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-div413" type="section" level="3" n="17">
              <pb o="179" rhead="DISPVTATIONES." n="191" file="0191" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0191"/>
              <p>
                <s xml:id="echoid-s2126" xml:space="preserve">Quod in vniuerſum nec etiam poteſt eſſe verum in pleno, quia cap .14. iam pro-
                  <lb/>
                baui, non eandem proportionem eſſe inter ſuperſicies corporum, & ipſa corpora.</s>
              </p>
            </div>
            <div xml:id="echoid-div414" type="section" level="3" n="18">
              <head xml:id="echoid-head277" style="it" xml:space="preserve">Quomodo dignoſcatur proportio uelocitatis duorum ſimilium
                <lb/>
              corporum omogeniorum inaqualium.</head>
              <head xml:id="echoid-head278" xml:space="preserve">CAP. XVIII.</head>
              <p>
                <s xml:id="echoid-s2127" xml:space="preserve">ETiam ſi reperire in qua proportione motus naturaliter moueantur duo corpo-
                  <lb/>
                ra, figura & materia ſimilia, inęqualia tamen ad inuicem, non facile ſit, oſten-
                  <lb/>
                dam tamen qua ratione id conſequi poſſimus.</s>
              </p>
              <p>
                <s xml:id="echoid-s2128" xml:space="preserve">Proponantur nobis, exempli gratia, duo corpora
                  <var>.a.</var>
                et
                  <var>.o.</var>
                ſphęrica, inęqualia inui-
                  <lb/>
                cem, omogenea tamen materia, quorum
                  <var>.a.</var>
                maius ſit; </s>
                <s xml:id="echoid-s2129" xml:space="preserve">ſi voluerimus inuenire in qua
                  <lb/>
                nam velocitatis proportione naturaliter mouerentur. </s>
                <s xml:id="echoid-s2130" xml:space="preserve">Volo vt inquiratur corpus
                  <var>.i.</var>
                  <lb/>
                ſphęricum, alia tamen & diuerſa materia conſtans, ſed pondere ęquale corpori
                  <var>.o.</var>
                &
                  <lb/>
                ſuperſicie tam proportionata ſuperficiei corp oris
                  <var>.a.</var>
                quàm eſt ea, quæ eſt ſui ponde-
                  <lb/>
                ris ad pondus ipſius
                  <var>.a</var>
                . </s>
                <s xml:id="echoid-s2131" xml:space="preserve">Hoc facto, indagetur, quænam erit proportio inter ſu-
                  <lb/>
                perficies corporum
                  <var>.i.</var>
                et
                  <var>.o.</var>
                quę ſemper dupla eſt, vel ſubdupla ei quæ eſt diametro-
                  <lb/>
                rum; </s>
                <s xml:id="echoid-s2132" xml:space="preserve">ut iam cap .15. dixi, & hęc proportio ſuperficierum ſphęricarum
                  <reg norm="ipſius" type="simple">ipſiꝰ</reg>
                  <var>.o.</var>
                et
                  <var>.i.</var>
                ſub
                  <lb/>
                trahatur ab æqualitate, quod igitur remanebit, erit proportio
                  <reg norm="velocitatum" type="context">velocitatũ</reg>
                inter duo
                  <lb/>
                corpora
                  <var>.o.</var>
                et
                  <var>.i.</var>
                ideſt inter
                  <var>.o.</var>
                et
                  <var>.a.</var>
                vt exempli gratia, ſi proportio ſuperficiei
                  <var>.o.</var>
                ſuperfi
                  <lb/>
                ciei ipſius
                  <var>.i.</var>
                ſeſquitertiα
                  <unsure/>
                eſſet, ſub
                  <lb/>
                trahendo eam ab ęqualitate, rema-
                  <lb/>
                  <figure xlink:label="fig-0191-01" xlink:href="fig-0191-01a" number="256">
                    <image file="0191-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0191-01"/>
                  </figure>
                neret
                  <reg norm="proportio" type="simple">ꝓportio</reg>
                ſubſeſquitertia, vnde
                  <lb/>
                velocitas corporis maioris ( quod in
                  <lb/>
                pręſenti loco ſupponitur eſſe
                  <var>.o.</var>
                ) ei,
                  <lb/>
                quę eſt corporis minoris, quale eſt
                  <lb/>
                corpus
                  <var>.i.</var>
                ſubſeſquitertia eſſet; </s>
                <s xml:id="echoid-s2133" xml:space="preserve">aut
                  <lb/>
                dicamus quòd
                  <var>.i.</var>
                eſſet velocius ipſo
                  <lb/>
                o. in proportione ſeſquitertia ex ſe
                  <lb/>
                cundo ſuppoſito ſecundi capitis huius libri. </s>
                <s xml:id="echoid-s2134" xml:space="preserve">Sed
                  <var>.i.</var>
                tam velox eſt quam ipſum
                  <var>.a.</var>
                ex
                  <num value="11">.
                    <lb/>
                  11.</num>
                cap. ergo proportio velocitatis ipſius
                  <var>.a.</var>
                ſeſquitertia erit ei. quæ eſt ipſius
                  <var>.o</var>
                .</s>
              </p>
            </div>
            <div xml:id="echoid-div416" type="section" level="3" n="19">
              <head xml:id="echoid-head279" style="it" xml:space="preserve">Quam ſit inanis ab Ariſtotele ſuſcepta demonſtratio quod
                <lb/>
              uacuum non detur.</head>
              <head xml:id="echoid-head280" xml:space="preserve">CAP. XIX.</head>
              <p>
                <s xml:id="echoid-s2135" xml:space="preserve">EX ijs, quæ ſuperius
                  <reg norm="demonſtrauimus" type="context">demõſtrauimus</reg>
                facilè cognoſci poteſt irritam eſſc eam ratio
                  <lb/>
                nem, quam Ariſtoteles .8. cap. lib. 4. phyſicorum ad deſtruendum vacuum,
                  <reg norm="con" type="context">cõ</reg>
                  <lb/>
                finxit. </s>
                <s xml:id="echoid-s2136" xml:space="preserve">Vtigitur idem facilius oſtendamus, compræhendamus imaginatione infini-
                  <lb/>
                ta media corporea, quorum vnum altero rarius ſit, in qua placuerit nobis ex propor
                  <lb/>
                tionibus, incipiendo ab uno, imaginemur etiam corpus
                  <var>.Q.</var>
                denſius primo medio, cu-
                  <lb/>
                ius corporis, totalis grauitas ſit
                  <var>.a.b.</var>
                & poſitum in ipſo medio, amittat partem
                  <var>.e.b.</var>
                ip-
                  <lb/>
                ſius grauitatis, & in ſecundo medio amittat
                  <var>.i.b.</var>
                & ſic per gradus vnde nobis patebie
                  <unsure/>
                </s>
              </p>
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