Cardano, Geronimo, Opvs novvm de proportionibvs nvmerorvm, motvvm, pondervm, sonorvm, aliarvmqv'e rervm mensurandarum, non solùm geometrico more stabilitum, sed etiam uarijs experimentis & observationibus rerum in natura, solerti demonstratione illustratum, ad multiplices usus accommodatum, & in V libros digestum. Praeterea Artis Magnae, sive de regvlis algebraicis, liber vnvs abstrvsissimvs & inexhaustus planetotius Ariothmeticae thesaurus ... Item De Aliza Regvla Liber, hoc est, algebraicae logisticae suae, numeros recondita numerandi subtilitate, secundum Geometricas quantitates inquirentis ...

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb pagenum="160" xlink:href="015/01/179.jpg"/>
            <p type="main">
              <s id="id002808">Sit angulus a b c duabus peripherijs æqualium circulorum con
                <lb/>
                <arrow.to.target n="marg537"/>
                <lb/>
              tentus, uolo ei æqualem rectilineum fabricare, ducantur b d & b e
                <lb/>
                <arrow.to.target n="marg538"/>
                <lb/>
              æquales, ut pote facto b centro eritque angulus d b a æqualis angu­
                <lb/>
              lo e b c, addito utrique communi d b e ex peri
                <lb/>
                <figure id="id.015.01.179.1.jpg" xlink:href="015/01/179/1.jpg" number="187"/>
                <lb/>
              pheria & recta, fiet angulus d b e ex rectis
                <lb/>
              æqualis a b c ex peripherijs, quod crat de­
                <lb/>
              monſtrandum.</s>
            </p>
            <p type="margin">
              <s id="id002809">
                <margin.target id="marg537"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id002810">
                <margin.target id="marg538"/>
              P
                <emph type="italics"/>
              er modum
                <emph.end type="italics"/>
                <lb/>
              8.
                <emph type="italics"/>
              primi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              l.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id002811">Ex hoc patet quod reliqua duo ſpatia
                <lb/>
                <arrow.to.target n="marg539"/>
                <lb/>
              non poſſunt eſſe æqualia rectilineo. </s>
              <s id="id002812">Nam
                <lb/>
              ſpatium b a c demonſtratum eſt æquale eſ­
                <lb/>
              ſe rectilineo, & b ad non eſt æquale rectili­
                <lb/>
              neo,
                <expan abbr="igit̃">igitur</expan>
                <expan abbr="ſpatiũ">ſpatium</expan>
              c a d non poteſt eſſe æquale
                <lb/>
              angulo rectilineo, nam ſi ſic ſit b a c ęquale
                <lb/>
              f g h & c a d h g k,
                <expan abbr="igit̃">igitur</expan>
                <expan abbr="totũ">totum</expan>
              , b a d erit ęquale
                <lb/>
                <arrow.to.target n="marg540"/>
                <lb/>
              toti f g k quod eſt contra
                <expan abbr="ſuppoſitũ">ſuppoſitum</expan>
              , ideò neque
                <lb/>
              b a e quia b a c & d a e ſunt
                <expan abbr="æq̃lia">æqualia</expan>
              rectilineis
                <lb/>
              per ſe, &
                <expan abbr="etiã">etiam</expan>
              pariter accepta. </s>
              <s id="id002813">Totum
                <expan abbr="aũt">aunt</expan>
                <expan abbr="ſpatiũ">ſpatium</expan>
              a eſt
                <expan abbr="ęq̃le">ęquale</expan>
              quatuor, re­
                <lb/>
              ctis ergo
                <expan abbr="reſiduũ">reſiduum</expan>
              , ſcilicet ſpatia c a d & b a c pariter accepta ſunt
                <expan abbr="ęq̃­lia">ęqua­
                  <lb/>
                lia</expan>
              rectilineis ſpatijs, ſed
                <expan abbr="ſpatiũ">ſpatium</expan>
              e a d non eſt
                <expan abbr="æq̃le">æquale</expan>
              rectilineo, ergo per
                <lb/>
              demonſtrata hic, nec b a e,
                <expan abbr="nã">nam</expan>
              ſi ſit, ſit ergo b a e æquale h g k & quia
                <lb/>
              ambo ſpatia b a e & c a d ſunt
                <expan abbr="æq̃lia">æqualia</expan>
              rectilineo ex demonſtratis, ſit
                <lb/>
              ergo æqualia f g k, erit ergo ex communi animi ſententia ſpatium f
                <lb/>
              g h æquale ſpatio c a d, quod eſt contra primam partem corrolarij.</s>
            </p>
            <p type="margin">
              <s id="id002814">
                <margin.target id="marg539"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 4.</s>
            </p>
            <p type="margin">
              <s id="id002815">
                <margin.target id="marg540"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              3. C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.
