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="id002700">
                <pb pagenum="152" xlink:href="015/01/171.jpg"/>
              qui diuiſus per 6 ſupererit 3, & in paribus qui poterit diuidi per 6.
                <lb/>
              Quia
                <expan abbr="componunt̃">componuntur</expan>
              ex huiuſmodi: uelut 3 in ſe facit 9, & 25 in ſe facit
                <lb/>
              225, qui
                <expan abbr="iũcti">iuncti</expan>
                <expan abbr="faciũt">faciunt</expan>
              234, diuiſo 235 per 6 exit 39, qui
                <expan abbr="iterũ">iterum</expan>
              diuiſus per 6
                <lb/>
              ſupereſt 3, & ſimiliter capio 6 & 12,
                <expan abbr="quorũ">quorum</expan>
                <expan abbr="q̃drata">quadrata</expan>
              ſunt 36 & 144, &
                <lb/>
                <expan abbr="aggregatũ">aggregatum</expan>
              180, qui diuiſus per 6 exit 30, qui
                <expan abbr="iterũ">iterum</expan>
              poteſt diuidi per
                <lb/>
              6. Et hoc quia
                <expan abbr="quilibetillorũ">quilibet illorum</expan>
              poteſt diuidi per
                <expan abbr="q̃dratũ">quadratum</expan>
              6 in paribus,
                <lb/>
              ergo aggregato diuiſo per 6 q̊d prodit,
                <expan abbr="iterũ">iterum</expan>
              poterit diuidi per 6.
                <lb/>
              Et in imparibus quodlibet
                <expan abbr="q̃dratorũ">quadratorum</expan>
              exuperat ſupra ſenarios in 3,
                <lb/>
                <expan abbr="igit̃">igitur</expan>
                <expan abbr="aggregatũ">aggregatum</expan>
              diuiſum in 2 pariet
                <expan abbr="numerũ">numerum</expan>
              qui diuiſus per 3, exibit
                <lb/>
              numerus impar
                <expan abbr="cõpoſitus">compoſitus</expan>
              ex ſenarijs & 3. Illud ergo
                <expan abbr="quadratũ">quadratum</expan>
              , q̊d
                <lb/>
              prodibit, uel erit
                <expan abbr="cõpoſitum">compoſitum</expan>
              ex ſenarijs, uel ſupererit 3. Sed
                <expan abbr="cũ">cum</expan>
              3 nume
                <lb/>
              ret 6, ergo tres
                <expan abbr="q̃drati">quadrati</expan>
              numeri ſcilicet duo, qui
                <expan abbr="cõponunt">componunt</expan>
                <expan abbr="numerũ">numerum</expan>
              ,
                <lb/>
                <arrow.to.target n="marg521"/>
                <lb/>
              & qui prodit per
                <expan abbr="diuiſionẽ">diuiſionem</expan>
              6, erunt
                <expan abbr="cõpoſiti">compoſiti</expan>
              inter ſe, ergo & radices il
                <lb/>
              lorum. </s>
              <s id="id002701">
                <expan abbr="Igit̃">Igitur</expan>
              radix numeri
                <expan abbr="q̃drati">quadrati</expan>
              , qui prouenit diuiſo aggregato
                <expan abbr="qua­dratorũ">qua­
                  <lb/>
                dratorum</expan>
              per 6 eſt ex
                <expan abbr="eodẽ">eodem</expan>
              ordine
                <expan abbr="impariũ">imparium</expan>
              , ſi impares numeri
                <expan abbr="q̃drati">quadrati</expan>
                <lb/>
                <expan abbr="fuerũt">fuerunt</expan>
              , aut
                <expan abbr="pariũ">parium</expan>
              ſi pares. </s>
              <s id="id002702">At hoc eſſe
                <expan abbr="nõ">non</expan>
              poteſt,
                <expan abbr="nã">nam</expan>
              fracti illi numeri,
                <lb/>
              qui
                <expan abbr="erũt">erunt</expan>
              radices,
                <expan abbr="nõ">non</expan>
                <expan abbr="erũt">erunt</expan>
              minimi, ſed diuiſi per 3 oſtendent minores,
                <lb/>
              quod eſt contra ſuppoſitum, quare nullo modo 6 poteſt diuidi in
                <lb/>
              duos numeros quadratos, neque integros, neque fractos, quod erat
                <lb/>
              demonſtrandum. </s>
              <s id="id002703">Habes igitur ex hoc demonſtrationem quando
                <lb/>
                <expan abbr="nõ">non</expan>
              poſsit diuidi, & quando poſsit, quod poſsit, & quomodo ſimul.</s>
            </p>
            <p type="margin">
              <s id="id002704">
                <margin.target id="marg521"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              29.
