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="id004064">
                <pb pagenum="238" xlink:href="015/01/257.jpg"/>
              nec minuet. </s>
              <s id="id004065">Patet quia mouebitur, gratia exempli, primo motu ex l
                <lb/>
              in f, & pòſt motu circulari, & uerè erit motum ex a in f, qui motus
                <lb/>
              eſt æqualis motui priori propriò, & ſolo ex l in f.</s>
            </p>
            <p type="margin">
              <s id="id004066">
                <margin.target id="marg795"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 2.</s>
            </p>
            <p type="main">
              <s id="id004067">Propoſitio ducenteſima ſeptima.</s>
            </p>
            <p type="main">
              <s id="id004068">Proportionem agentium naturalium in tranſmutatione con­
                <lb/>
              ſyderare.
                <lb/>
                <arrow.to.target n="marg796"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004069">
                <margin.target id="marg796"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id004070">Sit latitudo a b ad conuerſionem terræ in aurum me­
                <lb/>
              dium perfectionis a b ſit c, & medium a c d b, cuius dimi­
                <lb/>
              dium ſit e b. </s>
              <s id="id004071">Et fiat commutatio a c in f g, tempore dimi­
                <lb/>
              dium f g, g h in g h deberet peruenire ad perfectionem d,
                <lb/>
              quoniam ratio a c ad c d, ut f g ad g h. </s>
              <s id="id004072">At uerò dum tranſi­
                <lb/>
              ret terra ad perfectionem c tota reſiſtebat, iam adepta per­
                <lb/>
              fectione a c non reſiſtit, niſi pro medietate, at proportio cu
                <lb/>
              iuslibet quantitatis ad dimidium alterius producitur ex
                <lb/>
              proportione eadem & dupla, dupla igitur eſt proportio
                <lb/>
              agentis ad imperfectionem a c ei quæ eſt ad a b, igitur in di
                <lb/>
              midio temporis g h acquiret perfectionem c d, & ſit g k di
                <lb/>
              midium g h, erit ergo tempus totum fk, in quo acquiret
                <lb/>
              a d. </s>
              <s id="id004073">At ratio hæc conſtare non poteſt, nam ſi diuidatur ſpa
                <lb/>
                <figure id="id.015.01.257.1.jpg" xlink:href="015/01/257/1.jpg" number="256"/>
                <lb/>
              tium a b in trientes fient trientes duo, & quarta pars in perfectione
                <lb/>
              a d: ſed iam multo citius acquiret quam in fk tempore, quod eſt di­
                <lb/>
              midium & octaua pars. </s>
              <s id="id004074">Sed hoc non cogit, quoniam partes primæ
                <lb/>
              ſunt ſemper contumaciores, & ut diſponuntur fiunt magis obedi­
                <lb/>
              entes, non iuxta proportionem ſimpliciter, ſed ut ſunt in materia,
                <lb/>
              & ideò hæc actio eſt ſimilior proportioni exceſſus, & eſt Arithme­
                <lb/>
              tica quam capacitatis ſcilicet Geometricæ.</s>
            </p>
            <p type="main">
              <s id="id004075">
                <arrow.to.target n="marg797"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004076">
                <margin.target id="marg797"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id004077">Ex hoc patet, quod res quæ ad ſummam maturitatem perueni­
                <lb/>
              unt, maximè
                <expan abbr="acquirũt">acquirunt</expan>
              perfectionem in exiguo tempore, ut gemmę,
                <lb/>
              aurum, infans. </s>
              <s id="id004078">Ergo oportet maximè iuxta finem cauere, ne detur
                <lb/>
              occaſio ulla accelerandi partum.</s>
            </p>
            <p type="main">
              <s id="id004079">Propoſitio ducenteſima octaua.</s>
            </p>
            <p type="main">
              <s id="id004080">Mota res à centro grauitatis per priorem motum in reditu uelo­
                <lb/>
              cius mouetur, quam ſi quieuerit.</s>
            </p>
            <p type="main">
              <s id="id004081">
                <arrow.to.target n="marg798"/>
              </s>
            </p>
            <p type="margin">
              <s id="id004082">
                <margin.target id="marg798"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id004083">Sit a b c lectus penſilis, in quo ho
                <lb/>
              mo aut patera, in qua aqua uel
                <expan abbr="ui­nũ">ui­
                  <lb/>
                num</expan>
              , & ſit
                <expan abbr="cẽtrum">centrum</expan>
              grauitatis d, quod
                <lb/>
              neceſſariò eſt in linea loci, cui anne
                <lb/>
              xus eſt lectus a g, & in patera lo ci
                <lb/>
              medij manus continentis pateram
                <lb/>
                <expan abbr="cũ">cum</expan>
              centro quæ ſit a g, quibus ſtan­
                <lb/>
              tibus oſtendendum eſt primo.</s>
            </p>
            <figure id="id.015.01.257.2.jpg" xlink:href="015/01/257/2.jpg" number="257"/>
          </chap>
        </body>
      </text>
    </archimedes>
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