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

Page concordance

< >
Scan Original
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
< >
page |< < of 579 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000110">
                <pb pagenum="21" xlink:href="010/01/029.jpg"/>
                <arrow.to.target n="marg21"/>
                <lb/>
              punctum I eſſe centrum grauitatis communis ponde­
                <lb/>
              rum A, & B (cum funes nullius ponderis
                <expan abbr="ſupponãtur">ſupponantur</expan>
              )
                <lb/>
              deinde reuoluta trochlea
                <expan abbr="aſcẽdat">aſcendat</expan>
              pondus B ad L, &
                <lb/>
              oppoſitum pondus A deſcendat vſque ad K
                <expan abbr="coniũga-turque">coniunga­
                  <lb/>
                turque</expan>
              recta KL ſecans rectam AB
                <lb/>
                <figure id="id.010.01.029.1.jpg" xlink:href="010/01/029/1.jpg" number="11"/>
                <lb/>
              in G. dico duo pondera A, & B iņ
                <lb/>
              communi eorum centro grauitatis
                <lb/>
              I circa libræ centrum ſtabile G mo­
                <lb/>
              tu directo, & perpendiculari ad
                <lb/>
              horizontem
                <expan abbr="deſcẽdere">deſcendere</expan>
              . </s>
              <s id="s.000111">quia in tro­
                <lb/>
              chleæ reuolutione
                <expan abbr="tãtumdẽ">tantumdem</expan>
                <expan abbr="deſcẽ-dit">deſcen­
                  <lb/>
                dit</expan>
              terminus funis A quanta eſt ex­
                <lb/>
              plicatio funis è rota CDE, & pon­
                <lb/>
              dus B aſcendit quantum funis BQS
                <lb/>
              circumuoluitur circa rotam QSR
                <lb/>
              cùmque duæ rotæ concentricè con­
                <lb/>
              nexæ ſimul tempore
                <expan abbr="reuoluãtur">reuoluantur</expan>
              cir­
                <lb/>
              ca fixum axim F, ergo deſcenſus AK
                <lb/>
              ad
                <expan abbr="aſcẽſum">aſcenſum</expan>
              BL eamdem proportio­
                <lb/>
              nem habet, quam peripheria CDE ad peripheriam R
                <lb/>
              SQ, ſeu
                <expan abbr="eamdẽ">eamdem</expan>
              proportionem, quam habet radius
                <lb/>
              FE ad radium
                <expan abbr="Fq;">Fque</expan>
              quare in triangulis AGK, & BGL
                <lb/>
              ſimilibus, ob æquidiſtantiam laterum AK, & BL, erit
                <lb/>
              AG ad GB vt KG ad GL, ſeu vt AK ad BL;
                <expan abbr="proindeq;">proindeque</expan>
                <lb/>
              in eodem puncto fixo G duæ libræ AB, & KL ſe mutuò
                <lb/>
              ſecabunt in eadem proportione, quam habent motus
                <lb/>
              eorumdem terminorum, vnde, ex mechanicis, erit
                <lb/>
              punctum G centrum, & fulcimentum firmum̨
                <lb/>
              vtriuſque libræ AB, & KL poſtremò ducatur per I </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>