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 ...

Table of figures

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[Figure 31]
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[Figure 32]
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[Figure 33]
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[Figure 34]
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[Figure 36]
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[Figure 37]
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[Figure 38]
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[Figure 39]
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[Figure 40]
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[Figure 41]
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[Figure 42]
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[Figure 43]
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[Figure 45]
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[Figure 46]
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[Figure 47]
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[Figure 48]
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[Figure 49]
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[Figure 50]
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[Figure 51]
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[Figure 52]
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[Figure 53]
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page |< < of 291 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id000585">
                <pb pagenum="41 [=31]" xlink:href="015/01/050.jpg"/>
              uerent unusque per ſe mouere non poſſet, adderetur ſi proportio
                <lb/>
              produceretur, fieret minor, ergo minus mouerent quinque quàm
                <lb/>
              quatuor ex ijſdem, quod eſt abſurdum.</s>
            </p>
            <p type="main">
              <s id="id000586">Propoſitio trigeſima octaua.</s>
            </p>
            <p type="main">
              <s id="id000587">Omne corpus tantùm reſiſtit motui contrario ſuo naturali quan
                <lb/>
              cum mouetur occulto motu quieſcendo.</s>
            </p>
            <p type="main">
              <s id="id000588">
                <arrow.to.target n="marg95"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000589">
                <margin.target id="marg95"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              m.</s>
            </p>
            <p type="main">
              <s id="id000590">Sit a corpus quieſcens in pauimento b, & mouetur in eo occul­</s>
            </p>
            <p type="main">
              <s id="id000591">
                <arrow.to.target n="marg96"/>
                <lb/>
              to motu uerſus centrum, ut ſuprà uiſum eſt, contra­
                <lb/>
                <figure id="id.015.01.050.1.jpg" xlink:href="015/01/050/1.jpg" number="45"/>
                <lb/>
              rius illi ſit motus ad c, ſi ergo a quieſceret in c moue­
                <lb/>
              retur ad b occulto motu certa ui, ergo eadem reſtitit,
                <lb/>
              ne traheretur ad c. </s>
              <s id="id000592">Manifeſtum eſt autem, quod hic
                <lb/>
                <arrow.to.target n="marg97"/>
                <lb/>
              motus occultus eſt minor manifeſto.
                <lb/>
                <arrow.to.target n="marg98"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000593">
                <margin.target id="marg96"/>
              I
                <emph type="italics"/>
              n commen.
                <emph.end type="italics"/>
                <lb/>
              26. P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000594">
                <margin.target id="marg97"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              30. P
                <emph type="italics"/>
              ro
                <lb/>
              poſ.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000595">
                <margin.target id="marg98"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000596">Ex hoc patet cur naues & currus ab initio tardè & difficulter mo
                <lb/>
              ueantur, ubi moueri cœperint motus augetur: quoniam reſiſtunt </s>
            </p>
            <p type="main">
              <s id="id000597">
                <arrow.to.target n="marg99"/>
                <lb/>
              per motum occultum naturalem qui maximus eſt dum quieſcunt,
                <lb/>
              ut etiam docebat philoſophus in mechanicis, nam motus ille natu­
                <lb/>
              ralis eſt, & ideò contrarius uiolento: Ergo cum iam mouetur uio­
                <lb/>
              lenter minus, mouetur naturaliter, igitur minus reſiſtit. </s>
              <s id="id000598">Declarabi­
                <lb/>
              tur enim infrà quòd omne quod mouetur duobus motibus tanto
                <lb/>
                <arrow.to.target n="marg100"/>
                <lb/>
              minus uno mouetur quanto magis altero.</s>
            </p>
            <p type="margin">
              <s id="id000599">
                <margin.target id="marg99"/>
              Q
                <emph type="italics"/>
              ueſt.
                <emph.end type="italics"/>
              31.</s>
            </p>
            <p type="margin">
              <s id="id000600">
                <margin.target id="marg100"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              59.</s>
            </p>
            <p type="main">
              <s id="id000601">Propoſitio trigeſima nona.</s>
            </p>
            <p type="main">
              <s id="id000602">Ab æquali aut minore ui, quàm ſit
                <expan abbr="impedimentũ">impedimentum</expan>
              , non fit motus.</s>
            </p>
            <p type="main">
              <s id="id000603">Sit a quod reſiſtat, ne ſurſum trahatur per decem, dico, quod
                <expan abbr="nõ">non</expan>
                <lb/>
                <arrow.to.target n="marg101"/>
                <lb/>
              ſurſum trahetur neque à decem, neque minore: nam ſi impedimen­
                <lb/>
              tum non eſſet, moueretur infra ut decem, ergo ſi traheretur ſurſum
                <lb/>
              per decem tantum moueretur ſurſum,
                <expan abbr="quantũ">quantum</expan>
              deorſum, ergo quie­
                <lb/>
              ſceret. </s>
              <s id="id000604">Si uerò à minore moueretur à maiore ui deorſum, quam ſur­
                <lb/>
              ſum, ergo deorſum ſimpliciter non ſurſum.</s>
            </p>
            <p type="margin">
              <s id="id000605">
                <margin.target id="marg101"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000606">Propoſitio quadrageſima.</s>
            </p>
            <p type="main">
              <s id="id000607">Omne corpus ſphæricum tangens planum in puncto mouetur
                <lb/>
              ad latus per quancunque uim, quæ medium diuidere poteſt.</s>
            </p>
            <figure id="id.015.01.050.2.jpg" xlink:href="015/01/050/2.jpg" number="46"/>
            <p type="main">
              <s id="id000608">Sit corpus ad unguem ſphæricum a tan­
                <lb/>
                <arrow.to.target n="marg102"/>
                <lb/>
              gens planum b in puncto c (eſt enim hoc
                <lb/>
              neceſſarium ex demonſtratis ab Euclide in
                <lb/>
              decimaſexta Propoſitione tertij Elemento­
                <lb/>
              rum) dico, quod mouebitur à ui, quæ poteſt
                <lb/>
              ſcindere aërem. </s>
              <s id="id000609">Nam cum non aſcendat, nec
                <lb/>
              deſcendat, ſed quaſi in circulo ad centrum
                <lb/>
              mundi moueatur, pondus non affert. </s>
              <s id="id000610">Neque
                <lb/>
              ratione magnitudinis contactus, cum ſit in
                <lb/>
              puncto ſolo, igitur remanet ſolum aëris </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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