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]

Page concordance

< >
Scan Original
101 89
102 90
103 91
104 92
105 93
106 94
107 95
108 96
109 97
110 98
111 99
112 100
113 101
114 102
115 103
116 104
117 105
118 106
119 107
120 108
121 109
122 110
123 111
124 112
125 113
126 114
127 115
128 116
129 117
130 118
< >
page |< < (171) of 445 > >|
    <echo version="1.0">
      <text type="book" xml:lang="la">
        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <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/>
                  <figure xlink:label="fig-0183-01" xlink:href="fig-0183-01a" number="245">
                    <image file="0183-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0183-01"/>
                  </figure>
                eſſe cum velocitate eorundem per aquam,
                  <lb/>
                quemadmodum Ariſtoteles ſenſit.</s>
              </p>
            </div>
            <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/>
                  <figure xlink:label="fig-0183-02" xlink:href="fig-0183-02a" number="246">
                    <image file="0183-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0183-02"/>
                  </figure>
                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>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum