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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baſi C B parieti infixum, ita ut axis A T ſit horizontalis, ſua gra-
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vitate eſſe in omni ſectione æqualis Cohærentiæ.</
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<
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">Propoſuit hoc Cl. </
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ditamenti, quod abſque demonſtratione reliquit, quam hic adde-
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mus: </
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<
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xml:space
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">Vocetur A T, a. </
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<
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<
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">circumferentia circuli, cujus T B
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eſt radius, ſit = c. </
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<
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xml:space
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">Erit ſoliditas corporis A C B = {1/10} a c r. </
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<
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xml:space
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trum vero gravitatis eſt in axe A T, diſſitum a puncto T = {1/6} a, un-
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de momentum gravitatis in hoc corpore A C B eſt = {1/60} a a c r. </
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<
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xml:space
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hærentia autem eſt ut Cubus baſeos C B = 8 r
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. </
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<
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xml:space
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">fiat ſectio in O, pla-
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no F O E parallelo baſi C T B. </
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<
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xml:space
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">voceturque A O = d. </
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<
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xml:space
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">erit O E = {d d r/a a}.
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</
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<
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">quia T B. </
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xml:space
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">: peripheria circuli â B deſcripti, ad peripheriam ab E. </
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erit hæc peripheria = {c d d/a a}. </
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<
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xml:space
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">quare ſoliditas corporis A F O E
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= {c d
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r.</
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<
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} Centrum gravitatis in A F E diſtat ab O = {1/6} d. </
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">adeoque
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erit momentum hujus corporis ex gravitate = {c d
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r.</
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">/60 a
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} Cohærentia
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baſeos E O F eſt uti Cubus ex E F = {8d
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r
<
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.</
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} Si igitur momenta
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gravitatis in corpore A C B & </
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xml:space
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baſium in eadem ratione, erunt quantitates proportionales, ordi-
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nentur igitur in proportionem
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{1/60} a a c r. </
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:</
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r/60 a
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}, {8d
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r
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.</
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}</
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<
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{1/60} a a c r X {8 d
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r
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.</
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} & </
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r/60 a
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} X 8 r
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.
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">quæ quantitates ſunt inter ſe æquales, adeoque priores erant pro-
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portionales, unde momenta cujuslibet ſectionis in hoc corpore
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paraboliformi ſunt ſemper ad ſuas Cohærentias in eadem propor-
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tione, hoc eſt, erit corpus grave ubivis æquabilis reſiſtentiæ. </
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Q. </
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<
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rizontali tranſeunte per axem A T, erit corpus A T B E A in qua-
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libet Sectione O E æquabilis Cohærentiæ.</
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