Fabri, Honoré, Tractatus physicus de motu locali, 1646

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          <chap id="N15AC3">
            <pb pagenum="125" xlink:href="026/01/157.jpg"/>
            <p id="N1897F" type="main">
              <s id="N18981">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              107.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1898D" type="main">
              <s id="N1898F">
                <emph type="italics"/>
              Plures partes reſistunt, quando plures pelluntur à mobili deorſum
                <emph.end type="italics"/>
              ; </s>
              <s id="N18998">quip­
                <lb/>
              pe in tantum reſiſtunt, in quantum ab aliis ſeparantur; </s>
              <s id="N1899E">atqui in tantum
                <lb/>
              ſeparantur, in quantum amouentur è ſuo loco; </s>
              <s id="N189A4">ſed ideo amouentur è
                <lb/>
              ſuo loco, in quantum pelluntur; </s>
              <s id="N189AA">igitur cum plures pelluntur tunc plures
                <lb/>
              reſiſtunt; igitur tunc maior eſt reſiſtentia. </s>
            </p>
            <p id="N189B0" type="main">
              <s id="N189B2">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              108.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N189BE" type="main">
              <s id="N189C0">
                <emph type="italics"/>
              Plures pelluntur à maiori ſuperficie, quàm à minori, quæ tendit deorſum
                <lb/>
              parallela horizonti.
                <emph.end type="italics"/>
              v.g. à ſuperficie cubi maioris, quàm minoris; quippe
                <lb/>
              tot pelluntur quot reſpondent primæ faciei, ſeu primo plano, quod eſt in
                <lb/>
              fronte. </s>
            </p>
            <p id="N189D1" type="main">
              <s id="N189D3">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              109.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N189DF" type="main">
              <s id="N189E1">
                <emph type="italics"/>
              Si diuidatur cubus in cubos minores, ratio ſuperficierum erit duplicat a la­
                <lb/>
              terum, & ratio ſolidorum triplicata,
                <emph.end type="italics"/>
              conſtat ex Geometria, ſit enim cubus </s>
            </p>
            <p id="N189EB" type="main">
              <s id="N189ED">
                <arrow.to.target n="note2"/>
                <lb/>
              GK, nam in gratiam eorum qui Geometriam ignorant hoc ipſum ocu­
                <lb/>
              lis ſubiiciendum eſſe videtur; diuidantur 6. eius facies in 4. quadrata
                <lb/>
              æqualia v. g. facies AI in quad. </s>
              <s id="N189FD">AE. EC. EG. EI. idem fiat in aliis
                <lb/>
              5. faciebus, quarum duæ hîc tantum apparent; ſcilicet AK. KL; </s>
              <s id="N18A03">ſed
                <lb/>
              tribus aliis parallelis; </s>
              <s id="N18A09">his tribus cædem diuiſiones reſpondent; </s>
              <s id="N18A0D">haud
                <lb/>
              dubiè erunt cubi minores, quorum latus ſit æquale AB, & quælibet fa­
                <lb/>
              cies æqualis quadrato AE, ſed facies maior AI, eſt quadrupla minoris
                <lb/>
              AE, ergo AI eſt ad AE vt quadratum lateris AG ad quadratum lateris
                <lb/>
              AD; ſed hæc eſt ratio duplicata laterum 1. 2. 4. ſimiliter cubus maior
                <lb/>
              GK eſt octuplum minoris DN, igitur vt cubus lateris AG ad cubum
                <lb/>
              lateris AD. ſed hæc eſt ratio triplicata. </s>
              <s id="N18A1D">1.2.4.8. </s>
            </p>
            <p id="N18A20" type="margin">
              <s id="N18A22">
                <margin.target id="note2"/>
              a
                <emph type="italics"/>
              Fig.
                <emph.end type="italics"/>
              26
                <lb/>
                <emph type="italics"/>
              Tab.
                <emph.end type="italics"/>
              1.</s>
            </p>
            <p id="N18A35" type="main">
              <s id="N18A37">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              110.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N18A43" type="main">
              <s id="N18A45">
                <emph type="italics"/>
              Hinc plùs minuitur ſolidum in diuerſione cubi quam facies, & plùs facies
                <lb/>
              quàm latus
                <emph.end type="italics"/>
              ; </s>
              <s id="N18A50">patet ex dictis, nam latus minoris cubi eſt tantùm ſubdu­
                <lb/>
              plum lateris maioris, & facies ſubquadrupla; ſolidum verò ſub­
                <lb/>
              octuplum. </s>
            </p>
            <p id="N18A58" type="main">
              <s id="N18A5A">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              111.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N18A66" type="main">
              <s id="N18A68">
                <emph type="italics"/>
              Hinc plùs minuitur grauitas, quàm reſiſtentia minoris cubi
                <emph.end type="italics"/>
              ; </s>
              <s id="N18A71">quia grauitas
                <lb/>
              reſpondet ſolido, & reſiſtentia primę faciei; </s>
              <s id="N18A77">reſiſtentia
                <expan abbr="inquā">inquam</expan>
              ratione par­
                <lb/>
              tium medij; </s>
              <s id="N18A81">ſed ſolidum plus minuitur quàm facies, vt dictum eſt; </s>
              <s id="N18A85">igitur
                <lb/>
              plus minuitur grauitas, quæ eſt cauſa virium quàm hæc reſiſtentia; ergo
                <lb/>
              decreſcunt vires in maiore proportione quàm hæc reſiſtentia, quod be­
                <lb/>
              nè obſeruauit Galileus in dìalogis. </s>
            </p>
            <p id="N18A8F" type="main">
              <s id="N18A91">Hinc concludit Galileus duos cubos eiuſdem materiæ, ſed inæquales
                <lb/>
              deſcendere inæquali motu; </s>
              <s id="N18A97">maiorem ſcilicet velociùs minori; </s>
              <s id="N18A9B">demon­
                <lb/>
              ſtrare videtur, quia maior habet maiorem proportionem virium ad re­
                <lb/>
              ſiſtentiam, quàm minor; igitur maiorem habet effectum per Ax. 5. igi­
                <lb/>
              tur maiorem, & velociorem motum. </s>
            </p>
            <p id="N18AA5" type="main">
              <s id="N18AA7">Scio non deeſſe multos viros doctos qui acriter in hanc ſententiam </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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