Fabri, Honoré, Tractatus physicus de motu locali, 1646

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          <chap id="N15AC3">
            <pb pagenum="87" xlink:href="026/01/119.jpg"/>
            <p id="N166E0" type="main">
              <s id="N166E2">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              31.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N166EE" type="main">
              <s id="N166F0">
                <emph type="italics"/>
              Si duo mobilia ferantur motu æquabili per diuerſa ſpatia, & diuerſa velo­
                <lb/>
              citate, tempora erunt in ratione compoſita ex ratione ſpatiorum & ratione
                <lb/>
              velocitatum permutata
                <emph.end type="italics"/>
              ; </s>
              <s id="N166FD">probatur eodem modo quo ſuperius Th. 30. ſit
                <lb/>
              ratio ſpatiorum 4/1, velocitatum 4/2; </s>
              <s id="N16703">permutetur hæc 1/4; componetur ex
                <lb/>
              vtraque 4/1, ideſt 1/2, quæ eſt ratio temporum. </s>
            </p>
            <p id="N16709" type="main">
              <s id="N1670B">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              32.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N16717" type="main">
              <s id="N16719">
                <emph type="italics"/>
              Si duo mobilia æquabili motu ferantur per diuerſa ſpatia, & inæqualibus
                <lb/>
              temporibus; </s>
              <s id="N16721">ratio velocitatum erit compoſita ex ratione ſpatiorum, & ex ra­
                <lb/>
              tione temporum permutata
                <emph.end type="italics"/>
              ; Probatur eodem modo; ſit ratio ſpatiorum
                <lb/>
              4/2 temporum 1/2, permutetur 2/1, compoſita ex vtraque erit 2/2, ideſt 4.
                <lb/>
              quæ eſt ratio velocitatum. </s>
            </p>
            <p id="N1672E" type="main">
              <s id="N16730">
                <emph type="center"/>
                <emph type="italics"/>
              Scholium.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1673C" type="main">
              <s id="N1673E">Obſeruabis hæc omnia à vigeſimo Theoremate maiori ex parte tradi
                <lb/>
              à Galileo ſuo modo, optimo quidem, ſed fortè longiore quàm par ſit,
                <lb/>
              nulla habita ratione cauſarum phyſicarum. </s>
            </p>
            <p id="N16745" type="main">
              <s id="N16747">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              33.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N16753" type="main">
              <s id="N16755">
                <emph type="italics"/>
              In motu naturaliter accelerato impetus nouus acquiritur ſingulis inſtanti­
                <lb/>
              bus
                <emph.end type="italics"/>
              ; Probatur quia ſingulis inſtantibus eſt eadem cauſa neceſſaria, igi­
                <lb/>
              tur ſingulis inſtantibus aliquem effectum producit, per Ax. 12. l.1. ſed
                <lb/>
              priorem non conſeruat, vt dictum eſt ſuprà, igitur nouum producit. </s>
            </p>
            <p id="N16764" type="main">
              <s id="N16766">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              34.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N16772" type="main">
              <s id="N16774">
                <emph type="italics"/>
              Hinc ſingulis inſtantibus æqualibus nouus impetus æqualis acquiritur,
                <emph.end type="italics"/>
              quip­
                <lb/>
              pe eſt æqualis, imò eadem cauſa, igitur æqualem effectum producit per
                <lb/>
              Ax.12. l.1. </s>
            </p>
            <p id="N16780" type="main">
              <s id="N16782">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              35.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1678E" type="main">
              <s id="N16790">
                <emph type="italics"/>
              Hinc ſingulis inſtantibus intenditur impetus in hoc motu
                <emph.end type="italics"/>
              ; cum ſingulis
                <lb/>
              inſtantibus producatur nouus, & prior conſeruetur, cui cum addatur,
                <lb/>
              intenditur per Ax. 1. </s>
            </p>
            <p id="N1679E" type="main">
              <s id="N167A0">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              36.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N167AC" type="main">
              <s id="N167AE">
                <emph type="italics"/>
              Hinc ſingulis inſtantibus æqualiter creſcit & intenditur impetus
                <emph.end type="italics"/>
              per Th.
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              34. igitur æqualiter etiam ſingulis inſtantibus creſcit velocitas motus
                <lb/>
              per Ax.2. </s>
            </p>
            <p id="N167BB" type="main">
              <s id="N167BD">
                <emph type="center"/>
                <emph type="italics"/>
              Scholium
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N167C8" type="main">
              <s id="N167CA">Obſeruabis
                <expan abbr="dictū">dictum</expan>
              eſſe ſuprà
                <emph type="italics"/>
              instantibus æqualibus,
                <emph.end type="italics"/>
              quia temporis natura
                <lb/>
              aliter explicari non poteſt, quàm per inſtantia finita, vt demonſtrabimus
                <lb/>
              in Metaphyſica; </s>
              <s id="N167DC">quid quid ſit, voco inſtans totum illud tempus, quo res
                <lb/>
              aliqua ſimul producitur, ſiue ſit maius, ſiue minus, ſiue ſit pars maior,
                <lb/>
              vel minor, quod ad rem noſtram nihil facit penitus; </s>
              <s id="N167E4">nam dato quocun­
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              que tempore finito poteſt dari maius & minus, quod certum eſt; </s>
              <s id="N167EA">igitur
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              totum illud tempus, quo producitur primus impetus acquiſitus, vo-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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