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

Page concordance

< >
Scan Original
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
< >
page |< < of 579 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <pb pagenum="20" xlink:href="010/01/028.jpg"/>
            <p type="main">
              <s id="s.000106">
                <arrow.to.target n="marg20"/>
                <lb/>
              ad M, ſuntque latera AK & BL æqualia interſę
                <lb/>
              ergo ſe mutuò bifariam ſecabunt rectæ coniungentes
                <lb/>
              AB, & KL in eodem puncto G; idemque continget
                <lb/>
              translatis ponderibus in N, & O, & ideo punctum G
                <lb/>
              erit centrum, ſeu ſtabile
                <expan abbr="fulcimentũ">fulcimentum</expan>
              libræ AB quo­
                <lb/>
              modolibet reuolutæ: ducatur tandem per I recta li­
                <lb/>
              nea IP parallela funibus ſecans libras KL, & NO iņ
                <lb/>
              punctis M, & P patet libras in eadem proportione re­
                <lb/>
              ciproca ſecari in punctis I, M, P, quam habent oppoſi­
                <lb/>
              ta pondera proindeque eadem puncta erunt centrą
                <lb/>
              grauitatum, earumdem librarum cum ponderibus ap­
                <lb/>
              penſis; quapropter licet minus pondus B aſcendat per
                <lb/>
              BLO, tamen ambo pondera A, & B in communi
                <expan abbr="cẽ-tro">cen­
                  <lb/>
                tro</expan>
              grauitatis eorum I ſuſpenſa circa centrum
                <expan abbr="firmũ">firmum</expan>
                <lb/>
              G, & in extremo fune-penduli GI deſcendunt noņ
                <lb/>
              circulari, ſed directo motu perpendiculari ad hori­
                <lb/>
              zontem ab I per M & P, quod fuerat oſtendendum. </s>
            </p>
            <p type="margin">
              <s id="s.000107">
                <margin.target id="marg20"/>
              Cap. 2. de
                <lb/>
              momentis
                <lb/>
              grauium in
                <lb/>
              fluido inna­
                <lb/>
              tantium.</s>
            </p>
            <p type="main">
              <s id="s.000108">
                <emph type="center"/>
              PROP. VII.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s id="s.000109">
                <emph type="center"/>
                <emph type="italics"/>
              Id ipſum osten ditur, cùm pondera in peripherijs inæqua­
                <lb/>
              libus, & concentricis eiuſdem trochleæ reuoluuntur.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s id="s.000110">SIt trochlea CDE circa axim F conuertibilis, & in
                <lb/>
              ea ſit alia concentrica circumferentia RSQ, &
                <lb/>
              funi SQB alligetur pondus B, alij verò funi DEA alli­
                <lb/>
              getur pondus A
                <expan abbr="ſintq;">ſintque</expan>
              funes nullius ponderis; oſten­
                <lb/>
              detur, vt in præcedenti, funes EA, & BQ eſſe interſe
                <lb/>
              parallelos; poſtea
                <expan abbr="coniũgatur">coniungatur</expan>
              recta AB, atque vt
                <expan abbr="põ-dus">pon­
                  <lb/>
                dus</expan>
              A ad B ita reciprocè fiat diſtantia BI ad IA; patet </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>