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="id003699">
                <pb pagenum="219" xlink:href="015/01/238.jpg"/>
              lum contranitatur. </s>
              <s id="id003700">Secundò, quia pondus in plano non inchoat
                <lb/>
              motum ſed pendens inchoat, ideo quòd eſt in plano habet pror­
                <lb/>
              ſus occultum, quod pendet non: & ſi ſit lignum eiuſdem molis &
                <lb/>
              duritiei cui appenſum ſit f & cui inſideat, magis atteretur id cui ap­
                <lb/>
                <figure id="id.015.01.238.1.jpg" xlink:href="015/01/238/1.jpg" number="232"/>
                <lb/>
              penditur, & prius<08> cui inſidet. </s>
              <s id="id003701">Cæterúm quod
                <lb/>
              ad grauitatem attinet æqualia ſunt, nam aër in
                <lb/>
              utroque pellit deorſum, ac magis quod quieſcit
                <lb/>
              in plano: ſolum enim planum reſiſtit, in pendu­
                <lb/>
              lo onere etiam aer ſuppoſitus, quo fit ut quod
                <lb/>
              pendet, minus graue ſit. </s>
              <s id="id003702">Sed æqualia uidentur.</s>
            </p>
            <p type="margin">
              <s id="id003703">
                <margin.target id="marg693"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              26.
                <lb/>
                <emph type="italics"/>
              &
                <emph.end type="italics"/>
              38.</s>
            </p>
            <p type="margin">
              <s id="id003704">
                <margin.target id="marg694"/>
              Q
                <emph type="italics"/>
              uæſt.
                <emph.end type="italics"/>
              19.
                <lb/>
              M
                <emph type="italics"/>
              echan.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id003705">Propoſitio centeſima nonageſima quarta.</s>
            </p>
            <p type="main">
              <s id="id003706">Proportionem ponderis longioris in medio ſuſpenſi ad breuius.
                <lb/>
              </s>
              <s id="id003707">illi æquale & in medio ſuſpenſum, declarare.
                <lb/>
                <arrow.to.target n="marg695"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003708">
                <margin.target id="marg695"/>
              Q
                <emph type="italics"/>
              uæſt.
                <emph.end type="italics"/>
              27.</s>
            </p>
            <p type="main">
              <s id="id003709">Hanc generaliter propoſuit Ariſtoteles in Mechanicis,
                <expan abbr="oſtendit̃">oſtenditur</expan>
                <lb/>
                <expan abbr="em̃">emm</expan>
              quod ſi a b in e, & d e in f æqualia
                <lb/>
              pondera in medio
                <expan abbr="ſuſpendãtur">ſuſpendantur</expan>
              , quod
                <lb/>
                <figure id="id.015.01.238.2.jpg" xlink:href="015/01/238/2.jpg" number="233"/>
                <lb/>
              grauius erit a b quam d e. </s>
              <s id="id003710">Et hoc eſt
                <lb/>
              certum quia a & b extrema plus di­
                <lb/>
              ſtant ab hypomochlio. </s>
              <s id="id003711">Sit igitur g h reſecta æqualis hic cinde d e,
                <lb/>
              pondus eſt æquale a b, erit g h minus pondere d e in k, igitur per
                <lb/>
              communem animi ſententiam k eſt æquale uerò ponderi a g & h b,
                <lb/>
              igitur cum a g & h b plus ponderent in ſitu ſuo quam in ſitu d e,
                <lb/>
              patet propoſitum quoad Ariſtotelem attinet, ſcilicet quod a b eſt
                <lb/>
              grauior d e.</s>
            </p>
            <p type="main">
              <s id="id003712">Vt modò oſtendam proportionem, erit proportio h b ad g h ut
                <lb/>
              ponderis h b ad totum
                <expan abbr="põdus">pondus</expan>
              g b, eadem ratione a g ad g h ut pon­</s>
            </p>
            <p type="main">
              <s id="id003713">
                <arrow.to.target n="marg696"/>
                <lb/>
              deris a g ad totum a h, a h autem eſt æqualis g b & a g æqualis h b
                <lb/>
              ex communi animi
                <expan abbr="ſentẽtia">ſententia</expan>
              , & pondus a h ęquale ponderi b g, quia
                <lb/>
              ſunt æquales & in eodem ſitu: igitur a g, h b ad g h, ut ponderum
                <lb/>
              a g h b ad pondus g b. </s>
              <s id="id003714">Et ita patet quod quanto longior eſt a b in
                <lb/>
              comparatione ad d e, tanto a g & h b in comparatione ad g h, igitur
                <lb/>
              tanto maior proportio ponderum a g h b ad pondus a h. </s>
              <s id="id003715">rurſus eſt
                <lb/>
              tanto maius quanto a b eſt longior per
                <expan abbr="demõſtrata">demonſtrata</expan>
              in prima parte,
                <lb/>
              igitur multo maius eſt pondus a g h b, quanto longior a b in com­
                <lb/>
              paratione ad d e.</s>
            </p>
            <p type="margin">
              <s id="id003716">
                <margin.target id="marg696"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              92.
                <emph type="italics"/>
              hu­
                <lb/>
              ius.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id003717">
                <expan abbr="Exemplũ">Exemplum</expan>
              ſit ponderis a b 12 ponderis
                <expan abbr="lõgitudinis">longitudinis</expan>
                <expan abbr="pedũ">pedum</expan>
              quatuor,
                <lb/>
              d e pondus 12 longitudinis
                <expan abbr="duorũ">duorum</expan>
              pedum,
                <expan abbr="eruntigit̃">erunt igitur</expan>
              a g, g e, c h, h b
                <lb/>
              unius pedis ſingulę. </s>
              <s id="id003718">Et quia a g & b h ſunt
                <expan abbr="dimidiũ">dimidium</expan>
              g h erunt ambæ
                <lb/>
              pariter æquales g h & ideo pondus a g h b æqualia g b ponderi,
                <lb/>
              ſed pondus g b eſt librarum nouem, quia g b eſt dodratus a b, igi­
                <lb/>
              tur tota a b eſt ponderis quindecim, nam g h eſt ponderis ſex, eſt er­
                <lb/>
              go pondus a b quadrante maius d e.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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