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="id002711">
                <pb pagenum="153" xlink:href="015/01/172.jpg"/>
              poſitum igitur eſt, ut pondera tardius ferantur, index
                <expan abbr="aũt">aut</expan>
              , & quę ad
                <lb/>
              indicem ſequuntur horarum demonſtrationes celerius aut eodem
                <lb/>
              modo ferantur. </s>
              <s id="id002712">Ponamus ergo poſt<08> eadem eſt ratio celerioris &
                <lb/>
              æqué uelocis, ponderis
                <expan abbr="aũt">aut</expan>
              tardius deſcendentis, aut
                <expan abbr="cõtrà">contrà</expan>
              tardio­
                <lb/>
              ris, aut æqualiter circumducti in dicis, celerioris
                <expan abbr="aũt">aut</expan>
              deſcenſus pon­
                <lb/>
              deris, quod ad nullam
                <expan abbr="utilitatẽ">utilitatem</expan>
              profuturum uideo. </s>
              <s id="id002713">Sit ergo ut pon
                <lb/>
              dus uelim tardius deſcendere, rotam
                <expan abbr="aũt">aut</expan>
              ęqualiter circumferri, dico
                <lb/>
              quod ex tempore mobili ſeu uerſatili (& eſt ferrum, quod in ſum­
                <lb/>
              mo horologij citra ultraque
                <expan abbr="fert̃">fertur</expan>
              tam in horologijs ponderum <08> mo
                <lb/>
              læ) id fieri non poteſt: nam quantum tardabitur rota tertia ſecunda
                <lb/>
              & prima, atque ob id deſcenſus ponderum, tantum remorabitur rota
                <lb/>
              prima quæ indicem oſtendit, ergo tantum index tardabitur quan­
                <lb/>
              tum
                <expan abbr="põdera">pondera</expan>
              , & ut uno uerbo dicam, cùm
                <expan abbr="eadẽ">eadem</expan>
              rota index circumfe­
                <lb/>
              ratur, &
                <expan abbr="põdus">pondus</expan>
              deſcendat,
                <expan abbr="quantũ">quantum</expan>
              unum tardatur tantum & aliud.</s>
            </p>
            <p type="main">
              <s id="id002714">Secundus modus eſt, ut rota una totum tempus cum indice in ui
                <lb/>
              gintiquatuor horis circumuoluatur, & currulis in quo funis minor
                <lb/>
              fiat: neceſſe eſt
                <expan abbr="igit̃">igitur</expan>
              , ut circumuoluta rota aut ſemel aut bis,
                <expan abbr="t̃er">tur</expan>
              , qua­
                <lb/>
              ter decies, &
                <expan abbr="circumuoluat̃">circumuoluatur</expan>
              pleno circuitu index, et ſine errore: quo­
                <lb/>
              niam tempus & dentes menſuræ reſpondent: igitur ſub eiſdem cir­
                <lb/>
              cuitibus numero eodemque tempore minus ex fune
                <expan abbr="deſcendẽt">deſcendent</expan>
              in cur
                <lb/>
              ruli paruo <08> magno: quare mutatione indiget currulis, aut ut funis
                <lb/>
              circumuoluens rotam curriculum habeat
                <expan abbr="annexũ">annexum</expan>
              rotæ oſten denti
                <lb/>
              horas, in qua pauciores ſint dentes: nam in eodem tempore, & cir­
                <lb/>
              cuitu paucioribus uicibus circumuoluitur rota funis quæ grauita­
                <lb/>
              te temporis, & multitudine
                <expan abbr="dentiũ">dentium</expan>
              certam
                <lb/>
                <figure id="id.015.01.172.1.jpg" xlink:href="015/01/172/1.jpg" number="177"/>
                <lb/>
              ſeruabit
                <expan abbr="menſurã">menſuram</expan>
              . </s>
              <s id="id002715">Sed in hoc neceſſe eſt gra
                <lb/>
              uius efficere pondus, aut leuius
                <expan abbr="tẽpus">tempus</expan>
                <expan abbr="quo­niã">quo­
                  <lb/>
                niam</expan>
              funis debilius circumuertit
                <expan abbr="rotã">rotam</expan>
              : minus
                <lb/>
                <expan abbr="tñ">tn</expan>
              tardè quod ſit pro paruitatis circuitus ratione.</s>
            </p>
            <p type="main">
              <s id="id002716">Tertius modus facilior eſt, & magis com
                <lb/>
                <expan abbr="pẽdioſus">pendioſus</expan>
              : Sit horologium a b c, in quo rota
                <lb/>
              d quæ funem
                <expan abbr="cõtinet">continet</expan>
              baſis horologij e f, cui
                <lb/>
              firmiter ſint
                <expan abbr="appẽſę">appenſę</expan>
              duę trochleę g & h, & fu
                <lb/>
              nis una parte trochleę appenſus in k,
                <expan abbr="ducat̃">ducatur</expan>
                <lb/>
              ad inferiorem aliam trochleam l inſeraturque
                <lb/>
              ibi orbiculo ſuo, & redeat à dextra ſuperius
                <lb/>
                <expan abbr="inſerat̃que">inſeraturque</expan>
              orbiculo ſuperioris trochleę, dedu
                <lb/>
                <expan abbr="cat̃que">caturque</expan>
              uerſus
                <expan abbr="ſiniſtrã">ſiniſtram</expan>
              : atque ibi
                <expan abbr="deſcendẽs">deſcendens</expan>
              habe
                <lb/>
              at
                <expan abbr="põdus">pondus</expan>
              tractorium in m,
                <expan abbr="deducat̃que">deducaturque</expan>
              ſupra
                <lb/>
              ad
                <expan abbr="rotã">rotam</expan>
              horologij d, et circumuolutus exeat
                <lb/>
              ipſum, &
                <expan abbr="deſcẽdat">deſcendat</expan>
              ad tro
                <expan abbr="chleãn">chlean</expan>
              , ſub que ea circumuolutus
                <expan abbr="iterũ">iterum</expan>
              aſcen</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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