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-div388" type="section" level="3" n="2">
              <p>
                <s xml:id="echoid-s2028" xml:space="preserve">
                  <pb o="170" rhead="IO. BABPT. BENED." n="182" file="0182" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0182"/>
                dio minus denſo, quàm ipſum ſit, (quia in medio ſe denſiore ſi poner etur, non graue
                  <lb/>
                e
                  <gap extent="2"/>
                et, ſed leue, quemadmodum Archimedes oſtendit) illud medium ſubtrahat par-
                  <lb/>
                tem
                  <var>.e.i.</var>
                vnde pars
                  <var>.a.e.</var>
                eiuſdem ponderis libera manear; </s>
                <s xml:id="echoid-s2029" xml:space="preserve">& poſito deinde eodem cor
                  <lb/>
                pore in aliquo alio medio denſiore, minus tamen denſo quam ipſum ſit corpus,
                  <lb/>
                hoc medium ſubtrahat partem
                  <var>.u.i.</var>
                dicti ponderis, vnde pars
                  <var>.a.u.</var>
                ei uſdem
                  <lb/>
                ponderis remanebit. </s>
                <s xml:id="echoid-s2030" xml:space="preserve">Dico proportionem velocitatis eiuſdem corporis per
                  <reg norm="medium" type="context">mediũ</reg>
                  <lb/>
                minus denſum, ad velocitatem eiuſdem per medium magis denſum futuram vt
                  <var>.a.e.</var>
                  <lb/>
                ad
                  <var>.a.u.</var>
                vt eſt etiam rationi conſonum, magis quàm ſi dicamus huiuſmodi velocitates
                  <lb/>
                eſſe, vt
                  <var>.u.i.</var>
                ad
                  <var>.e.i.</var>
                cum velocitates à virtutibus mouentibus ſolum (cum figura vna,
                  <lb/>
                  <reg norm="eademque" type="simple">eademq́;</reg>
                in qualitate, quantitate
                  <reg norm="ſituque" type="simple">ſituq́</reg>
                erit) proportionentur. </s>
                <s xml:id="echoid-s2031" xml:space="preserve">Quæne
                  <unsure/>
                nc diximus,
                  <lb/>
                planè ſimilia ſuntijs, quæ ſupra ſcripſimus, quia idem eſt dicere, proportionem velo
                  <lb/>
                citatum, duorum corporum hetereogeneorum, ſed ſimilium figura, & magnitudine
                  <lb/>
                æ qualium, in vno ſolo medio, æqualem eſſe
                  <lb/>
                proportioni ponderum ipſorum, vt ſi dicam?</s>
                <s xml:id="echoid-s2032" xml:space="preserve">
                  <unsure/>
                  <lb/>
                proportionem velocitatum vnius ſolum cor-
                  <lb/>
                  <figure xlink:label="fig-0182-01" xlink:href="fig-0182-01a" number="243">
                    <image file="0182-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0182-01"/>
                  </figure>
                poris per diuerſa media eandem eſſe cum ea.
                  <lb/>
                quæ eſt
                  <reg norm="ponderum" type="context">ponderũ</reg>
                dicti corporis in iſidem medijs.</s>
              </p>
            </div>
            <div xml:id="echoid-div390" type="section" level="3" n="3">
              <head xml:id="echoid-head247" style="it" xml:space="preserve">Poſſe uelocitatem alicuius corporis proportionem contrariam
                <lb/>
              in diuerſis medijs habere cum denſitate eorum.</head>
              <head xml:id="echoid-head248" xml:space="preserve">CAP. III.</head>
              <p>
                <s xml:id="echoid-s2033" xml:space="preserve">POſſibile eſt in rerum natura corpus aliquod huiuſmodi denſitate præditum re-
                  <lb/>
                periri, vt velocitas eius motus naturalis per aerem, velocitati per aquamita pro
                  <lb/>
                portionata exiſtat, vt eſt
                  <reg norm="denſitas" type="context">dẽſitas</reg>
                aquæ denſitati aeris. </s>
                <s xml:id="echoid-s2034" xml:space="preserve">Denſitas aquæ notetur (exem-
                  <lb/>
                pli gratia) per
                  <var>.u.i.</var>
                & ea, quæaeris eſt per
                  <var>.e.i.</var>
                & pondus alicuius corporis in aere per
                  <lb/>
                  <var>e.a.</var>
                & pondus eiuſdem corporis in aqua per
                  <var>.u.a.</var>
                ita tamen, quod eadem proportio
                  <lb/>
                ſit
                  <var>.e.a.</var>
                ad
                  <var>.u.a.</var>
                vt
                  <var>.u.i.</var>
                ad
                  <var>.e.i.</var>
                vnde per vltimam ſuppoſitionem
                  <reg norm="præcedentis" type="context">præcedẽtis</reg>
                capitis, pro
                  <lb/>
                portio velocitatis prædicti corporis per aerem,
                  <lb/>
                proportioni eiuſdem corporis per aquam erit, vt
                  <lb/>
                  <figure xlink:label="fig-0182-02" xlink:href="fig-0182-02a" number="244">
                    <image file="0182-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0182-02"/>
                  </figure>
                  <var>e.a.</var>
                ad
                  <var>.u.a.</var>
                ergo per .11. quinti, vt
                  <var>.u.i.</var>
                ad
                  <var>.e.i</var>
                .</s>
              </p>
            </div>
            <div xml:id="echoid-div392" type="section" level="3" n="4">
              <head xml:id="echoid-head249" style="it" xml:space="preserve">Oſcitanter ab Ariſtotele nonnibil prolatum cap 8.
                <lb/>
              lib. 4 Phyſicorum.</head>
              <head xml:id="echoid-head250" xml:space="preserve">CAP. IIII.</head>
              <p>
                <s xml:id="echoid-s2035" xml:space="preserve">EX ſupradictis patet in vniuerſum non eſſe verum quod Ariſto .8. cap .4. lib. phy­
                  <lb/>
                ſicorum ſcribit, velocitates ſcilicet motuum alicuius corporis per diuerſa me-
                  <lb/>
                dia, proportionatas eſſe denſitatibus eorundem mediorum. </s>
                <s xml:id="echoid-s2036" xml:space="preserve">Quocirca, ſit propor-
                  <lb/>
                tio
                  <var>.u.i.</var>
                ad
                  <var>.e.i.</var>
                vt
                  <reg norm="denſitatis" type="context">dẽſitatis</reg>
                aquę ad
                  <reg norm="aeream" type="context">aereã</reg>
                  <reg norm="denſitatem" type="context">dẽſitatem</reg>
                .et
                  <var>.e.a.</var>
                ad
                  <var>.u.a.</var>
                vt ponderis alicuius
                  <lb/>
                corporis in aere ad pondus eiuſdem in aqua, ita tamen vt maior aut minor propor-
                  <lb/>
                tio ſit
                  <var>.e.a.</var>
                ad
                  <var>.u.a.</var>
                quam
                  <var>.u.i.</var>
                ad
                  <var>.e.i.</var>
                vnde exiſtente proportione velocitatis per
                  <reg norm="aerem" type="context">aerẽ</reg>
                </s>
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