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-div403" type="section" level="3" n="10">
              <p>
                <s xml:id="echoid-s2083" xml:space="preserve">
                  <pb o="175" rhead="DISPVTATIONES." n="187" file="0187" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0187"/>
                tem mutarent, quorum quodlibet eſſet quoque tam velox, quam eſt .g: igitur
                  <var>.g.</var>
                  <lb/>
                tam velox eſſet quam
                  <var>.o</var>
                .</s>
              </p>
            </div>
            <div xml:id="echoid-div405" type="section" level="3" n="11">
              <head xml:id="echoid-head263" style="it" xml:space="preserve">Corpora licet inæqualia eiuſdem materiæ & figuræ, ſireſiſten-
                <lb/>
              tias habuerint ponderibus proportionales
                <lb/>
              æqualiter mouebuntur.</head>
              <head xml:id="echoid-head264" xml:space="preserve">CAP. XI.</head>
              <p>
                <s xml:id="echoid-s2084" xml:space="preserve">EAdem ratione, quam cap. antecedente præſcripſimus, poſſet oſtendi, ſi duo cor-
                  <lb/>
                pora
                  <var>.o.</var>
                et
                  <var>.g.</var>
                ſuas reſiſtentias, ita ad inuicem proportionatas haberent, utſunt
                  <lb/>
                eorum pondera, in pleno pari velocitate prædita eſſe, quod in fine capitis noni leui
                  <lb/>
                ter attigi, quia punctum
                  <var>.i.</var>
                tam velox eſſet, ut centrum ipſius
                  <var>.o.</var>
                cum à tanto pondere
                  <lb/>
                i. motum eſſet; </s>
                <s xml:id="echoid-s2085" xml:space="preserve">quanto centrum ipſius
                  <var>.o.</var>
                atquetan
                  <lb/>
                  <figure xlink:label="fig-0187-01" xlink:href="fig-0187-01a" number="252">
                    <image file="0187-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0187-01"/>
                  </figure>
                tam reſiſtentiam duo corpora
                  <var>.a.</var>
                et
                  <var>.e.</var>
                  <reg norm="quanta" type="context">quãta</reg>
                ipſum
                  <lb/>
                o. ſolum haberet ex hypotheſi, dicta tamen corpo
                  <lb/>
                ra
                  <var>.a.</var>
                et
                  <var>.e.</var>
                tam ſeparata, quam coniuncta, eandem
                  <lb/>
                velocitatem retinerent
                  <var>.g.</var>
                igitur tam velox eſſet,
                  <lb/>
                quam
                  <var>.o</var>
                .</s>
              </p>
            </div>
            <div xml:id="echoid-div407" type="section" level="3" n="12">
              <head xml:id="echoid-head265" style="it" xml:space="preserve">Maior hic demonſir atur eſſe proportio ponder is corpor is den
                <lb/>
              ſioris ad pondus minus denſi in
                <reg norm="medijs" type="lig">medijs</reg>
                <reg norm="denſioribus" type="context">dẽſioribus</reg>
              , quam
                <lb/>
              ſit eorundem corporum in medio minus denſo, nec
                <lb/>
              corporum ponder a ſeruare proportionem
                <lb/>
              denſitatis mediorum.</head>
              <head xml:id="echoid-head266" xml:space="preserve">CAP. XII.</head>
              <p>
                <s xml:id="echoid-s2086" xml:space="preserve">PRopoſita nobis cum fuerint duo corpora
                  <var>.A.</var>
                et
                  <var>.B.</var>
                area corporea æqualia, quo-
                  <lb/>
                rum
                  <var>.A.</var>
                denſius ſit ipſo
                  <var>.B.</var>
                probabo in medio magis denſo, maiorem proportio
                  <lb/>
                nem futuram ponderis ipſius
                  <var>.A.</var>
                ad pondus
                  <var>.B.</var>
                quàm in medio minus denſo.</s>
              </p>
              <p>
                <s xml:id="echoid-s2087" xml:space="preserve">Sit igitur
                  <var>.p.g.</var>
                pondus totale ipſius corporis
                  <var>.A.</var>
                et
                  <var>.q.k.</var>
                ipſius corporis
                  <var>.B.</var>
                vnde
                  <var>.p.g.</var>
                  <lb/>
                maius erit ipſo
                  <var>.q.k</var>
                . </s>
                <s xml:id="echoid-s2088" xml:space="preserve">Sit quoque
                  <var>.o.g.</var>
                pondus, quod medium magis denſum ſubtra-
                  <lb/>
                hit à pondere
                  <var>.p.g.</var>
                et
                  <var>.n.k.</var>
                ſit pondus, quod idem medium ſubtrahit à pondere
                  <var>.q.k.</var>
                et
                  <lb/>
                  <var>f.g.</var>
                ſit pondus, quod medium minus denſum ſubtrahit à
                  <var>.p.g.</var>
                et
                  <var>.i.k.</var>
                illud, quodid@m
                  <lb/>
                  <reg norm="medium" type="context">mediũ</reg>
                ſubtrahit ab
                  <var>.q.k.</var>
                vnde
                  <var>.o.g.</var>
                æquale erit
                  <var>.n.k.</var>
                et
                  <var>.f.g.</var>
                ipſi
                  <var>.i.k.</var>
                quia quod ad
                  <reg norm="aream" type="context">areã</reg>
                  <lb/>
                attinet, corpora ſupponuntur æqualia, vnde proportio
                  <var>.p.f.</var>
                ad
                  <var>.q.i.</var>
                maior erit ea, quæ
                  <lb/>
                eſt
                  <var>.o.f.</var>
                ad
                  <var>.n.i.</var>
                communi
                  <lb/>
                  <figure xlink:label="fig-0187-02" xlink:href="fig-0187-02a" number="253">
                    <image file="0187-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0187-02"/>
                  </figure>
                ſcientiæ notione, quia ſi
                  <lb/>
                ſcinderet
                  <reg norm="aliquis" type="simple">aliꝗs</reg>
                .p.f. in pun
                  <lb/>
                cto
                  <var>.c.</var>
                ita. vt
                  <var>.c.f.</var>
                æquale eſ-
                  <lb/>
                ſet ipſi
                  <var>.q.i.</var>
                proportio
                  <var>.c.f.</var>
                  <lb/>
                ad
                  <var>.q.i.</var>
                eſſet vt ea, quæ eſt
                  <var>.
                    <lb/>
                  o.f.</var>
                ad
                  <var>.n.i.</var>
                (hoc eſt nulla) </s>
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