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

Table of figures

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <p id="N1562B" type="main">
              <s id="N1562D">
                <pb xlink:href="077/01/149.jpg" pagenum="145"/>
                <emph type="italics"/>
              OR.
                <expan abbr="iungãturq́">iungantur〈que〉</expan>
              ; E
                <emph.end type="italics"/>
              k
                <emph type="italics"/>
              FI GH.
                <emph.end type="italics"/>
              quæ inter ſe, & ipſi AC
                <expan abbr="çquidiſtãtes">çquidiſtantes</expan>
                <arrow.to.target n="marg247"/>
                <lb/>
              erunt; bifariam què à diametro BD in punctis LMN diuiſæ e­
                <lb/>
              runt. </s>
              <s id="N1565C">Iungantur ſimiliter
                <emph type="italics"/>
              & ST YV QZ
                <emph.end type="italics"/>
              , quas bifariam dia­
                <lb/>
              meter OR in punctis 9
                <foreign lang="grc">αβ</foreign>
              diuidet. </s>
              <s id="N1566A">eruntquè ductæ lineæ ipſi
                <lb/>
              XP, & inter ſe æquidiſtantes.
                <emph type="italics"/>
              Quoniam igitur BD diuiditur à lineis
                <lb/>
              æquidiſtantibus
                <emph.end type="italics"/>
              GH FI EK
                <emph type="italics"/>
              in proportionibus numeris deinceps impa­
                <lb/>
              ribus;
                <emph.end type="italics"/>
              poſito enim vno BN, eſt quidem NM tria, ML quin〈que〉,
                <lb/>
              & LD ſeptem. </s>
              <s id="N15680">ſed
                <emph type="italics"/>
              & RO ſimiliter
                <emph.end type="italics"/>
              à lineis QZ YV ST in pro­
                <lb/>
              portionibus diuiditur numeris deinceps imparibus,
                <expan abbr="eadẽ">eadem</expan>
              .
                <expan abbr="n.">enim</expan>
                <lb/>
              ratione ſi ponatur O
                <foreign lang="grc">β</foreign>
              vnum, erit
                <foreign lang="grc">βα</foreign>
              tria,
                <foreign lang="grc">α</foreign>
              9
                <expan abbr="quinq́">quin〈que〉</expan>
              ;, & 9R
                <lb/>
              ſeptem.
                <emph type="italics"/>
              & portiones ipſorum
                <emph.end type="italics"/>
              diametrorum BD OR
                <emph type="italics"/>
              ſunt numero æ
                <lb/>
              quales.
                <emph.end type="italics"/>
              quot.n ſunt BN NM ML LD, tot ſunt O
                <foreign lang="grc">β βα α</foreign>
              9 9R.
                <emph type="italics"/>
              pa
                <lb/>
              tet diametrorum portiones in eadem eſſe proportione
                <emph.end type="italics"/>
              , vt 〈que〉m
                <expan abbr="admodũ">admodum</expan>
                <lb/>
              eſt BN ad NM, & NM ad ML, & ML ad LD, ita eſſe O
                <foreign lang="grc">β</foreign>
              ad
                <lb/>
                <foreign lang="grc">βα</foreign>
              , &
                <foreign lang="grc">βα</foreign>
              ad
                <foreign lang="grc">α</foreign>
              9, &
                <foreign lang="grc">α</foreign>
              9 ad 9R. Atverò quoniam ita eſt DB ad BL,
                <lb/>
              vt RO ad O9; (ſunt.n.ut ſexdecim ad nouem) & ut DB ad
                <arrow.to.target n="marg248"/>
                <lb/>
              ita eſt quadratum ex AD ad
                <expan abbr="quadratũ">quadratum</expan>
              ex EL; & vt RO ad O9,
                <lb/>
              ita eſt
                <expan abbr="quadratũ">quadratum</expan>
              ex XR ad quadratum ex S
                <emph type="italics"/>
              9
                <emph.end type="italics"/>
              ; erit
                <expan abbr="quadratũ">quadratum</expan>
              ex
                <lb/>
              AD ad
                <expan abbr="quadratũ">quadratum</expan>
              ex EL, vt
                <expan abbr="quadratũ">quadratum</expan>
              ex XR ad ex S9
                <expan abbr="quadratũ">quadratum</expan>
              .
                <lb/>
              ergo ut AD ad EL, ita XR ad S9. & horum dupla
                <expan abbr="nẽpè">nempè</expan>
              AC ad
                <lb/>
              EK, vt XP ad ST:
                <expan abbr="eademq́">eadem〈que〉</expan>
              ; prorſus
                <expan abbr="rõne">ronne</expan>
              , quoniam ita eſt
                <arrow.to.target n="marg249"/>
                <lb/>
              ad BM, vt 9O ad O
                <foreign lang="grc">α</foreign>
              (ſunt.n.ut nouem ad quatuor) oſtendetur
                <lb/>
              EL ad FM ita eſſeut S9 ad Y
                <foreign lang="grc">α</foreign>
              , & horum dupla, ſcilicet EK ad FI
                <lb/>
              ita eſſe, ut ST ad YV.
                <expan abbr="Cùmq́">Cùm〈que〉</expan>
              ; ſit MB ad BN, vt
                <foreign lang="grc">α</foreign>
              O ad O
                <foreign lang="grc">β</foreign>
              , ut ſci
                <lb/>
              licet quatuor ad vnum; ſimiliter oſtendetur FM ad GN ita eſſe
                <lb/>
              vt Y
                <foreign lang="grc">α</foreign>
              ad Q
                <foreign lang="grc">β</foreign>
              ; FI uerò ad GH, vt YV ad QZ. vnde colligitur
                <expan abbr="nõ">non</expan>
                <lb/>
              ſolùm portiones diametrorum (ut dixim us) in eadem eſſe pro­
                <lb/>
              portione, ſed
                <emph type="italics"/>
              & parallelas
                <emph.end type="italics"/>
              AC EK FI GH, & XP ST YV QZ
                <emph type="italics"/>
              in
                <lb/>
                <expan abbr="eadē">eadem</expan>
              eſſe proportione. </s>
              <s id="N15753">& T rapeziorum ipſius quidem AE
                <emph.end type="italics"/>
              k
                <emph type="italics"/>
              C, & ipſius
                <emph.end type="italics"/>
                <arrow.to.target n="marg250"/>
                <lb/>
                <emph type="italics"/>
              XSTP centra grauitatum eſſe in lineis LD 9R ſimiliter poſita, cùm
                <lb/>
              eandem habeant proportionem AC EK, quam XP ST.
                <emph.end type="italics"/>
              lineæquè
                <lb/>
              LD 9R bifariam diuidant ſuas æquidiſtantes AC EK.
                <lb/>
              & XP ST. etenim ſi ponatur trapezij AK centrum graui
                <lb/>
              tatis
                <foreign lang="grc">γ</foreign>
              , ipſius vcrò XT centrum grauitatis
                <foreign lang="grc">δ</foreign>
              , erit L
                <foreign lang="grc">γ</foreign>
              ad
                <foreign lang="grc">γ</foreign>
              D,
                <lb/>
              vt dupla ipſius AC cum EK ad duplam ipſius
                <arrow.to.target n="marg251"/>
                <lb/>
              cum AC. & 9
                <foreign lang="grc">δ</foreign>
              ad
                <foreign lang="grc">δ</foreign>
              R erit, vt dupla ipſius XP cum
                <lb/>
              ST ad duplam ST cum XP. quoniam autem ita eſt AC ad EK, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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