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="130" xlink:href="015/01/149.jpg"/>
            <p type="main">
              <s id="id002345">Quarta regula propoſita quantitate ab uno in continua propor
                <lb/>
              tione, ſi uis ſcire cuius naturæ ſit detracto uno conſidera, an poſsit
                <lb/>
              diuidi per duo, eſt quadratum medietatis, & ita procedes diuiden­
                <lb/>
              do uſque ad numerum primum, qui uel eſt 2, & erit ex genere quad
                <lb/>
              quad. </s>
              <s id="id002346">uel 3, & erit ex genere quadratorum cuborum, & ſimiliter ſi
                <lb/>
              ſit 9, erit ex genere quadratorum cubi cubi. </s>
              <s id="id002347">Et ſi proueniat alius nu
                <lb/>
              merus primus, ut 5. 7. 11. 13. erit quadratum relati illius ordinis. </s>
              <s id="id002348">Et ſi
                <lb/>
              non poteſt diuidi numerus quantitatum per 2 uide, ſi poſsit diuidi
                <lb/>
              per 3, tunc erit cubus illius quantitatis, & ſi illa quantitas, quæ pro­
                <lb/>
              uenit ex diuiſione: fuerit 3, uel potuerit diuidi per 3, erit cubus, uel
                <lb/>
              cubus cubi, & ita deinceps. </s>
              <s id="id002349">Si uerò ſit alius numerus primus, ut 5.
                <lb/>
              7. 11. erit cubus relati. </s>
              <s id="id002350">Et ita ſi
                <expan abbr="nõ">non</expan>
              poſsit diuidi per 2, nec per 3, erit ex
                <lb/>
              genere relati. </s>
              <s id="id002351">Et tunc ſi poſsit diuidi per alium numerum, ut 35, erit
                <lb/>
              relatum ex eo genere. </s>
              <s id="id002352">Vtpotè trigeſima quinta quantitas eſt rela­
                <lb/>
              tum ſecundum relati primi, ſeu relatum primum relati ſecundi.
                <lb/>
              </s>
              <s id="id002353">Nam quoties quantitas poteſt diuidi per duos numeros, dicetur
                <lb/>
              ſub utro que uiciſsim, ut duodecima poteſt diuidi per 4 & 3, ideò di­
                <lb/>
              cetur cubus quad quad. </s>
              <s id="id002354">uel quad quad. </s>
              <s id="id002355">cub. </s>
              <s id="id002356">& per 2 & 6, & dicetur
                <lb/>
              quadratum cubi quadrati, & quadratum cubicum quadrati ipſius
                <lb/>
              proportionis, ad quam omnia referri debent.</s>
            </p>
            <p type="main">
              <s id="id002357">Quinta regula ex præcedenti pendet, & eſt, quod denomina­
                <lb/>
              tiones, & proportiones uiciſsim commutantur: uelut 256 eſt quad
                <lb/>
              quad quad, & inter quad quad quad, & quad quad ſunt quatuor ter
                <lb/>
              mini ipſo computato, & inter quad quad, & quod uiſi duo, ergo
                <lb/>
              quad quad quad continet plures proportiones, & proportiones
                <lb/>
              duplicatæ non conſtituunt quad: nam 64 continet duas duplas
                <lb/>
              ad 16, non tamen eſt quadratum 16, ideo oportet diligenter ani­
                <lb/>
              maduertere.</s>
            </p>
            <p type="main">
              <s id="id002358">Sexta regula ſimiliter ex dictis pendet, & eſt, quòd gratia exem­
                <lb/>
              pli relatum primum comparatum ad primum terminum eſt ſexta
                <lb/>
              quantitas, cum autem comparatur ad rem, iam præſupponit pro­
                <lb/>
              portionem. </s>
              <s id="id002359">Exemplum relatum primum proportionis 21/20 eſt 4084101/3200000
                <lb/>
              & eſt aliquanto maior ſexquiquarta, & ſi colligas terminos 100.
                <lb/>
              105. 110 1/4 115 61/80 121 861/1600 127 19681/32000. Tu uides quòd ſunt ſex termini in
                <lb/>
              utra que computando primum, ſed in 21/20 ſunt duo termini, & in qua­
                <lb/>
              drato tres, & in quadrato quadrati per præcedentem, adduntur
                <lb/>
              duo & ultimus ſcilicet ſextus fit ex relato ipſo. </s>
              <s id="id002360">Ergo ultra propor­
                <lb/>
              tionem ſunt tantum quatuor termini.</s>
            </p>
            <p type="main">
              <s id="id002361">Septima regula ad effugiendum omnes errores tu ſcis, quòd
                <lb/>
              4096 quadratum 64 eſt ſextus a 64, ad quem habet proportionem
                <lb/>
              quadrati, & 64 eſt ſimiliter ſextus ab uno illo ſcilicet non </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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