DelMonte, Guidubaldo, In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <p id="N120F4" type="main">
              <s id="N12120">
                <pb xlink:href="077/01/064.jpg" pagenum="60"/>
              nec non magnitudines STVX in ſuis diſtantijs circa
                <expan abbr="centrũ">centrum</expan>
                <lb/>
              grauitatis E circumuerti poſſe; veluti diſtantias DZ DM, ma
                <lb/>
              gnitudineſquè ZM circacentrum D. moueantur autem
                <lb/>
              SEX, & ZDM, donec in centrum mundi vergant. </s>
              <s id="N12132">ſimiliter
                <lb/>
              oſtendetur magnitudines STVX eſſe, ac ſi in E eſſent appen
                <lb/>
              ſę, ſiue conſtitutę; magnitudines verò ZM ac ſi in D poſi­
                <lb/>
              tæ fuerint. </s>
              <s id="N1213A">&c. </s>
              <s id="N1213C">Ex quibus ſequitur, ſi punctum C centrum
                <lb/>
              eſt grauitatis magnitudinum STVXZM. ponatur magnitu­
                <lb/>
              do ipſis STVX ſimul ſumptis ęqualis in E; magnitudo au
                <lb/>
              tem ipſis ZM ſimul æqualis in D; punctum C ſimiliter
                <lb/>
              ipſarum quo〈que〉 centrum grauitatis exiſtet. </s>
              <s id="N12146">vnde vtro〈que〉 mo
                <lb/>
              do æ〈que〉ponderabunt. </s>
              <s id="N1214A">& ita in alijs, ſi plures fuerint magni­
                <lb/>
              tudines. </s>
            </p>
            <p id="N1214E" type="head">
              <s id="N12150">PROPOSITIO. VI.</s>
            </p>
            <p id="N12152" type="main">
              <s id="N12154">Magnitudines commenſurabiles ex diſtantijs
                <lb/>
              eandem permutatim proportionem habentibus,
                <lb/>
              vt grauitates, æ〈que〉ponderant. </s>
            </p>
            <p id="N1215A" type="main">
              <s id="N1215C">
                <emph type="italics"/>
              Commenſurabiles ſint magnitudines AB quarum centra
                <emph.end type="italics"/>
              grauita­
                <lb/>
              tis
                <emph type="italics"/>
              AB, & quædam ſit diſtantia E D, & vt
                <emph.end type="italics"/>
              ſe habet grauitas ma­
                <lb/>
              gnitudinis
                <emph type="italics"/>
              A ad
                <emph.end type="italics"/>
              grauitatem magnitudinis
                <emph type="italics"/>
              B, ua ſit
                <expan abbr="diſtãtia">diſtantia</expan>
                <lb/>
              DC ad distantiam CE.
                <expan abbr="ostendẽdũ">ostendendum</expan>
              eſi
                <emph.end type="italics"/>
              , ſi centra grauitatis AB fue
                <lb/>
              rint in punctis ED conſtituta, hoc eſt A in E, & B in D;
                <lb/>
                <emph type="italics"/>
              magnitudinis ex vtriſquè
                <emph.end type="italics"/>
              magnitudinibus
                <emph type="italics"/>
              AB compoſitæ centrum
                <lb/>
              grauitatis eſſe punctum C. Quoniam enim ita est
                <emph.end type="italics"/>
              magnitudo
                <emph type="italics"/>
              A ad
                <emph.end type="italics"/>
                <lb/>
              magnitudinem
                <emph type="italics"/>
              B, vt DC ad CE. eſt autem
                <emph.end type="italics"/>
              magnitudo
                <emph type="italics"/>
              A ipſi
                <lb/>
                <arrow.to.target n="marg45"/>
              B commenſurabilis; erit & CD ipſi CE commenſurabilis; hoc eſt
                <lb/>
              recta linea rectæ lineæ
                <emph.end type="italics"/>
              commenſurabilis exiſtet.
                <emph type="italics"/>
              Quare ipſarum EC
                <lb/>
              CD communis reperitur menſura. </s>
              <s id="N121B4">quæ quidem ſit N. deinde ponatur
                <lb/>
              ipſi EC æqualis vtra〈que〉 DG DK; ipſi verò DC æqualis EL. &
                <lb/>
              quoniam æqualis est DG ipſi CE
                <emph.end type="italics"/>
              , communi addita CG,
                <emph type="italics"/>
              erit DC
                <lb/>
              ipſi EG æqualis
                <emph.end type="italics"/>
              ; ſed DC eſt ipſi EL ęqualis:
                <emph type="italics"/>
              erit igitur LE æqua­
                <lb/>
              lis ipſi EG.
                <emph.end type="italics"/>
              quare vtra〈que〉 LE EG ęqualis eſt ipſi DC.
                <emph type="italics"/>
              ac propte
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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