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

List of thumbnails

< >
51
51
52
52
53
53
54
54
55
55
56
56
57
57
58
58
59
59
60
60
< >
page |< < of 579 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000082">
                <pb pagenum="15" xlink:href="010/01/023.jpg"/>
                <arrow.to.target n="marg15"/>
                <lb/>
              Y in ſecundo & ſubleuata vſque ad V; tunc quidem̨
                <lb/>
              centrum grauitatis prædictæ aquæ horizontaliter
                <expan abbr="cõ-ſtitutæ">con­
                  <lb/>
                ſtitutæ</expan>
              præcisè incidet in
                <expan abbr="cẽtro">centro</expan>
              ſuſpenſionis M, prop­
                <lb/>
              terea quòd vt baſis V ad baſim A ſeù vt cylindrus a­
                <lb/>
              queus GLV ad equè altum cy­
                <lb/>
                <figure id="id.010.01.023.1.jpg" xlink:href="010/01/023/1.jpg" number="8"/>
                <lb/>
              lindrum AEF in primo caſu vel
                <lb/>
              ad CEF in ſecundo, ita fuit reci­
                <lb/>
              procè diſtantia EM ad ML. o­
                <lb/>
              ſtendendum modò eſt punctą
                <lb/>
              A, Q, R, S, M in eadèm linea pa­
                <lb/>
              rabolica eſſe. </s>
              <s id="s.000083">quia moles aquæ
                <lb/>
              TX æqualis eſt æquæ moli GH
                <lb/>
              I, ergo, XBF vnà cum GHI æ­
                <lb/>
              qualis eſt moli aqueæ TAF; e­
                <lb/>
              rat verò moles aquæ XBF vnà
                <lb/>
              cum GHI ad GHI vt linea HB
                <lb/>
              ad BQ ſeu (ducta QN parallel­
                <lb/>
              là AE) vt LE ad EN, ergo FAT
                <lb/>
              ad TX atque ſemiſſis illius FA
                <lb/>
              ad huius ſemiſſem AB eamdem
                <lb/>
              proportionem habebit quam̨
                <lb/>
              LE ad EN, eſt verò EA ad AF vt MA ad AG, ſeù vt
                <lb/>
              ME ad EL, ergo ex æqualitate ordinata EA ad AB
                <lb/>
              eamdem proportionem habebit quam ME ad EN, &
                <lb/>
              per conuerſionem rationis EA ad EB erit vt EM ad
                <lb/>
              MN, ſeù vt EB ad NQ, erunt igitur tres continuæ pro
                <lb/>
              portionales EA, EB, & NQ in eadem ratione quam̨
                <lb/>
              habet EM ad MN, quare quadratum ex EM ad qua­
                <lb/>
              dratum ex MN eam proportionem habebit, quam̨ </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>