Borelli, Giovanni Alfonso, De motionibus naturalibus a gravitate pendentibus, 1670

Page concordance

< >
Scan Original
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
< >
page |< < of 579 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.001025">
                <pb pagenum="198" xlink:href="010/01/206.jpg"/>
                <arrow.to.target n="marg262"/>
                <lb/>
              contentum in vaſe FDE tantæ profunditatis, vt cy­
                <lb/>
              lindrus AC vniuersè, & perpendicularitèr ad Hori­
                <lb/>
              zontem mergi poſſit, vt eius baſis non contingat
                <expan abbr="fũ-dum">fun­
                  <lb/>
                dum</expan>
              vaſis FDE, atque ſupremus terminus C fluidi li­
                <lb/>
              bellam contingat. </s>
              <s id="s.001026">Præterea applicari debet pondus
                <lb/>
              P ſupra verticem cylindri CA, itaut pondus P immi­
                <lb/>
              neat ſupra fluidi libellam, neque aliqua eius portio
                <lb/>
                <figure id="id.010.01.206.1.jpg" xlink:href="010/01/206/1.jpg"/>
                <lb/>
              demergatur. </s>
              <s id="s.001027">His præparatis
                <lb/>
              quia exceſſus
                <expan abbr="põderis">ponderis</expan>
              R ſupra
                <lb/>
              S ad ipſum pondus S maiorem
                <lb/>
                <expan abbr="proportionẽ">proportionem</expan>
              habet quam gra­
                <lb/>
              uitas P ad pondus cylindri
                <lb/>
              ACB, ergò componendo, gra­
                <lb/>
              uitas R ad S
                <expan abbr="maiorẽ">maiorem</expan>
              proportio
                <lb/>
              nem habebit quàm duo
                <expan abbr="põde-ra">ponde­
                  <lb/>
                ra</expan>
              P, & CAB, ſimul ſumpta, ad
                <lb/>
              pondus CAB; verùm grauitas
                <lb/>
              molis fluidi M æqualis ſolido AC ad pondus abſolu­
                <lb/>
              tum eiuſdem ſolidi AC habet eamdem
                <expan abbr="proportionẽ">proportionem</expan>
              ,
                <lb/>
              quam R ad S, ergò moles fluidi M æqualis ſolido AC
                <lb/>
              ad ſolidum idipſum AC, ſeù illius pondus ad graui­
                <lb/>
              tatem huius habebit maiorem proportionem quàm
                <lb/>
              pondera P, & CAB ſimùl ſumpta ad pondus AC, &
                <lb/>
              proindè pondus abſolutum molis fluidi M æqualis
                <lb/>
              AC maius erit grauitate ipſius P vnà cum ponderę
                <lb/>
              cylindri AC. </s>
              <s id="s.001028">Verumtamen Archimedes demonſtra­
                <lb/>
                <arrow.to.target n="marg263"/>
                <lb/>
              uit ſolidum innatans tunc ſolummodò in fluido quie­
                <lb/>
              ſcere quando eius pondus abſolutum æquale fuerit
                <lb/>
              grauitati molis fluidi ambientis, quæ ſit æqualis por-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>