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]

Table of contents

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[5.1.7. SEPTIMVM. Euclidis uerò undecima propoſitio.]
[5.1.8. OCTAVVM. εuclidis uerò duodecima propoſitio.]
[5.1.9. NONVM. Euclidis uero tertiadecima propoſitio.]
[5.1.10. DECIMVM.]
[5.1.11. VNDECIMVM.]
[5.1.12. DVODECIMVM.]
[5.2. None]
[5.2.1. THEOR.I. II. ET III.]
[5.2.2. THEOREM. IIII.]
[5.2.3. THEOR.V. ET VI.]
[5.2.4. THEOR. VII. VIII. IX.X. XI. XII. XIII.]
[5.2.5. THEOREM. XIIII.]
[5.2.6. THEOR. XV.]
[5.2.7. THEOREM. XVI.]
[5.2.8. THEOR. XVII.]
[5.2.9. THEOREM. XVIII.]
[5.2.10. THEOREM. XIX.]
[5.2.11. THEOREM. XX.]
[5.2.12. THEOREM. XXI.]
[5.2.13. THEOREM. XXII. XXIII.]
[6. PHYSICA, ET MATHEMATICA RESPONSA. FO. BAPTISTAE BεNεDICTI PATRITII Veneti, Philoſophi Mathematici.]
[6.1. None]
[6.2. None]
[6.3. None]
[6.4. None]
[6.5. None]
[6.6. None]
[6.7. None]
[6.8. None]
[6.9. None]
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DISPVTATIONES.
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          <div xml:id="echoid-div387" type="chapter" level="2" n="4">
            <div xml:id="echoid-div392" type="section" level="3" n="4">
              <p>
                <s xml:id="echoid-s2036" xml:space="preserve">
                  <pb o="171" rhead="DISPVTATIONES." n="183" file="0183" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0183"/>
                ad velocitatem per aquam vt
                  <var>.e.a.</var>
                ad
                  <var>.a.u.</var>
                non erit ergo vt
                  <var>.u.i.</var>
                ad
                  <var>.e.i</var>
                . </s>
                <s xml:id="echoid-s2037" xml:space="preserve">Ob hanc igitur
                  <lb/>
                cauſam nimis diſſentaneum eſt rationi, opi-
                  <lb/>
                nari proportionem velocitatis omnium cor
                  <lb/>
                porum grauium per aerem vnam
                  <reg norm="eandemque" type="simple">eandemq́;</reg>
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0183-01a" xlink:href="fig-0183-01"/>
                eſſe cum velocitate eorundem per aquam,
                  <lb/>
                quemadmodum Ariſtoteles ſenſit.</s>
              </p>
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                <figure xlink:label="fig-0183-01" xlink:href="fig-0183-01a">
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            <div xml:id="echoid-div394" type="section" level="3" n="5">
              <head xml:id="echoid-head251" style="it" xml:space="preserve">Exempla dictorum.</head>
              <head xml:id="echoid-head252" xml:space="preserve">CAP.V.</head>
              <p>
                <s xml:id="echoid-s2038" xml:space="preserve">POnamus, exempli gratia, aquam eſſe in denſitate dupla ad aerem, & aliquod
                  <lb/>
                graue corpus in aqua duplum ad denſitatem ipſius aquæ, vnde dictum corpus in
                  <lb/>
                denſitate ad aerem quadruplum erit; </s>
                <s xml:id="echoid-s2039" xml:space="preserve">quam ob cauſam, mediam ſui ponderis tota-
                  <lb/>
                lis partem in aqua, & in aere quartam partem, ex .7. lib. de inſidentibus aquæ ab Ar-
                  <lb/>
                chimede conſcripto, amitteret. </s>
                <s xml:id="echoid-s2040" xml:space="preserve">Moueretur igitur in aqua virtute illius mediæ partis
                  <lb/>
                  <reg norm="ponderis" type="context">põderis</reg>
                ſui, in aere
                  <reg norm="autem" type="wordlist">aũt</reg>
                uirtute
                  <reg norm="trium" type="context">triũ</reg>
                  <reg norm="quartarum" type="context">quartarũ</reg>
                ; </s>
                <s xml:id="echoid-s2041" xml:space="preserve">vnde proportio facultatis
                  <reg norm="mouentis" type="context">mouẽtis</reg>
                dicti
                  <lb/>
                corporis in aere ad facultatem mouentem eiuſde m in aqua ſeſquialtera erit. </s>
                <s xml:id="echoid-s2042" xml:space="preserve">
                  <reg norm="hocque" type="simple">hocq́;</reg>
                  <lb/>
                corpus appelletur
                  <var>.A</var>
                . </s>
                <s xml:id="echoid-s2043" xml:space="preserve">Sit aliud quoque corpus, quod
                  <var>.B.</var>
                nominetur, ſimile figura, &
                  <lb/>
                magnitudine corporea corpori
                  <var>.A.</var>
                ſed
                  <reg norm="denſitate" type="context">dẽſitate</reg>
                , in proportione ſeſquialtera ad
                  <reg norm="aquam" type="context">aquã</reg>
                ,
                  <lb/>
                & denſius erit aere in proportione tripla. </s>
                <s xml:id="echoid-s2044" xml:space="preserve">quamobrem corpus
                  <var>.A.</var>
                grauius erit cor-
                  <lb/>
                pore
                  <var>.B.</var>
                in aere in proportione ſeſquialtera, vnde etiam velocius erit ipſo
                  <var>.B.</var>
                in aere
                  <lb/>
                in eadem proportione, ſed corpus
                  <var>.B.</var>
                in aere, duplo maius pondus habebit,
                  <reg norm="quam" type="context">quã</reg>
                in
                  <lb/>
                aqua, cum in aere remaneant ei duæ ponderis tertiæ partes, & in aqua vna tantum,
                  <lb/>
                ita vt Ariſtoteli concedam corpus
                  <var>.B.</var>
                in aere, quam in aqua velocius futurum in ea-
                  <lb/>
                dem proportione, in qua, aqua eſt
                  <reg norm="denſior" type="context">dẽſior</reg>
                aere, ex Euclidis vndecima propoſitione
                  <lb/>
                lib. quinti. </s>
                <s xml:id="echoid-s2045" xml:space="preserve">Sed præter hæc omnia, ſi corpus
                  <var>.A.</var>
                eſſet etiam velocius in aere,
                  <reg norm="quam" type="context">quã</reg>
                in
                  <lb/>
                aqua, in eadem proportione, ſequeretur ex .16. dicti lib. quinti proportionem velo-
                  <lb/>
                citatis
                  <var>.A.</var>
                in aqua ad
                  <reg norm="velocitatem" type="context">velocitatẽ</reg>
                ipſius
                  <var>.B.</var>
                in aqua etiam ſeſquialteram eſſe. </s>
                <s xml:id="echoid-s2046" xml:space="preserve">Sed cum
                  <lb/>
                corpus
                  <var>.A.</var>
                in denſitate ad aquam
                  <reg norm="duplum" type="context">duplũ</reg>
                ſit, & corpus
                  <var>.B.</var>
                  <reg norm="ſeſquialterum" type="context">ſeſquialterũ</reg>
                ad ipſam
                  <reg norm="aquam" type="context">aquã</reg>
                ,
                  <lb/>
                ſequetur
                  <reg norm="proportionem" type="context">proportionẽ</reg>
                ponderis ipſius
                  <var>.A.</var>
                ad
                  <reg norm="pondus" type="context">põdus</reg>
                ipſius
                  <var>.B.</var>
                in aqua eſſe in propor-
                  <lb/>
                tione dupla; </s>
                <s xml:id="echoid-s2047" xml:space="preserve">Vnde ex primo ſuppoſito capitis ſecundi proportio velocitatis
                  <var>.A.</var>
                ad
                  <lb/>
                velocitatem
                  <var>.B.</var>
                in aqua dupla erit, non ſeſquialtera. </s>
                <s xml:id="echoid-s2048" xml:space="preserve">Si ergo proportio velocitatis
                  <var>.
                    <lb/>
                  A.</var>
                ad eam quæ eſt
                  <var>.B.</var>
                in aqua dupla eſt, & ea, quæeſt
                  <var>.B.</var>
                in aere, ad eam, quæ eſt ipſius
                  <lb/>
                per aquam eſt etiam dupla (vnde ea quę eſt
                  <var>.A.</var>
                per aquam ęqualis erit ei, quæ eſt
                  <var>.B.</var>
                  <lb/>
                peraerem, ex .9. lib. quinti) & cum ea, quæ eſt
                  <var>.A.</var>
                ſit ei, quæ eſt
                  <var>.B.</var>
                per aerem ſeſqui-
                  <lb/>
                altera, erit ergo ea, quæ eſt
                  <var>.A.</var>
                per aerem, ei, quæ eſt ſuimet ipſius per aquam ſeſqui
                  <lb/>
                altera, non autem dupla, ex .7. eiuſdem libr. quinti. </s>
                <s xml:id="echoid-s2049" xml:space="preserve">Hiſce rationibus accedimus ad
                  <lb/>
                confirmandam veritatem vltimi ſuppoſiti cap .2. proportionem videlicet velocita
                  <lb/>
                tis
                  <reg norm="motus" type="simple">motꝰ</reg>
                naturalis in diuerſis medijs
                  <reg norm="alicuius" type="simple">alicuiꝰ</reg>
                corporis
                  <reg norm="ponderoſi" type="context">põderoſi</reg>
                in ipſis medijs eſſe ean
                  <lb/>
                dem cum ea, quæeſt inter pondera
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0183-02a" xlink:href="fig-0183-02"/>
                dicti corporis in dictis medijs. de ijs
                  <lb/>
                tamen medijs intelligendo, quæ un-
                  <lb/>
                ctuoſa, aut pinguia non ſunt, ut ſunt
                  <lb/>
                oleum, lac, aut huiuſmodialia, quæà
                  <lb/>
                qualibet minima qualitate frigoris
                  <lb/>
                aut caloris alterantur, & impermea-
                  <lb/>
                biles fiunt.</s>
              </p>
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                <figure xlink:label="fig-0183-02" xlink:href="fig-0183-02a">
                  <image file="0183-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0183-02"/>
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