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

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      <text>
        <body>
          <chap>
            <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
                <lb/>
              biliter plures in ſemidiametro Mundi, quàm in ſpa­
                <lb/>
              tiolo DE, ſunt tamen gradus velocitatis incompara­
                <lb/>
              biliter etiam plures, ac proportione totidem; vt tem­
                <lb/>
              pora ſubmultipla illis ſuperandis ſufficere valeant. </s>
              <s id="s.000690">Vt
                <lb/>
              breue faciam, erroris origo ex eo profluxiſſe videtur,
                <lb/>
              quòd merè gratis conſtiteris in parte AD, eiuſque
                <lb/>
              dimidio inferiore SD; & rem perinde habueris, ac ſi
                <lb/>
              dimidium ſuperius AS diuidi perinde non poſſet, ne­
                <lb/>
              que haberet ſpeciatim dimidium eadem ratione, qua
                <lb/>
              habet AD. </s>
              <s id="s.000691">Proptereà enim accepiſti ſolùm omnia
                <lb/>
              deſignabilia punctaper totam DE, in quibus veloci­
                <lb/>
              tas eſſet dupla velocitatis in totidem punctis per to­
                <lb/>
              tam SD; neque reputaſti pergendum, vt haberes
                <lb/>
              eodem tenore puncta deſignabilia per totam SD, in
                <lb/>
              quibus velocitas eſſet dupla velocitatis in totidem
                <lb/>
              punctis deſignabilibus per totam PS, atque ita in in­
                <lb/>
              finitum; vt prorsùs neceſſarium eſt ex tua ipſius ſup­
                <lb/>
              poſitione. </s>
              <s id="s.000692">Quanquam res vberiùs cognoſcenda eſt
                <lb/>
              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
                <lb/>
              tiore ſchemate) tempus per tertiam partem DE æqua­
                <lb/>
              le eſſe tempori per trientem primæ partis IC,
                <emph type="italics"/>
              Sumpto,
                <emph.end type="italics"/>
                <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
                <lb/>
              treis parteis æqualeis
                <emph.end type="italics"/>
              AI, IN,
                <emph type="italics"/>
              &
                <emph.end type="italics"/>
              ND;
                <emph type="italics"/>
              eritque veloci­
                <lb/>
              tas in
                <emph.end type="italics"/>
              D
                <emph type="italics"/>
              ad velocitatem in
                <emph.end type="italics"/>
              I,
                <emph type="italics"/>
              vt tota
                <emph.end type="italics"/>
              AD
                <emph type="italics"/>
              ad ipſam
                <emph.end type="italics"/>
              AI,
                <emph type="italics"/>
              hoc
                <lb/>
              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
                <lb/>
                <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>
          </chap>
        </body>
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