Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

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          <div xml:id="echoid-div387" type="chapter" level="2" n="4">
            <div xml:id="echoid-div409" type="section" level="3" n="13">
              <p>
                <s xml:id="echoid-s2099" xml:space="preserve">
                  <pb o="177" rhead="DISPVTATIONES." n="189" file="0189" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0189"/>
                quam
                  <var>.u.</var>
                ad
                  <var>.m.e.</var>
                & ex .27. maior erit proportio
                  <var>.c.i.</var>
                ad
                  <var>.u.e.</var>
                quam
                  <var>.z.i.</var>
                ad
                  <var>.e.m.</var>
                ideſt
                  <var>.s.</var>
                g
                  <lb/>
                ad
                  <var>.r.x.</var>
                quod Ariſtoteli in mentem non venerat. </s>
                <s xml:id="echoid-s2100" xml:space="preserve">Alijs quoque modis idem proba-
                  <lb/>
                ri poteſt, vt ſi diceret aliquis, maiorem proportionem eſſe
                  <var>.e.m.</var>
                ad
                  <var>.m.u.</var>
                quam
                  <var>.i.z.</var>
                ad
                  <lb/>
                  <var>z.c.</var>
                (quia
                  <var>.e.m.</var>
                ad
                  <var>.m.u.</var>
                eadem eſt ratio vt ad
                  <var>.z.c.</var>
                ex .7. quinti, ſed proportio
                  <var>.e.m.</var>
                ad
                  <var>.
                    <lb/>
                  z.c.</var>
                maior eſt quam
                  <var>.i.z.</var>
                ad
                  <var>.z.c.</var>
                ex .8. eiuſdem, ergo ea, quæ eſt
                  <var>.e.m.</var>
                ad
                  <var>.m.u.</var>
                ex .12. ma
                  <lb/>
                for erit, quam
                  <var>.i.z.</var>
                ad
                  <var>.z.c.</var>
                ) vnde componendo, ea quæ eſt
                  <var>.e.u.</var>
                ad
                  <var>.m.u.</var>
                maior erit illa,
                  <lb/>
                quæ eſt
                  <var>.i.c.</var>
                ad
                  <var>.z.c.</var>
                &
                  <reg norm="permutando" type="context">permutãdo</reg>
                , quam ea, quæ eſt
                  <var>.e.u.</var>
                ad
                  <var>.i.c.</var>
                ea, quæ eſt
                  <var>.m.u.</var>
                ad
                  <var>.z.c.</var>
                  <lb/>
                & ex .33. quinti, ea, quæ eſt
                  <var>.e.m.</var>
                ad
                  <var>.i.z.</var>
                maior erit ea, quæ eſt
                  <var>.e.u.</var>
                ad
                  <var>.i.c</var>
                .</s>
              </p>
              <figure position="here" number="255">
                <image file="0189-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0189-01"/>
              </figure>
            </div>
            <div xml:id="echoid-div410" type="section" level="3" n="14">
              <head xml:id="echoid-head269" style="it" xml:space="preserve">Quid ſequatur ex ſupradistis.</head>
              <head xml:id="echoid-head270" xml:space="preserve">CAP. XIIII.</head>
              <p>
                <s xml:id="echoid-s2101" xml:space="preserve">EX præcedenti capite manifeſtè depræhenditur, in vniuerſum Ariſtotelis opi-
                  <lb/>
                nionem veram non eſſe in prima parte vltimi capitis. lib. 7. phyſicorum; </s>
                <s xml:id="echoid-s2102" xml:space="preserve">quia
                  <lb/>
                in eo loco ſupponens ipſe corpus
                  <var>.B.</var>
                pręcedentis capitis eſſe dimidiam partem ipſius
                  <lb/>
                D. quantum ad aream corpoream ſpectat (ſunt tamen pondere ad inuicem æqualia)
                  <lb/>
                ait
                  <var>.B.</var>
                futurum duplo velocius ipſo
                  <var>.D</var>
                . </s>
                <s xml:id="echoid-s2103" xml:space="preserve">Ego verò præcedenti capite accepi
                  <var>.e.u.</var>
                pro
                  <lb/>
                velocitate reſidua corporis
                  <var>.B.</var>
                (ſubtracta ea tamen parte, quam ei reſiſtentia adimit,
                  <lb/>
                quæ erat
                  <var>.e.a.</var>
                ) et
                  <var>.i.c.</var>
                pro ea, quæ eſt corporis
                  <var>.D.</var>
                et
                  <var>.r.x.</var>
                pro ea, quæ eſt corporis
                  <var>.V.</var>
                et
                  <var>.
                    <lb/>
                  s.g.</var>
                pro ea, quæ eſt corporis
                  <var>.M</var>
                . </s>
                <s xml:id="echoid-s2104" xml:space="preserve">Dicat nunc Ariſtoteles, quę nam harum duarum pro
                  <lb/>
                portionum dupla erit? </s>
                <s xml:id="echoid-s2105" xml:space="preserve">quia ſi earum aliqua talis erit, alia nullo modo eſſe poterit,
                  <lb/>
                vt iam oſtendi, etiamſi duo corpora
                  <var>.V.</var>
                et
                  <var>.M.</var>
                eaſdem conditiones habeant, quas
                  <var>.B.</var>
                  <lb/>
                et
                  <var>.D</var>
                . </s>
                <s xml:id="echoid-s2106" xml:space="preserve">Ratio autem, quæ Ariſtotelem induxerit ad illud credendum, nulla alia eſſe
                  <lb/>
                potuit, quàm quod putarit reſiſtentias proportionatas eſſe magnitudinibus corpo-
                  <lb/>
                reis, ideſt quemadmodum
                  <var>.B.</var>
                erat corporaliter dimidia pars ipſius
                  <var>.D.</var>
                ſic etiam habe
                  <lb/>
                ret medietatem eius reſiſtentiæ, quam habuiſſet corpus
                  <var>.D</var>
                . </s>
                <s xml:id="echoid-s2107" xml:space="preserve">Quod etſi verum eſſet,
                  <lb/>
                non tamen ſequeretur neceſſariò in quibuſlibet corporibus futuram velocitatum
                  <lb/>
                proportionem eandem, quæ reſiſtentiarum eſt, vt ſuperiore capite oſtendimus.</s>
              </p>
            </div>
            <div xml:id="echoid-div411" type="section" level="3" n="15">
              <head xml:id="echoid-head271" style="it" xml:space="preserve">Numrestè ſenſerit Philoſophus reſistentias proportionales
                <lb/>
              eße cum corporibus mobilibus.</head>
              <head xml:id="echoid-head272" xml:space="preserve">CAP. XV.</head>
              <p>
                <s xml:id="echoid-s2108" xml:space="preserve">QVòd Ariſtoteles crediderit reſiſtentias proportionatas eſſe corporibus, erra-
                  <lb/>
                uit. </s>
                <s xml:id="echoid-s2109" xml:space="preserve">Si ſuperficies ijſdem proportionatæ eſſent, dubium non eſt, quin
                  <lb/>
                reſiſtentiæ quoque ipſæ, ijſdem proportionatæ exiſterent, ſupponendo eas ſimiles
                  <lb/>
                ſitu, dum eadem corpora mouerentur. </s>
                <s xml:id="echoid-s2110" xml:space="preserve">Sed eadem proportio non eſt inter ſuperfi- </s>
              </p>
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