Borelli, Giovanni Alfonso, De motionibus naturalibus a gravitate pendentibus, 1670

Table of figures

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[171. Figure]
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[173. Figure]
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[175. Figure]
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                <pb pagenum="485" xlink:href="010/01/493.jpg"/>
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                <lb/>
              tempore V percurrat ſpatium Z, & fiat IB medią
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              proportionalis inter altitudines AB, & DE. dico
                <expan abbr="tẽ-pus">tem
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                pus</expan>
              T minus eſſe
                <expan abbr="tẽpore">tempore</expan>
              V, ſed
                <expan abbr="tẽpus">tempus</expan>
              V ad T
                <expan abbr="minorẽ">minorem</expan>
                <lb/>
                <expan abbr="proportionẽ">proportionem</expan>
              habere,
                <expan abbr="quã">quam</expan>
              IB habet ad DE; fiat vel in­
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              telligatur figura GBC æquè alta, ac eſt DEF
                <expan abbr="eiuſdẽ-que">eiuſdem­
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                que</expan>
              materiei habens
                <expan abbr="eãdẽ">eandem</expan>
              baſim BC, hac lege vt mo­
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              les ABC ad GBC eamdem
                <expan abbr="proportionẽ">proportionem</expan>
              habeat, quam
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              altitudo AB ad GB, ſitque Y tempus, quo GBC ſur­
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              ſum infra aquam aſcendendo percurrit idem ſpatium
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              X. quoniam ſunt duo folida homogenea ABC, & GB
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              C eamdem baſim BC habentia, quorum moles eam­
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              dem proportionem habent, quam altitudo AB ad G
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              B, ſeù ad DE, & ſimiliter poſita ſunt dum aſcendunt
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                <arrow.to.target n="marg668"/>
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              per ſpatia æqualia X, X; igitur tempus T, quo ABC
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              pertranſit ſpatium X ad tempus Y, quo GBC idipſum
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              ſpatium percurrit, eamdem proportionem habet,
                <expan abbr="quã">quam</expan>
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              DE ad IB. poſtea quia ſunt duo alia ſolida homogenea
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              æquè alta GBC, & DEF quorum baſes planæ BC, &
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              EF eamdem proportionem habent, quam moles eo­
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              rum, ergo tempora Y, & V, quibus in eodem fluido
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                <arrow.to.target n="marg669"/>
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              aqueo aſcendendo percurrunt ſpatia æqualia X, & Z
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              parùm inter ſe differunt, eritque tempus V minus
                <expan abbr="quã">quam</expan>
                <lb/>
              Y, ſed maiorem proportionem ad ipſum habet, quàm
                <lb/>
              DE ad IB, ac proindè tempus V maius erit, quàm T,
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              & ideò celeriùs aſcendet ABC, quàm DEF, ſed iņ
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              minori proportione, quam habet IB ad DE, idemque
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              concludetur in deſcenſu, quod erat &c. </s>
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