Borelli, Giovanni Alfonso
,
De motionibus naturalibus a gravitate pendentibus
,
1670
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Cap. 2. dę
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momentis
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grauium in
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fluido inna
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tantium</
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">SIt pondus A maius, B verò minus alligata extre
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mitatibus funis ADB, qui ſupponatur omninò
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grauitate carere, & reuoluatur circa trochleam CDE
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conuertibilem circa axim fixum F. patet quòd funes
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AC, & BE perpendiculariter ad ho
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rizontem CE prementes, & extenſi
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contingunt peripheriam rotæ in ter
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minis oppoſitis C, & E eiuſdem dia
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metri, ſeu libræ horizontalis, ergo
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funes CA, & EB ſunt inter ſe paralle
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li;
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coniũgatur
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poſtea recta linea AB,
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ſeceturque bifariam in G, & vt pon
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dus A ad B ita fiat diſtantia BI ad IA
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abbr
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manifeſtũ
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eſt (ex mechanicis) punc
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tum I eſſe centrum grauitatis com
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munis duorum colligatorum ponde
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rum A & B, funis enim hanc propor
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tionem non alterat, cùm nullius gra
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uitatis ſupponatur: aſcendat poſtea
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pondus minus B vbicumque ad L, & deprimatur ma
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ius pondus A vſque ad K. dico quod ambo in com
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muni centro grauitatis deſcendunt circa libræ cen
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trum, ſeu fulcimentum ſtabile G motu directo, & per
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pendiculari ad horizontem. </
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coniũgatur
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recta lineą
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KL quia funis ADB æqualis, imò idem eſt, quàm K
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DL, igitur ablato communi ADL erit deſcenſus AK
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æqualis aſcenſui BL; quare in triangulis ſimilibus
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ob æquidiſtantiam laterum AK & BL homologorum
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vt AK ad BL ita erit AG ad GB & ita pariter KML </
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