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="id000650">
                <pb pagenum="34" xlink:href="015/01/053.jpg"/>
              hominum notus. </s>
              <s id="id000651">Quoniam ergo notum eſt a & c, quia eſt æquale
                <lb/>
              b, igitur proportio a ad b nota eſt: ſed iuxta illam a mouet b in d
                <lb/>
              tempore per e ſpatium, igitur per præcedentem, ut f ad a ita ſpatij
                <lb/>
              ad e in d tempore. </s>
              <s id="id000652">Sed per eadem ut temporis d ad ſpatium illud,
                <lb/>
              ita g ad h, ergo cum nota ſint d e f g erit etiam h, & ita conuertendo.</s>
            </p>
            <p type="main">
              <s id="id000653">Propoſitio quadrageſima quinta.</s>
            </p>
            <p type="main">
              <s id="id000654">Rationem ſtateræ oſtendere.
                <lb/>
                <arrow.to.target n="marg111"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000655">
                <margin.target id="marg111"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000656">Archimedes nititur huic fundamento, quod pondera, quæ pro­
                <lb/>
              portionem mutuam habent, ut diſtantiæ à libella a, quæ ſuſpen­
                <lb/>
              duntur, æqualiter ponderant, ſit ergo libella a b, & ſuſpenſa in a cen
                <lb/>
              trum mundi c, ad quod dirigitur pondus, & liquet, quod ipſum
                <lb/>
              non ſe inclinabit ex uigeſima tertia propoſitione. </s>
              <s id="id000657">Si ergo ponantur
                <lb/>
              lo co lineæ b d in e & f, & ſit proportio e b
                <lb/>
                <figure id="id.015.01.053.1.jpg" xlink:href="015/01/053/1.jpg" number="50"/>
                <lb/>
              ad b f, ut g ad h, dico, quòd erit æquili­
                <lb/>
              brium, per eandem enim h mouebitur in k,
                <lb/>
              ſcilicet ut perueniat in rectam a d, ſi enim
                <lb/>
              non eſſet | ſuſpenſum h, moueretur in re­
                <lb/>
              cta e h per eandem, quia ergo retinetur, mo­
                <lb/>
              uetur per obliquam h k, & ſumatur in pro­
                <lb/>
              pin quum punctum in b e, & n in æquali di­
                <lb/>
              ſtantia in e f, quia ergo e b totum mouetur
                <lb/>
              eadem ui in ſingulis partibus, quia a pon­
                <lb/>
              dere h, & in h mouetur per h k in m per m
                <lb/>
              p, ergo qualis eſt proportio magnitudinis h k ad m p, talis eſt uis
                <lb/>
              in m p ad uim in h k, & ita in b erit penè infinita: quia quanta ui ex­
                <lb/>
              tenditur ex h in k tanta puncta b, ſe circumuertit ergo propor­
                <lb/>
              tio hypomochlij ad ſpatium, uelut roboris ad robur, at eadem n o
                <lb/>
              ad h k, eſt enim n o æqualis m p, & n b, & b m æquales, ut uerò g ad
                <lb/>
              h, ita e b ad b f: ergo ut e b ad b f, ita uirium n o ad h k, ut igitur g ad
                <lb/>
              h, ita uirium m p ad h k: ut etiam g l ad n o, ita uirium f b ad n b.
                <lb/>
              </s>
              <s id="id000658">nam idem pondus ſcilicet g mouet totam b f, igitur ut g ſe habet </s>
            </p>
            <p type="main">
              <s id="id000659">
                <arrow.to.target n="marg112"/>
                <lb/>
              ad n o, ita h ad m p, ſed m p & n o ſunt æquales, ergo tanta eſt uis g
                <lb/>
              in f, quanta h in e.
                <lb/>
                <arrow.to.target n="marg113"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000660">
                <margin.target id="marg112"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              9.
                <emph type="italics"/>
              quin­
                <lb/>
              ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000661">
                <margin.target id="marg113"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 1.</s>
            </p>
            <p type="main">
              <s id="id000662">Ex quo patet, quod hypomochlion moueretur infinita ui, ſi poſ­
                <lb/>
              ſet eſſe punctus: ſed quia in extrema ſuperficie cylindri, ideò poteſt
                <lb/>
              aliqua ui retineri.</s>
            </p>
            <p type="main">
              <s id="id000663">
                <arrow.to.target n="marg114"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000664">
                <margin.target id="marg114"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 2.</s>
            </p>
            <p type="main">
              <s id="id000665">Et ſi quis poſſet capere haſtam in extremo puncto, non poſſet
                <lb/>
              eam mouere, etiam quod haberet robur infinitum, quia ab æquali
                <lb/>
              non fit motus per trigeſimamnonam propoſitionem.</s>
            </p>
            <p type="main">
              <s id="id000666">
                <arrow.to.target n="marg115"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000667">
                <margin.target id="marg115"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 3.</s>
            </p>
            <p type="main">
              <s id="id000668">Et libella nihil retinet niſi quantum eſt pondus eius quod </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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