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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IO. BAPT. BENED.
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              <pb o="172" rhead="IO. BAPT. BENED." n="184" file="0184" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0184"/>
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            <div xml:id="echoid-div396" type="section" level="3" n="6">
              <head xml:id="echoid-head253" style="it" xml:space="preserve">Quod proportiones ponderum eiuſdem corporis in diuerſis medijs pro
                <lb/>
              portiones eorum mediorum denſit atum non ſeruant. Unde ne-
                <lb/>
              ceßariò inæquales proportiones uelocitatum
                <lb/>
              producuntur.</head>
              <head xml:id="echoid-head254" xml:space="preserve">CAP. VI.</head>
              <p>
                <s xml:id="echoid-s2050" xml:space="preserve">OMne corpus graue variat proportionem ponderis per diuerſa media, vnde
                  <lb/>
                proportiones velocitatum inæquales exiſtunt. </s>
                <s xml:id="echoid-s2051" xml:space="preserve">Vt exempli gratia, ſi fue-
                  <lb/>
                rit corpus
                  <var>.A.</var>
                cuius pondus totale ſit
                  <var>.o.a.</var>
                quod in aqua diminutum ſit ratione partis
                  <var>.
                    <lb/>
                  e.o.</var>
                ita vt ei ſolum relinquatur pondus
                  <var>.a.e.</var>
                & in aeie adempta ſit ei pars
                  <var>.i.o.</var>
                vnde ſo
                  <lb/>
                lum remaneat pondus
                  <var>.a.i</var>
                . </s>
                <s xml:id="echoid-s2052" xml:space="preserve">Supponamus aliud
                  <reg norm="quoque" type="simple">quoq;</reg>
                medium in eadem proportio-
                  <lb/>
                ne minus denſum, quàm aer, quemadmodum aer minus denſus eſt, aqua, in quo, cor
                  <lb/>
                pus
                  <var>.A.</var>
                ammittat partem
                  <var>.t.o.</var>
                ponderis ſui, vnde ex .7. lib. de inſidentibus aquæ Ar-
                  <lb/>
                chimedis, eadem proportio erit
                  <var>.e.o.</var>
                ad
                  <var>.i.o.</var>
                quæ eſt
                  <var>.i.o.</var>
                ad
                  <var>.t.o</var>
                . </s>
                <s xml:id="echoid-s2053" xml:space="preserve">Supponamus
                  <reg norm="quoque" type="simple">quoq;</reg>
                  <lb/>
                eandem proportionem eſſe
                  <var>.a.i.</var>
                ad
                  <var>.a.e.</var>
                eſt
                  <var>.e.o.</var>
                ad
                  <var>.i.o.</var>
                </s>
                <s xml:id="echoid-s2054" xml:space="preserve">tunc dico non futuram ean-
                  <lb/>
                dem proportionem
                  <var>.t.a.</var>
                ad
                  <var>.a.i.</var>
                quæ eſt
                  <var>.i.o.</var>
                ad
                  <var>.t.o</var>
                . </s>
                <s xml:id="echoid-s2055" xml:space="preserve">Cum ſit ergo proportio
                  <var>.a.i.</var>
                  <lb/>
                ad
                  <var>.a.e.</var>
                ut
                  <var>.e.o.</var>
                ad
                  <var>.i.o.</var>
                erit diſiunctim
                  <var>.e.i.</var>
                ad
                  <var>.e.a.</var>
                vt
                  <var>.e.i.</var>
                ad
                  <var>.i.o</var>
                . </s>
                <s xml:id="echoid-s2056" xml:space="preserve">Quare ex .9. libr. quin­
                  <lb/>
                ti erit
                  <var>.a.e.</var>
                æqualis
                  <var>.i.o.</var>
                ſed cum ita ſehabeat
                  <var>.e.o.</var>
                ad
                  <var>.i.o.</var>
                vt
                  <var>.i.o.</var>
                ad
                  <var>.t.o.</var>
                ita quoque
                  <lb/>
                ſe habebit, ex vndecima quinti
                  <var>.a.i.</var>
                ad
                  <var>.e.a.</var>
                ut
                  <var>.i.o.</var>
                ad
                  <var>.t.o</var>
                . </s>
                <s xml:id="echoid-s2057" xml:space="preserve">Cum autem (vt vidimus).
