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
131 119
132 120
133 121
134 122
135 123
136 124
137 125
138 126
139 127
140 128
141 129
142 130
143 131
144 132
145 133
146 134
147 135
148 136
149 137
150 138
151 139
152 140
153 141
154 142
155 143
156 144
157 145
158 146
159 147
160 148
< >
page |< < (170) 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-div388" type="section" level="3" n="2">
              <p>
                <s xml:id="echoid-s2028" xml:space="preserve">
                  <pb o="170" rhead="IO. BABPT. BENED." n="182" file="0182" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0182"/>
                dio minus denſo, quàm ipſum ſit, (quia in medio ſe denſiore ſi poner etur, non graue
                  <lb/>
                e
                  <gap extent="2"/>
                et, ſed leue, quemadmodum Archimedes oſtendit) illud medium ſubtrahat par-
                  <lb/>
                tem
                  <var>.e.i.</var>
                vnde pars
                  <var>.a.e.</var>
                eiuſdem ponderis libera manear; </s>
                <s xml:id="echoid-s2029" xml:space="preserve">& poſito deinde eodem cor
                  <lb/>
                pore in aliquo alio medio denſiore, minus tamen denſo quam ipſum ſit corpus,
                  <lb/>
                hoc medium ſubtrahat partem
                  <var>.u.i.</var>
                dicti ponderis, vnde pars
                  <var>.a.u.</var>
                ei uſdem
                  <lb/>
                ponderis remanebit. </s>
                <s xml:id="echoid-s2030" xml:space="preserve">Dico proportionem velocitatis eiuſdem corporis per
                  <reg norm="medium" type="context">mediũ</reg>
                  <lb/>
                minus denſum, ad velocitatem eiuſdem per medium magis denſum futuram vt
                  <var>.a.e.</var>
                  <lb/>
                ad
                  <var>.a.u.</var>
                vt eſt etiam rationi conſonum, magis quàm ſi dicamus huiuſmodi velocitates
                  <lb/>
                eſſe, vt
                  <var>.u.i.</var>
                ad
                  <var>.e.i.</var>
                cum velocitates à virtutibus mouentibus ſolum (cum figura vna,
                  <lb/>
                  <reg norm="eademque" type="simple">eademq́;</reg>
                in qualitate, quantitate
                  <reg norm="ſituque" type="simple">ſituq́</reg>
                erit) proportionentur. </s>
                <s xml:id="echoid-s2031" xml:space="preserve">Quæne
                  <unsure/>
                nc diximus,
                  <lb/>
                planè ſimilia ſuntijs, quæ ſupra ſcripſimus, quia idem eſt dicere, proportionem velo
                  <lb/>
                citatum, duorum corporum hetereogeneorum, ſed ſimilium figura, & magnitudine
                  <lb/>
                æ qualium, in vno ſolo medio, æqualem eſſe
                  <lb/>
                proportioni ponderum ipſorum, vt ſi dicam?</s>
                <s xml:id="echoid-s2032" xml:space="preserve">
                  <unsure/>
                  <lb/>
                proportionem velocitatum vnius ſolum cor-
                  <lb/>
                  <figure xlink:label="fig-0182-01" xlink:href="fig-0182-01a" number="243">
                    <image file="0182-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0182-01"/>
                  </figure>
                poris per diuerſa media eandem eſſe cum ea.
                  <lb/>
                quæ eſt
                  <reg norm="ponderum" type="context">ponderũ</reg>
                dicti corporis in iſidem medijs.</s>
              </p>
            </div>
            <div xml:id="echoid-div390" type="section" level="3" n="3">
              <head xml:id="echoid-head247" style="it" xml:space="preserve">Poſſe uelocitatem alicuius corporis proportionem contrariam
                <lb/>
              in diuerſis medijs habere cum denſitate eorum.</head>
              <head xml:id="echoid-head248" xml:space="preserve">CAP. III.</head>
              <p>
                <s xml:id="echoid-s2033" xml:space="preserve">POſſibile eſt in rerum natura corpus aliquod huiuſmodi denſitate præditum re-
                  <lb/>
                periri, vt velocitas eius motus naturalis per aerem, velocitati per aquamita pro
                  <lb/>
                portionata exiſtat, vt eſt
                  <reg norm="denſitas" type="context">dẽſitas</reg>
                aquæ denſitati aeris. </s>
                <s xml:id="echoid-s2034" xml:space="preserve">Denſitas aquæ notetur (exem-
                  <lb/>
                pli gratia) per
                  <var>.u.i.</var>
                & ea, quæaeris eſt per
                  <var>.e.i.</var>
                & pondus alicuius corporis in aere per
                  <lb/>
                  <var>e.a.</var>
                & pondus eiuſdem corporis in aqua per
                  <var>.u.a.</var>
                ita tamen, quod eadem proportio
                  <lb/>
                ſit
                  <var>.e.a.</var>
                ad
                  <var>.u.a.</var>
                vt
                  <var>.u.i.</var>
                ad
                  <var>.e.i.</var>
                vnde per vltimam ſuppoſitionem
                  <reg norm="præcedentis" type="context">præcedẽtis</reg>
                capitis, pro
                  <lb/>
                portio velocitatis prædicti corporis per aerem,
                  <lb/>
                proportioni eiuſdem corporis per aquam erit, vt
                  <lb/>
                  <figure xlink:label="fig-0182-02" xlink:href="fig-0182-02a" number="244">
                    <image file="0182-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0182-02"/>
                  </figure>
                  <var>e.a.</var>
                ad
                  <var>.u.a.</var>
                ergo per .11. quinti, vt
                  <var>.u.i.</var>
                ad
                  <var>.e.i</var>
                .</s>
              </p>
            </div>
            <div xml:id="echoid-div392" type="section" level="3" n="4">
              <head xml:id="echoid-head249" style="it" xml:space="preserve">Oſcitanter ab Ariſtotele nonnibil prolatum cap 8.
                <lb/>
              lib. 4 Phyſicorum.</head>
              <head xml:id="echoid-head250" xml:space="preserve">CAP. IIII.</head>
              <p>
                <s xml:id="echoid-s2035" xml:space="preserve">EX ſupradictis patet in vniuerſum non eſſe verum quod Ariſto .8. cap .4. lib. phy­
                  <lb/>
                ſicorum ſcribit, velocitates ſcilicet motuum alicuius corporis per diuerſa me-
                  <lb/>
                dia, proportionatas eſſe denſitatibus eorundem mediorum. </s>
                <s xml:id="echoid-s2036" xml:space="preserve">Quocirca, ſit propor-
                  <lb/>
                tio
                  <var>.u.i.</var>
                ad
                  <var>.e.i.</var>
                vt
                  <reg norm="denſitatis" type="context">dẽſitatis</reg>
                aquę ad
                  <reg norm="aeream" type="context">aereã</reg>
                  <reg norm="denſitatem" type="context">dẽſitatem</reg>
                .et
                  <var>.e.a.</var>
                ad
                  <var>.u.a.</var>
                vt ponderis alicuius
                  <lb/>
                corporis in aere ad pondus eiuſdem in aqua, ita tamen vt maior aut minor propor-
                  <lb/>
                tio ſit
                  <var>.e.a.</var>
                ad
                  <var>.u.a.</var>
                quam
                  <var>.u.i.</var>
                ad
                  <var>.e.i.</var>
                vnde exiſtente proportione velocitatis per
                  <reg norm="aerem" type="context">aerẽ</reg>
                </s>
              </p>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum