem rationem, {cddxx/12r}. </
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>
<
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xml:space
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">8x
<
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:</
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<
s
xml:id
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echoid-s14626
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xml:space
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">: {aacr/12} + ap. </
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>
<
s
xml:id
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xml:space
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">8r
<
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>
.</
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