                <lb/>
                <emph type="italics"/>
              præſentis.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s id="id002816">LEMMA TERTIVM.
                <lb/>
                <arrow.to.target n="marg541"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002817">
                <margin.target id="marg541"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              11.
                <emph type="italics"/>
              pri
                <lb/>
              mi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lement.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id002818">Inter duas rectas lineas ſe tangentes circuli dati peripheriam </s>
            </p>
            <p type="main">
              <s id="id002819">
                <arrow.to.target n="marg542"/>
                <lb/>
              ducere. </s>
              <s id="id002820">Sit circulus datus a b rectilineus
                <lb/>
                <figure id="id.015.01.179.2.jpg" xlink:href="015/01/179/2.jpg" number="188"/>
                <lb/>
              angulus c d e, uolo illum diuidere circuli
                <lb/>
              periferia data b f, duco perpendicularem
                <lb/>
              d g ex, d ſuper d c, & facio g d æqualem a b
                <lb/>
                <arrow.to.target n="marg543"/>
                <lb/>
              & duco circulum per d qui ſit d h qui cadet
                <lb/>
              infra d c & ob id etiam ſupra d e, igitur di­
                <lb/>
              uidet angulum c d e, quare cum circulus d h ſit æqualis circulo b f
                <lb/>
                <arrow.to.target n="marg544"/>
                <lb/>
              patet propoſitum.</s>
            </p>
            <p type="margin">
              <s id="id002821">
                <margin.target id="marg542"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              3.
                <emph type="italics"/>
                <expan abbr="eiuſdẽ">eiuſdem</expan>
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002822">
                <margin.target id="marg543"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              15.
                <emph type="italics"/>
              ter
                <lb/>
              tij
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002823">
                <margin.target id="marg544"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 6.</s>
            </p>
            <p type="main">
              <s id="id002824">Ex hoc patet quod infinitis modis poteſt diuidi angulus c d e
                <lb/>
                <arrow.to.target n="marg545"/>
                <lb/>
              peripheria b f, nam diuiſo per rectam c d e linea d k per ęqualia & di
                <lb/>
                <arrow.to.target n="marg546"/>
                <lb/>
              uiſo k d e per præſentem peripheria b f, patet propoſitum quoniam
                <lb/>
              angulus c d e poteſtin infinitum recta diuidi, & ita ſemper per peri­
                <lb/>
              pheriam, unde patet propoſitum.</s>
            </p>
            <p type="margin">
              <s id="id002825">
                <margin.target id="marg545"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              1.
                <emph type="italics"/>
              diff.
                <lb/>
              </s>
              <s id="id002826">tertij
                <expan abbr="eiuſdẽ">eiuſdem</expan>
              .
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002827">
                <margin.target id="marg546"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              9.
                <emph type="italics"/>
              primi
                <emph.end type="italics"/>
                <lb/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s id="id002828">SCHOLIVM.</s>
            </p>
            <p type="main">
              <s id="id002829">Atque hæc omnia ſequuntur de mente Euclidis, quæ tamen ui­
                <lb/>
              dentur difficillima creditu, quoniam anguli rectilinei, et ex periphe</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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