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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      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id002377">
                <pb pagenum="132" xlink:href="015/01/151.jpg"/>
              tus eſt ordo, & facere tot numeros ſequentes; quotus eſt ordo, &
                <lb/>
              ſemper minuere unam o, uelut quia quadrata <02> eſt prima ad 2 ad­
                <lb/>
              demus o, & fiet 20, nec alium quęremus numerum. </s>
              <s id="id002378">Sed quia cubi­
                <lb/>
              ca eſt ſecundo loco, habebit prima nota 00, & fiet 300, & ſecundum
                <lb/>
              3 unam 0, & fiet 30, & in quadrato quadrati addemus 000 primo,
                <lb/>
              & 00 ſecundo, & o tertio, & ita habebimus 4000. 600. 40. ſed quia
                <lb/>
              in tabula non eſt 4 ultimum, addemus ſimilem primo ſemper. </s>
              <s id="id002379">In
                <lb/>
              relato primo, ergo habebimus 50000. 1000. 1000. 50. & in cubo
                <lb/>
              quadrati 600000. 150000. 20000. 1500. 60. Manifeſtum eſt, quòd
                <lb/>
              his uice uerſa aſſumpſimus 15 & 6 ſimiles prioribus addendo ſem­
                <lb/>
              per ut dixi o minus, donec ad unam peruenerit. </s>
              <s id="id002380">Et ita in relato ſe­
                <lb/>
              cundo 7000000. 2100000. 350000. 35000. 2100. 70. & ita deinceps.</s>
            </p>
            <p type="margin">
              <s id="id002381">
                <margin.target id="marg464"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id002382">Propoſitio centeſima trigeſima nona.</s>
            </p>
            <p type="main">
              <s id="id002383">Radices omnes à propoſitis numeris extrahere.
                <lb/>
                <arrow.to.target n="marg465"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002384">
                <margin.target id="marg465"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id002385">Propoſitis quibuſuis numeris utpotè 916132832, uolo detrahere
                <lb/>
              <02> relatam primam, primum habebo in tabula deſcripta relata pri­
                <lb/>
              ma numerorum ſimplicium uſque ad 10 uelut in exemplo. </s>
              <s id="id002386">Dein de
                <lb/>
                <figure id="id.015.01.151.1.jpg" xlink:href="015/01/151/1.jpg" number="144"/>
                <lb/>
              ſubſcribam pun­
                <lb/>
              ctum ſub prima
                <lb/>
              nota à dextra, &
                <lb/>
              quia eſt quarta in
                <lb/>
                <figure id="id.015.01.151.2.jpg" xlink:href="015/01/151/2.jpg" number="145"/>
              ordine hoc, ſeu quinta denominatio ſecun­
                <lb/>
              dum noſtrum, omittam quatuor notas in­
                <lb/>
              ter medias, & ſubſcribam punctum aliud,
                <lb/>
              & ita facerem ſi eſſent plures quàm decem
                <lb/>
              notæ: relinquitur ergo ad
                <expan abbr="pũctum">punctum</expan>
              primum
                <lb/>
              à ſiniſtra 9161, cuius quęro <02> relatam pri­
                <lb/>
              mam in tabula, quam inuenio eſſe 6, nam
                <lb/>
                <figure id="id.015.01.151.3.jpg" xlink:href="015/01/151/3.jpg" number="146"/>
              7776 eius relatum primum eſt
                <lb/>
              proximius ex minoribus ad 9161,
                <lb/>
              detraho igitur 7776, ex numero
                <lb/>
              propoſitio relinquitur. </s>
              <s id="id002387">Dein de
                <lb/>
              póno 6 & quadratum eius, & cub. </s>
              <s id="id002388">& quadratum
                <lb/>
              quadrati, quia, ut dixi, eſt quarta denominatio a­
                <lb/>
                <figure id="id.015.01.151.4.jpg" xlink:href="015/01/151/4.jpg" number="147"/>
              pud illum, & è regione numeros præcedentes in­
                <lb/>
              uentos relati primi ex præcedenti propoſitione: & duco ſingulos
                <lb/>
              cum ſuis collateralibus, ut uides etiam in figura, et cum ultimo pro­
                <lb/>
              ducto, ſcilicet 64800000 diuido 138532832 exit 2, huius accipio o­
                <lb/>
              mnes numeros ad relatum primum uſque ut uides, & pono minores
                <lb/>
              è regione maiorum, utpotè 2 è regione 1296 & 50000, & 4 è </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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