                  <var>a.e.</var>
                  <lb/>
                ęqualis ſit ipſi
                  <var>.i.o.</var>
                non poterit eſſe proportio
                  <var>.t.a.</var>
                ad
                  <var>.i.a.</var>
                vt eſt
                  <var>.o.i.</var>
                ad
                  <var>.t.o.</var>
                quia ſi
                  <lb/>
                hoc eſſet, eſſet etiam diſiunctim proportio
                  <var>.i.t.</var>
                ad
                  <var>.i.a.</var>
                vt eſt
                  <var>.i.t.</var>
                ad
                  <var>.t.o.</var>
                & ex ſupradicta
                  <lb/>
                9. lib. quinti
                  <var>.a.i.</var>
                æqualis eſſet
                  <var>.t.o</var>
                . </s>
                <s xml:id="echoid-s2058" xml:space="preserve">Maximum autem inconueniens eſſet
                  <var>.t.o.</var>
                minorem
                  <lb/>
                  <var>o.i.</var>
                ideſt minorem
                  <var>.a.e.</var>
                æqualem eſſe
                  <var>.a.i.</var>
                quæ maior eſt
                  <var>.a.e</var>
                . </s>
                <s xml:id="echoid-s2059" xml:space="preserve">Oſtenſiuè tamen idem
                  <lb/>
                hoc modo probari poteſt, vt exiſtente
                  <var>.i.o.</var>
                ęquali ipſi
                  <var>.a.e.</var>
                per conſequens
                  <reg norm="quoque" type="simple">quoq;</reg>
                erit
                  <lb/>
                minor ipſa
                  <var>.a.i.</var>
                cum
                  <var>.a.e.</var>
                pars ſit ipſius
                  <var>a.i</var>
                . </s>
                <s xml:id="echoid-s2060" xml:space="preserve">
                  <reg norm="Pereandem" type="context">Pereãdem</reg>
                tamen rationem
                  <var>.o.t.</var>
                minoreſt
                  <var>.
                    <lb/>
                  o.i</var>
                . </s>
                <s xml:id="echoid-s2061" xml:space="preserve">Tanto magis igitur minor erit
                  <var>.t.o.</var>
                ipſa
                  <var>.i.a</var>
                . </s>
                <s xml:id="echoid-s2062" xml:space="preserve">Vnde ex .8. libri quinti maiorem pro
                  <lb/>
                portionem habebit
                  <var>.i.t.</var>
                  <lb/>
                ad
                  <var>.t.o.</var>
                quam ad
                  <var>.i.a.</var>
                &
                  <lb/>
                ex .28.
                  <reg norm="eiuſdem" type="context">eiuſdẽ</reg>
                lib
                  <var>.i.o.</var>
                ad
                  <lb/>
                  <var>t.o.</var>
                  <reg norm="maiorem" type="context">maiorẽ</reg>
                proportio-
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0184-01a" xlink:href="fig-0184-01"/>
                  <reg norm="nem" type="context">nẽ</reg>
                habebit, quàm.t.a.
                  <lb/>
                ad
                  <var>.i.a.</var>
                ex .12. igitur di-
                  <lb/>
                cti quinti maiorem pro
                  <lb/>
                portionem habebit
                  <var>.i.a.</var>
                ad
                  <var>.e.a.</var>
                quàm.t.a. ad
                  <var>.i.a.</var>
                ita ergo ſe habebunt ipſorum velo-
                  <lb/>
                citates.</s>
              </p>
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                <figure xlink:label="fig-0184-01" xlink:href="fig-0184-01a">
                  <image file="0184-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0184-01"/>
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              </div>
            </div>
            <div xml:id="echoid-div398" type="section" level="3" n="7">
              <head xml:id="echoid-head255" style="it" xml:space="preserve">Corpora grauia aut leuia eiuſdem figur æ et materiæ ſed inæqualis
                <lb/>
              magnitudinis, in ſuis motibus natur alibus uelocit atis, in eo
                <lb/>
              dem medio, proportionem longè diuerſam ſeruatura
                <lb/>
              eße quam Aristoteliuiſum fuerit.</head>
              <head xml:id="echoid-head256" xml:space="preserve">CAP. VII.</head>
              <p>
                <s xml:id="echoid-s2063" xml:space="preserve">ESt mihi nunc probandum
                  <reg norm="quod" type="simple">ꝙ</reg>
                in uno
                  <reg norm="eodemque" type="simple">eodemq́;</reg>
                mcdio duo corpora inæqualia, ſed
                  <lb/>
                ſimili figura & materia, mouebuntur naturali motu, diuerſa tamen ratione ab </s>
              </p>
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