Fabri, Honoré, Dialogi physici in quibus de motu terrae disputatur, 1665

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          <chap>
            <p type="main">
              <s id="s.000763">
                <pb pagenum="67" xlink:href="025/01/071.jpg"/>
              phyſicorum; hîc non diſcutio cauſæ merita, ne ſaltem extra chorum; id
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              vnum dumtaxat dico, illam progreſſionem alteri præferendam eſſe, quæ &
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              vtrique quantitatis hypotheſi ſatisfacit, & ipſis experimentis non repu­
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              gnat: quòd autem progreſſio Galileana in hypotheſi finitorum inſtan­
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              tium non ſubſiſtat, perſpicuè demonſtro; Sit enim motus quiſpiam natu­
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              ralis, qui duret per 4. inſtantia, in quorum primo, mobile acquirat ſpa­
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              tium 1. in ſecundo 3. in tertio 5. in quarto 7. cùm velocitas creſcat, vt
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              tempus, in ſecundo inſtanti velocitas erit dupla, quomodo igitur acquiri­
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              tur triplum ſpatium? </s>
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            <p type="main">
              <s id="s.000764">
                <emph type="italics"/>
              Auguſtin.
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              </s>
              <s id="s.000765"> Nihil facilius triangulo Galileano, in quo res iſta clariſſi­
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                <figure id="id.025.01.071.1.jpg" xlink:href="025/01/071/1.jpg" number="21"/>
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              mè demonſtratur: Sit enim triangulum AEI, ſit
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              tempus diviſum in 4.partes æquales, & primo tempo­
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              re AB, ſpatium acquiſitum ſit triangulum ABF, &
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              velocitas acquiſita BF, ſecundo tempore erit veloci­
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              tas acquiſita CG, creſcit enim, vt tempus, & vt AB
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              ad BF, ita AC ad CG ; idem dico de quolibet alio
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              temporis puncto accepto inter BC ; igitur ſpatium ac­
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              quiſitum erit trapezium BCGF, triplum trianguli
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              ABF, nempe cum velocitate BF æquabili motu, tem­
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              pore BC, acquireret rectangulum BM, ſed virtute ve­
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              locitatis acquiſitæ tempore BC æqualis velocitati BF, acquiritur triangu­
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              lum FMG æquale ABF; igitur ſecundo tempore triplum ſpatium
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              prioris. </s>
            </p>
            <p type="main">
              <s id="s.000766">
                <emph type="italics"/>
              Antim.
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              Hæc omittere poteras, quæ iam trita ſunt, nec à me negantur;
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              nempe velocitas BF acquiritur ſucceſtivè tempore AB, quod ſi ſuppona­
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              tur eſſe inſtans phyſicum, accipienda eſt velocitas. </s>
              <s id="s.000767">BF tota ſimul, re­
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              ſpondeo enim toti inſtanti, ac proinde tota ſimul eſt, non verò ſucceſſi­
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              vè acquiſita, igitur ſpatium debet accipi in rectangulo, non verò in trian­
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                <figure id="id.025.01.071.2.jpg" xlink:href="025/01/071/2.jpg" number="22"/>
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              gulo; v.g. Sit tempus AE 4. inſtantiam, ſit pri­
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              mus gradus velocitatis AG, & ſpatium acqui­
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              ſitum rectangulum AV; ſecundo inſtanti ve­
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              locitas acquiſita erit BH, dupla ſcilicet AG;
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              nempe tota prior remanet, & tantumdem ab ea­
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              dem cauſa, æquali tempore ponitur; igitur ſpa­
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              tium eſt duplum prioris, ac proinde erit rectan­
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              gulum CH duplum prioris. </s>
            </p>
            <p type="main">
              <s id="s.000768">
                <emph type="italics"/>
              Auguſtin.
                <emph.end type="italics"/>
              </s>
              <s id="s.000769"> Duo abſurda ex his mihi deducere videor; primò enim, pri­
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              mo tempore AB, duplum ſpatium trianguli Galileani aſſumis; nempe re­
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              ctangulum AV duplum eſt trianguli ABV, cùm tamen æquale primum
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              tempus aſſumi debeat, ad perfectam comparationem; ſecundò longè majus
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              ſpatium decurritur ſecundùm tuam progreſſionem, quàm ſecundùm Ga­
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              lileanam, in qua ſpatium decurſum tempore AE continet 16. triangula
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              æqualia triangulo ABV, in tua verò continet 10. rectangula æqualia
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              AV; igitur 20. triangula æqualia ABV, igitur ſpatium Galileanum erit
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              ad tuum vt 16. ad 20. ſeu vt 4. ad 5. igitur majus vna quarta parte, quod </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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