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

Page concordance

< >
Scan Original
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
< >
page |< < of 579 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000090">
                <pb pagenum="17" xlink:href="010/01/025.jpg"/>
                <arrow.to.target n="marg17"/>
                <lb/>
              A, B, C, D, E, & F, H, I, K, L, quæ centra grauitatum̨
                <lb/>
              partium aquæ eſſe intelligantur vt prius, & ductis ad
                <lb/>
              horizontalem perpendicularibus AG, BV, CN, DO,
                <lb/>
              FM, H3, &c. </s>
              <s id="s.000091">pariterque coniunctis rectis DK, CI,
                <lb/>
              BH. quia anguli ad L, E æquales ſunt in iſoſcele, &
                <lb/>
              ſunt quoque anguli recti O & T, & hypothenuſæ DE,
                <lb/>
              KL ſunt inter ſe æquales, ergo in ſimilibus triangulis
                <lb/>
              DOE, & KTL latera DO, KT æqualia erunt & recta
                <lb/>
              OE æqualis erit TL, & addita communi TE erit LE
                <lb/>
              æqualis OT quæ
                <expan abbr="">non</expan>
              minus quàm DK biſſecta erit in
                <lb/>
              puncto Z, propter æquidiſtantiam & æqualitatem la­
                <lb/>
              terum DO, & TK. ſimiliter reliquæ rectæ lineæ NY
                <lb/>
              & CI æquales erunt prioribus, & biſſectæ in puncto
                <lb/>
              P, idemque de reliquis
                <expan abbr="dicendũ">dicendum</expan>
              eſt. </s>
              <s id="s.000092">& quia canales,
                <lb/>
              & moles aqueæ in eis contentæ AB, & FH, æquales
                <lb/>
              ſunt, ergo BFH æqualis eſt AF; fiat iam HB ad BQ,
                <lb/>
              vt BFH ad FH, vel potius vt FA ad AB: quare ſemiſ­
                <lb/>
              ſes antecedentium ad eaſdem conſequentes in
                <expan abbr="eadẽ">eadem</expan>
                <lb/>
              ratione erunt, nempè vt EA ad AB, ita erit XB ad B
                <lb/>
              Q, & per conuerſionem rationis EA ad EB ſeu AG
                <lb/>
              ad BV, vel GE ad EV, & tandem vt duplum GM ad
                <lb/>
              duplum MN erit vt BX ad XQ, ſeu vt VX ad XN,
                <lb/>
              vel vt BV ad QN. igitur erunt tres continuæ propor­
                <lb/>
              tionales AG, BV, & QN in eadem ratione quam ha­
                <lb/>
              bet MG ad MN, quare vt quadratum MG ad quadra­
                <lb/>
              tum MN, ita erit longitudine AG ad QN ideoquę
                <lb/>
              duo puncta A & Q in parabola erunt. </s>
            </p>
            <p type="margin">
              <s id="s.000093">
                <margin.target id="marg17"/>
              Cap. 2. dę
                <lb/>
              momentis
                <lb/>
              grauium in
                <lb/>
              fluido inna­
                <lb/>
              tantium</s>
            </p>
            <p type="main">
              <s id="s.000094">Conſtat ergo quòd ſi brachia ſiphonis perpendicu­
                <lb/>
              laria fuerint ad horizontem, ſiuè ambo fuerint eiuſ-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>