Gassendi, Pierre, De proportione qua gravia decidentia accelerantur, 1646

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            <p type="main">
              <s id="s.000688">
                <pb pagenum="68" xlink:href="028/01/108.jpg"/>
              percurri. </s>
              <s id="s.000689">Quippe & tametſi partes ſint incompara­
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              biliter plures in ſemidiametro Mundi, quàm in ſpa­
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              tiolo DE, ſunt tamen gradus velocitatis incompara­
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              biliter etiam plures, ac proportione totidem; vt tem­
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              pora ſubmultipla illis ſuperandis ſufficere valeant. </s>
              <s id="s.000690">Vt
                <lb/>
              breue faciam, erroris origo ex eo profluxiſſe videtur,
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              quòd merè gratis conſtiteris in parte AD, eiuſque
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              dimidio inferiore SD; & rem perinde habueris, ac ſi
                <lb/>
              dimidium ſuperius AS diuidi perinde non poſſet, ne­
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              que haberet ſpeciatim dimidium eadem ratione, qua
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              habet AD. </s>
              <s id="s.000691">Proptereà enim accepiſti ſolùm omnia
                <lb/>
              deſignabilia punctaper totam DE, in quibus veloci­
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              tas eſſet dupla velocitatis in totidem punctis per to­
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              tam SD; neque reputaſti pergendum, vt haberes
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              eodem tenore puncta deſignabilia per totam SD, in
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              quibus velocitas eſſet dupla velocitatis in totidem
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              punctis deſignabilibus per totam PS, atque ita in in­
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              finitum; vt prorsùs neceſſarium eſt ex tua ipſius ſup­
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              poſitione. </s>
              <s id="s.000692">Quanquam res vberiùs cognoſcenda eſt
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              circa cæteras, quas deſcribis parteis. </s>
            </p>
            <p type="main">
              <s id="s.000693">XXXVII. </s>
              <s id="s.000694">Vt enim probes (reſumpto iam recen­
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              tiore ſchemate) tempus per tertiam partem DE æqua­
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              le eſſe tempori per trientem primæ partis IC,
                <emph type="italics"/>
              Sumpto,
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                <lb/>
              inquis, CN
                <emph type="italics"/>
              æquali ipſi
                <emph.end type="italics"/>
              CE,
                <emph type="italics"/>
              erit tota
                <emph.end type="italics"/>
              AD
                <emph type="italics"/>
              diuiſa in
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              treis parteis æqualeis
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              AI, IN,
                <emph type="italics"/>
              &
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              ND;
                <emph type="italics"/>
              eritque veloci­
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              tas in
                <emph.end type="italics"/>
              D
                <emph type="italics"/>
              ad velocitatem in
                <emph.end type="italics"/>
              I,
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              vt tota
                <emph.end type="italics"/>
              AD
                <emph type="italics"/>
              ad ipſam
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              AI,
                <emph type="italics"/>
              hoc
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              eſt tripla. </s>
              <s id="s.000695">Cumque ob eandem cauſſam velocitas quoque in
                <emph.end type="italics"/>
              E
                <lb/>
                <emph type="italics"/>
              tripla etiam ſit velocitatis in
                <emph.end type="italics"/>
              C,
                <emph type="italics"/>
              erit velocitas per totam
                <emph.end type="italics"/>
              DE
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                <emph type="italics"/>
              tripla velocitatis per totam
                <emph.end type="italics"/>
              IC,
                <emph type="italics"/>
              ſicut tota
                <emph.end type="italics"/>
              DE
                <emph type="italics"/>
              tripla eſt ipſius
                <emph.end type="italics"/>
                <lb/>
              IC;
                <emph type="italics"/>
              ac proinde percurrentur
                <emph.end type="italics"/>
              IC,
                <emph type="italics"/>
              &
                <emph.end type="italics"/>
              DE
                <emph type="italics"/>
              æquali tempore.
                <emph.end type="italics"/>
              </s>
            </p>
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