                <emph type="italics"/>
              ſe­
                <lb/>
              ptimi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id002705">Propoſitio centeſima quinquageſima ſexta.</s>
            </p>
            <p type="main">
              <s id="id002706">Horologiorum tempus multiplicare.
                <lb/>
                <arrow.to.target n="marg522"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002707">
                <margin.target id="marg522"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id002708">Contingit quandoque q̊d
                <expan abbr="horologiorũ">horologiorum</expan>
              tem
                <lb/>
                <figure id="id.015.01.171.1.jpg" xlink:href="015/01/171/1.jpg" number="176"/>
                <lb/>
              pus breue eſt, uolumus
                <expan abbr="aũt">aut</expan>
              maius efficere: id
                <lb/>
              duob. </s>
              <s id="id002709">modis poſſumus,
                <expan abbr="quorũ">quorum</expan>
              unus diffici­
                <lb/>
              lior eſt ſed perpetuus, & longè nobilior, nam
                <lb/>
              grauitas ponderis uerſatilis efficit
                <expan abbr="quidẽ">quidem</expan>
                <expan abbr="tar­diorẽ">tar­
                  <lb/>
                diorem</expan>
              , ſed difficilius
                <expan abbr="mobilẽ">mobilem</expan>
              , & ob id grauio­
                <lb/>
              re
                <expan abbr="põdere">pondere</expan>
              in
                <expan abbr="digentẽ">digentem</expan>
              . </s>
              <s id="id002710">Sit ergo rota a b uerſati­
                <lb/>
              lis, quæ certam menſuram exigit pro quacunque funis parte correſperon
                <lb/>
              dentis uni denti ex centum, in quos diſtincta ſit, curriculum
                <expan abbr="aũt">aut</expan>
              c d
                <lb/>
              quinque
                <expan abbr="dentiũ">dentium</expan>
              , per q̊drota ſexaginta dentes
                <expan abbr="habẽs">habens</expan>
                <expan abbr="circumuoluat̃">circumuoluatur</expan>
              in
                <lb/>
                <expan abbr="cõuerſione">conuerſione</expan>
              ,
                <expan abbr="igit̃">igitur</expan>
              primę rotę uities
                <expan abbr="circumferet̃">circumferetur</expan>
              ,
                <expan abbr="ſecũda">ſecunda</expan>
                <expan abbr="dẽtesque">dentesque</expan>
              M. CC.
                <lb/>
              rurſus ad
                <expan abbr="hãc">hanc</expan>
                <expan abbr="ſecundã">ſecundam</expan>
              tertia
                <expan abbr="nectat̃">nectatur</expan>
              cum curriculo ſex
                <expan abbr="dentiũ">dentium</expan>
              , atque in
                <lb/>
              ea
                <expan abbr="dẽtes">dentes</expan>
              ſeptuaginta duo, ut in una
                <expan abbr="cõuerſione">conuerſione</expan>
              ſint xiiij cccc, dentes
                <lb/>
                <expan abbr="igit̃">igitur</expan>
              tot dentes in una
                <expan abbr="cõuerſione">conuerſione</expan>
              primę rotę circumuoluentur. </s>
              <s id="id002711">Iam
                <lb/>
              uerò tempus illud poterit duplicari ac triplicari iuxta
                <expan abbr="tarditatẽ">tarditatem</expan>
              tem
                <lb/>
              poris uerſatilis:
                <expan abbr="quãto">quanto</expan>
                <expan abbr="igit̃">igitur</expan>
              ponderoſius fuerit illud
                <expan abbr="tẽpus">tempus</expan>
              , tanto tar­
                <lb/>
              dius
                <expan abbr="mouebit̃">mouebitur</expan>
              , pauciores que circumuolutiones neceſſarię
                <expan abbr="erũt">erunt</expan>
              ad
                <expan abbr="ex­plẽdam">ex­
                  <lb/>
                plendam</expan>
              unam
                <expan abbr="diẽ">diem</expan>
              : id eſt horas 24, ſed hoc in
                <expan abbr="cõmodi">commodi</expan>
              accedet, quòd
                <lb/>
              reuolutio indicis tanto tardior erit, ut
                <expan abbr="nõ">non</expan>
              iuſtè oſten dat horas: </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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