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="129" xlink:href="015/01/148.jpg"/>
            <p type="main">
              <s id="id002325">Propoſitio centeſima trigeſima ſexta.</s>
            </p>
            <p type="main">
              <s id="id002326">Denominationes in infinitum extendere.</s>
            </p>
            <p type="main">
              <s id="id002327">Inquit Euclides, ſi fuerint quotlibet quantitates ab uno in conti­</s>
            </p>
            <p type="main">
              <s id="id002328">
                <arrow.to.target n="marg459"/>
                <lb/>
                <arrow.to.target n="marg460"/>
                <lb/>
              nua proportione, erit tertius numerus quadratus, & omnes alij ſe­
                <lb/>
              quentes uno intermiſſo. </s>
              <s id="id002329">Tertia igitur in comparatione ad ſecun­
                <lb/>
              dam etiam, quod non ſit numerus, eſt quadratum: eſt enim tertia
                <lb/>
              ab uno quadratum ſecundæ, quæ eſt proportio. </s>
              <s id="id002330">Detracto igitur
                <lb/>
              uno omnes quantitates lo co pari ſunt quadratæ: ut ſcias ergo cu­
                <lb/>
              ius ſunt quadratæ diuide per medium, & erit quadratum illius, er­
                <lb/>
              go quadrageſima erit quadratum uigeſimæ, & uigeſima decimæ,
                <lb/>
              & decima quintæ, & uigeſima ſexta tertiæ decimæ, & ita de alijs.
                <lb/>
              </s>
              <s id="id002331">Iuxta hoc dicemus, quod ſecunda erit
                <expan abbr="quadratũ">quadratum</expan>
              , & quarta quadra­
                <lb/>
              tum quadrati, & octaua
                <expan abbr="quadratũ">quadratum</expan>
              quadrati quadrati. </s>
              <s id="id002332">Et ſextadeci­
                <lb/>
              ma quad quad quad quad. </s>
              <s id="id002333">& ita trigeſima ſecunda quad quad quad
                <lb/>
              quad quad. </s>
              <s id="id002334">Quod autem quad. </s>
              <s id="id002335">eſt quarta in ordine, ideo & octa­
                <lb/>
              ua & duodecima & decimaſexta, & ſic de alijs ſunt quadrata qua­
                <lb/>
              drati, & ſicut quarta eſt quadratum quadrati primæ, ita octaua ſe­
                <lb/>
              cundæ, & duodecima tertiæ, & ſexta decima quartæ, & uigeſima
                <lb/>
              quintæ, & ita ſemper diuidendo per quatuor.</s>
            </p>
            <p type="margin">
              <s id="id002336">
                <margin.target id="marg459"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id002337">
                <margin.target id="marg460"/>
              L
                <emph type="italics"/>
              ib.
                <emph.end type="italics"/>
              9. P
                <emph type="italics"/>
              ro
                <lb/>
              poſ.
                <emph.end type="italics"/>
              8.</s>
            </p>
            <p type="main">
              <s id="id002338">Secunda regula dicebat ibidem Euclides, ſi fuerint quotlibet
                <lb/>
                <arrow.to.target n="marg461"/>
                <lb/>
              quantitates ab uno in continua proportione quartus, ab uno erit
                <lb/>
              cubus ſupple ſecundæ, & ita duobus ſemper intermiſsis, uno igi­
                <lb/>
              tur ipſo relicto quolibet loco ternario, ut tertia, ſexta, nona, duode­
                <lb/>
              cima ſunt cubi, & cubi eius quantitatis, quę exit diuiſo numero per
                <lb/>
              tria, uelut tertia primæ, ſexta ſecundæ, nona tertię, duo decima quar
                <lb/>
              tæ: & ita tertia erit cubus nona cubus cubi, & uigeſima ſeptima cu­
                <lb/>
              bus cubi cubi ſcilicet primæ. </s>
              <s id="id002339">Et trigeſima nona eſt cubus ter­
                <lb/>
              tiæ decimæ.</s>
            </p>
            <p type="margin">
              <s id="id002340">
                <margin.target id="marg461"/>
              L
                <emph type="italics"/>
              ib.
                <emph.end type="italics"/>
              9. P
                <emph type="italics"/>
              ro­
                <lb/>
              poſ.
                <emph.end type="italics"/>
              8.</s>
            </p>
            <p type="main">
              <s id="id002341">Tertia regula quarta quantitas, ut uiſum eſt: eſt quad quad. </s>
              <s id="id002342">Et
                <lb/>
              quinta eſt relatum primum, quia 5 eſt numerus primus, & 7 eſt re­
                <lb/>
              latum ſecundum, quia eſt ſecundus numerus primus: & undecima
                <lb/>
              tertium: & tertiadecima quartum: & decimaſeptima quintum: &
                <lb/>
              decimanona ſextum: & uigeſima tertia ſeptimum & uigeſima quin­
                <lb/>
              ta, quia eſt primus numerus præter quam ad quintam, ideò eſt rela­
                <lb/>
              tum quintæ, quæ eſt relatum primum primæ, omnes ergo numeri
                <lb/>
              primi ſunt relata, alij omnes ſunt ex natura cubi uel quadrati. </s>
              <s id="id002343">Sed
                <lb/>
              relata ſunt inter ſe omnia diuerſorum generum niſi
                <expan abbr="uigeſimũ">uigeſimum</expan>
              quin­
                <lb/>
              tum, quod eſt relatum primum primi relati, & quadrageſimum no­
                <lb/>
              num eſt relatum ſecundum relati ſecundi. </s>
              <s id="id002344">Et ita centeſimum uigeſi­
                <lb/>
              mum primum eſt relatum tertium tertij relati, reliqua, ut dixi, me­
                <lb/>
              dia inter hæc ſunt ſui generis.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>