Ceva, Giovanni, Geometria motus, 1692

Table of figures

< >
< >
page |< < of 110 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <pb pagenum="85" xlink:href="022/01/091.jpg"/>
            <p type="main">
              <s id="s.000840">Funiculi AB, GH trahantur à ponderibus quibuſcunque
                <lb/>
              C, I in C, et I. </s>
              <s id="s.000841">Dico ſi exempta ſint pondera, fore, vt ſpatia
                <lb/>
              quæ acceleratis motibus exiguntur ab extremitatibus ſo­
                <lb/>
              lutis C, I ſint in ratione compoſita ex duplicata IH ad BC,
                <lb/>
              craſſitudinis ad craſſitudinem funiculorum AB, GH; dein­
                <lb/>
              de ex funiculi longitudine HG ad longitudinem AB, pon­
                <lb/>
              deriſque I ad pondus C. </s>
              <s id="s.000842">Intelligatur funiculus, ſeu chor­
                <lb/>
              da, æque craſſa, ac ſimiliter cedens, quàm GH (id quod
                <lb/>
              ſemper intelligimus quoties funiculi, interſe comparantur)
                <lb/>
              ſed æquè longa, ac AB, ſitque illi pondus F adiectum, ad
                <lb/>
              quod C eandem habeat rationem, ac craſſities AB ad craſ­
                <lb/>
              ſitiem DE, conſtat elongationem EF æqualem fieri ipſi
                <lb/>
              CB, & cum primæ velocitates, ſeu amplitudines æquè al­
                <lb/>
              tarum geneſum ſimilium, ſimpliciumque motuum ſint
                <expan abbr="etiã">etiam</expan>
                <lb/>
              æquales, ſpatia decurſuum acceleratis motibus exacta
                <expan abbr="erũt">erunt</expan>
                <lb/>
              prorſus æqualia; ſunt verò funiculi DE, GH eiuſdem craſ­
                <lb/>
              ſitiei, eiſque ſunt ſuſpenſa duo'pondera inæqualia F, I; ergo
                <lb/>
              decurſuum ſpatia ab extremitatibus ſolutis exacta
                <expan abbr="nectẽ-tur">necten­
                  <lb/>
                tur</expan>
              ex ratione duplicata elongationum FE, ſeu CB ad IH,
                <lb/>
              ex ratione, quam habent longitudines funiculorum HG ad
                <lb/>
              DE, ſeu AB, & ex ea ponderum I ad F; verùm pondera I
                <lb/>
              ad F nectuntur ex rationibus ponderum I ad C et C ad F,
                <lb/>
              quæ poſtrema eſt ratio craſſitiei funiculi AB ad craſſitiem
                <lb/>
              funiculi DE, ſeu GH; ergo vt propoſuimus ſpatia accele­
                <lb/>
              ratis motibus exacta, nectentur ex rationibus
                <expan abbr="quadratorũ">quadratorum</expan>
                <lb/>
              CB ad HI; craſſitudinum funiculorum AB, GH;
                <expan abbr="ponderũ">ponderum</expan>
                <lb/>
              I ad C, & longitudinum HG ad AB. </s>
              <s id="s.000843">Quod &c. </s>
            </p>
            <p type="main">
              <s id="s.000844">
                <emph type="center"/>
              PROP. XXXXVI. THEOR. XXXIX.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s id="s.000845">TEmpora geneſum ſimplicium, dum chordis ſuſpen­
                <lb/>
              duntur quæcunque grauia, nectuntur, ex ratione
                <lb/>
              elongationum funiculorum, & ex contrariè ſumptis ratio
                <lb/>
              nibus, craſſitudinum, longitudinumque funiculorum, nec </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum