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="id001562">
                <pb pagenum="86" xlink:href="015/01/105.jpg"/>
              unum. </s>
              <s id="id001563">Et rurſus feci a b quintam partem a f, & fuit a b unciarum
                <lb/>
              quatuor, & pondus quod æquauit librarum quatuor, ideò du­
                <lb/>
              plum ad pondus b f, ſicut c f ad c b: conſtat enim quòd pondus ap­
                <lb/>
              penſum eſt æquale ponderi cf. </s>
              <s id="id001564">Et rurſus poſui b a quartam partem
                <lb/>
              b f, & fuit pondus, quod æquauit in b duæ libræ: ex quo manife­
                <lb/>
              ſtum eſt, quòd proportio c f ad c b eſt ſemper uelut ponderis c f ad
                <lb/>
              totam b f. </s>
              <s id="id001565">Et hoc eſt, ac ſi dicamus, quòd proportio ponderis c f ad
                <lb/>
              totam eſt confuſa ex proportione e f ad c b, & c f, quod eſt 1 p. </s>
              <s id="id001566">Id
                <lb/>
                <arrow.to.target n="marg315"/>
                <lb/>
              etiam declaratum eſt in primo de Subtilitate. </s>
              <s id="id001567">Proponatur ergo
                <lb/>
              lemma, iam ſic proportio ponderis cf ad pondus b c, eſt primum
                <lb/>
              ut longitudinis cf, ſi eſſet ſuſpenſa in medio ad longitudinem b c,
                <lb/>
              quia ſupponuntur proportione ſimiles ſuis longitudinibus ma­
                <lb/>
              gnitudines, & pondera. </s>
              <s id="id001568">At c f ſuſpenſa in c, tanto eſt grauior pon­
                <lb/>
              dere proprio, quanto proportionis longitudinis cf ad cb quadra­
                <lb/>
              tum, quia in ſe ducitur proportio: igitur proportio ponderis c f in
                <lb/>
              loco ſuo ad b c pondus eſt confuſa ex proportione longitudinis
                <lb/>
              cf ad c b, & quadratis eiuſdem proportionis longitudinis cf ad c
                <lb/>
              b. </s>
              <s id="id001569">Sed quadratum proportionis longitudinis cf ad cb eſt æquale
                <lb/>
              producto proportionis longitudinis c f in ipſam c f, propterea
                <lb/>
              quòd ex proportione longitudinis cf ad cb in ipſam c b fit c f, igi­
                <lb/>
              tur proportio ponderis c f ad pondus c b eſt confuſa ex propor­
                <lb/>
              tione ponderis c f ad pondus c b, & proportione ponderis cf alicu
                <lb/>
              ius ſe habentis ad pondus cf, ut cf longitudo ad longitudinem
                <lb/>
              c b, igitur proportio ponderis cf ad pondus b f, ut cf ad c b in lon­
                <lb/>
              gitudine, quod erat probandum.</s>
            </p>
            <p type="margin">
              <s id="id001570">
                <margin.target id="marg314"/>
              C
                <emph type="italics"/>
              om.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001571">
                <margin.target id="marg315"/>
              E
                <emph type="italics"/>
              x
                <emph.end type="italics"/>
              18.
                <emph type="italics"/>
              diff.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id001572">Propoſitio nonageſima tertia.</s>
            </p>
            <p type="main">
              <s id="id001573">Propter quid in concuſsione etiam leui nauis loco moueatur
                <lb/>
              oſtendere. </s>
              <s id="id001574">Vnde manifeſtum eſt, duas naues ſibi inuicem occurſan
                <lb/>
              tes retrocedere, & quantum retrocedant ambæ.
                <lb/>
                <arrow.to.target n="marg316"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001575">
                <margin.target id="marg316"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id001576">Proponatur, quod proportio motus grauis in a d graue in aqua
                <lb/>
              ſit, uelut proportio ponderis attracti in terra ad denſitatem aquæ
                <lb/>
              cum profunditate, nam ubi pondus ſupernataret aquæ, quia aqua
                <lb/>
              eſt rotunda, eſt ac ſi tangeret in puncto. </s>
              <s id="id001577">Quare per demonſtrata ſu­
                <lb/>
              periùs mouebitur à quacunque ui, ergo nixus contrarius aduenit ob </s>
            </p>
            <p type="main">
              <s id="id001578">
                <arrow.to.target n="marg317"/>
                <lb/>
              profunditatem, & aquæ denſitatem, ſed quanto aqua denſior eſt,
                <lb/>
              tanto minus nauis deſcendit, & quanto minus denſa, tanto magis:
                <lb/>
              ergo pari modo fermè redduntur mobiles, & in aqua dulci & ſalſa,
                <lb/>
              ubi naues ſint ſimiles forma, pondere, magnitudine. </s>
              <s id="id001579">Quia ergo ne­
                <lb/>
              ceſſe eſt tabulam nauis eſſe duriorem, quam aqua ad reſiſtendum,
                <lb/>
              ergo pars maior ictus mouebit primo nauim, quam tabulam pe­
                <lb/>
              netret, cum ergo quod facilius eſt, præcedat, difficilius ergo naues </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>