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>
            <p type="main">
              <s id="id000815">
                <pb pagenum="43" xlink:href="015/01/062.jpg"/>
                <figure id="id.015.01.062.1.jpg" xlink:href="015/01/062/1.jpg" number="57"/>
                <lb/>
              ueniant in f, erunt ergo in g tempore re­
                <lb/>
              uolutiones integræ, & portio a f inſuper.
                <lb/>
              </s>
              <s id="id000816">Et quia hæ conſtituuntur per congreſſus
                <lb/>
              b cum a, & ſunt ſpatia a d, & b cum c, &
                <lb/>
              ſunt ſpatia e f, igitur ſpatium a f erit ex ge­
                <lb/>
              nere quantitatis a d, & a e per quinqua­
                <lb/>
              geſimam, harum ergo erunt commenſæ:
                <lb/>
              quod eſt contra ſuppoſitum. </s>
              <s id="id000817">Et harum
                <lb/>
              propoſitionum principium eſt traditum
                <lb/>
              à Campano Nouarienſi Euclidis expoſitore, in quodam libello
                <lb/>
              non edito qui diligentia patris mei Facij ad me peruenit.</s>
            </p>
            <p type="main">
              <s id="id000818">Propoſitio quinquageſima tertia.</s>
            </p>
            <p type="main">
              <s id="id000819">
                <expan abbr="Circulorũ">Circulorum</expan>
              ſe in aduerſum mouentium proportionem declarare.</s>
            </p>
            <p type="main">
              <s id="id000820">
                <arrow.to.target n="marg141"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000821">
                <margin.target id="marg141"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000822">Sit orbis a b cuius cen­
                <lb/>
                <figure id="id.015.01.062.2.jpg" xlink:href="015/01/062/2.jpg" number="58"/>
                <lb/>
              centrum c, manubrium c
                <lb/>
              d f e, ſeu uero tangat circu
                <lb/>
              lum g, ſeu more gemmas
                <lb/>
              ſculpentium aligetur al­
                <lb/>
              teri orbi funiculo a l b, &
                <lb/>
              ſit in uertice axis k m or­
                <lb/>
              biculus ſolidus aut ſemi­
                <lb/>
              circulari forma m, dico
                <lb/>
              quod proportio motus a
                <lb/>
              b ad motum m eſt produ
                <lb/>
              cta ex duabus proportio­
                <lb/>
              nibus c n
                <expan abbr="ſemidimetiẽtis">ſemidimetientis</expan>
              ,
                <lb/>
              & ſemidimetientis m ad k
                <lb/>
              o, quare ut rectanguli c n
                <lb/>
              in dimidium dimetientis
                <lb/>
              m ad quadratum o, ut enim a b ad ol orbem, id eſt
                <expan abbr="peripheriarũ">peripheriarum</expan>
              ita
                <lb/>
              c n ad o k, quoniam o l mouetur toties in una circuitione a b, quo­
                <lb/>
              ties
                <expan abbr="peripheriã">peripheriam</expan>
              o l
                <expan abbr="continet̃">continetur</expan>
              in peripheria a b, ergo quoties o k con­
                <lb/>
              tinetur in c n toties in una circuitione a b o l circumuertitur, ſed
                <lb/>
              quoties circumuertitur ol, toties etiam m, quia uterque mouetur eo­
                <lb/>
              dem circuitu k m axis, ergo quoties m circumducitur in circuitu a
                <lb/>
              b toties o k continetur in c n, ergo ſi fiat comparatio ſemidiametri
                <lb/>
              m ad c n, erit producta proportio circuitus a b ad circuitum m ex
                <lb/>
              proportione c n ad o k, et ſemidimetientis m ad
                <expan abbr="idẽ">idem</expan>
              o k, ergo per 26
                <lb/>
              proportio numeri circuitus unius p
                <expan abbr="alterũ">alterum</expan>
              eſt, ut rectanguli ſub c n,
                <lb/>
              & ſemidimetiente m ad quadratum k o, quod erat
                <expan abbr="demonſtrandũ">demonſtrandum</expan>
              .</s>
            </p>
            <p type="main">
              <s id="id000823">Manifeſtum eſt autem ex ipſa ſola conſtitutione, quod ſi a b mo­</s>
            </p>
            <p type="main">
              <s id="id000824">
                <arrow.to.target n="marg142"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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