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="id000368">
                <pb pagenum="17" xlink:href="015/01/036.jpg"/>
              plum 512, & aggregatum 18. 12. 8. 5 2/3, & ita deinceps in ſexquialtera
                <lb/>
              erit 54 duplum 27 primæ in eo ordine.</s>
            </p>
            <p type="head">
              <s id="id000369">SCHOLIVM.</s>
            </p>
            <p type="main">
              <s id="id000370">Ex quo patet genus demonſtrandi nouun & pulchrum: nam
                <lb/>
              ſupponatur 54, aggregatum duplum 27, primæ igitur addito 27
                <lb/>
              ad 54, cum ſit dimidium, & addito 13 1/2, dimidio 27 ad 27, nam ex
                <lb/>
              ſuppoſito quantitas ſequens eſt ſexquialtera ad 27, igitur 81 eſt du­</s>
            </p>
            <p type="main">
              <s id="id000371">
                <arrow.to.target n="marg62"/>
                <lb/>
              plum ad 40 1/2. Igitur conuertendo eſt proportio aggregati prioris
                <lb/>
              ad 27 eſt dupla, ergo aggregatum eſt 54.
                <lb/>
                <arrow.to.target n="marg63"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000372">
                <margin.target id="marg62"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              18.
                <emph type="italics"/>
              quin
                <lb/>
              ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000373">
                <margin.target id="marg63"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 4.</s>
            </p>
            <p type="main">
              <s id="id000374">Ex hoc patet eandem generaliter quod proportio maioris quan
                <lb/>
              titatis ad aggregatum reliquarum analogarum eſt, uelut eius quod
                <lb/>
              prouenit diuiſo quadrato maioris termini per differentiam eius, &
                <lb/>
              ſequentis maioris in eadem proportione ad ipſum maiorem.</s>
            </p>
            <p type="main">
              <s id="id000375">
                <arrow.to.target n="marg64"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000376">
                <margin.target id="marg64"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000377">Exemplum ſit proportio augens 25 & 35 duarum quintarum, uo
                <lb/>
              lo ſcire quantum ſit aggregatum omnium citra 25, maximam acci­
                <lb/>
              pio 35, ulteriorem ad 25, cuius differentia a 25 eſt 10, cum quo diui­
                <lb/>
              do 625 quadratum, exit 62 1/2 aggregatum quantitatum. </s>
              <s id="id000378">Et facile po­</s>
            </p>
            <p type="main">
              <s id="id000379">
                <arrow.to.target n="marg65"/>
                <lb/>
              reſt demonſtrari. </s>
              <s id="id000380">Si quis dicat in qua proportione ſunt infinitæ
                <lb/>
              quantitates analogæ cum 12, quæ iunctæ efficiunt 10, iunge 10 cum
                <lb/>
              12 fit 22, duc 22 in 12 fit 264, diuide 264 per 10, exit 26 2/3, & in ea pro­
                <lb/>
              portione
                <expan abbr="erũt">erunt</expan>
              illæ quantitates, in qua ſunt 26 2/3 ad 12: duc per 5 fiunt
                <lb/>
              60, & 132 diuide per 12, exeunt 11 & 5, & ita erunt in proportione 11
                <lb/>
              ad 5 experiaris, & inuenies, & demonſtratur ex prioribus.</s>
            </p>
            <p type="margin">
              <s id="id000381">
                <margin.target id="marg65"/>
              Q
                <emph type="italics"/>
              uæſtio.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000382">Propoſitio decimanona.</s>
            </p>
            <p type="main">
              <s id="id000383">Si fuerint aliquot quantitates arithmeticæ omiologæ, quarum
                <lb/>
              exceſſus ſit æqualis minimè, omnibus autem deficientibus ſupple­
                <lb/>
              menta ad ęqualitatem maximè adiungantur, erunt quadrata omni­
                <lb/>
              um quantitatum æqualium adiecto rurſus quadrato primæ cum
                <lb/>
              eo quod fit ex minima primi ordinis in
                <expan abbr="aggregatũ">aggregatum</expan>
              omnium quan­
                <lb/>
              titatum eiuſdem tripla aggregato quadra­
                <lb/>
                <figure id="id.015.01.036.1.jpg" xlink:href="015/01/036/1.jpg" number="31"/>
                <lb/>
              torum omnium quantitatum primi ordinis
                <lb/>
                <arrow.to.target n="marg66"/>
                <lb/>
              pariter acceptis.</s>
            </p>
            <p type="margin">
              <s id="id000384">
                <margin.target id="marg66"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000385">Sint aliquot quantitates a b c d e f g h in
                <lb/>
              continua proportione. </s>
              <s id="id000386">Arithmetica diſpoſitę
                <lb/>
              ita ut minima
                <expan abbr="earũ">earum</expan>
              quę ſit h, ſit ęqualis diffe­
                <lb/>
              rentię quantitatum
                <expan abbr="ſecundũ">ſecundum</expan>
              ordinem diſpo
                <lb/>
                <expan abbr="ſitarũ">ſitarum</expan>
              , uelut differentia a & b, & b & c, & c &
                <lb/>
              d, et ita de alijs, addantur
                <expan abbr="aũt">aut</expan>
                <expan abbr="ſupplemẽta">ſupplementa</expan>
              ſin
                <lb/>
              gulis harum, quæ ſint i k l m n o p, ita ut
                <expan abbr="oẽs">oes</expan>
                <lb/>
              fiant ęquales
                <expan abbr="cũ">cum</expan>
              ſuis ſupplementis ipſi lineę
                <lb/>
              à maiori. </s>
              <s id="id000387">Eſtque
                <expan abbr="idẽ">idem</expan>
              ac ſi eſſent aliquot quanti</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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