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>
            <pb pagenum="241" xlink:href="015/01/260.jpg"/>
            <p type="margin">
              <s id="id004114">
                <margin.target id="marg810"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id004115">
                <margin.target id="marg811"/>
              L
                <emph type="italics"/>
              emmate
                <emph.end type="italics"/>
              2.</s>
            </p>
            <p type="margin">
              <s id="id004116">
                <margin.target id="marg812"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              30.
                <emph type="italics"/>
              hu
                <lb/>
              ius.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id004117">Ex his omnibus concluditur propoſitum in prima figura, & eſt
                <lb/>
                <arrow.to.target n="marg813"/>
                <lb/>
              quod ſi b c inclinetur uerſus e, mouebitur a d, certo impetu uerſus
                <lb/>
              e. </s>
              <s id="id004118">Et quia ſi prius b c inclinatum fuerit in f, redit a d, dum b c reuer­
                <lb/>
              titur ad proprium ſitum ultra lineam a d g uſque ad h per primum
                <lb/>
              lemma. </s>
              <s id="id004119">Et cum b c inclinatur ad b f peruenit, quantum b c inclina­
                <lb/>
              ta ad f, ſcilicet ad e, igitur ex motibus b c in f & in e tanto plus mo­
                <lb/>
              uetur d ultra e, quantum eſt productum d e in d h, ‘ideo multo plus
                <lb/>
              quam ſi ſolum motum fuiſſet d ex recta a g, etiam quod non moue­
                <lb/>
              retur b c. </s>
              <s id="id004120">Multo plus ergo moto etiam b c, ut diximus.</s>
            </p>
            <p type="margin">
              <s id="id004121">
                <margin.target id="marg813"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id004122">Propoſitio ducenteſima nona.</s>
            </p>
            <p type="main">
              <s id="id004123">Si ſuperficies rectangula in duas partes æquales diuiſa intelli­
                <lb/>
              gatur, quæ ambę quadratæ ſint, itemque in duas inæquales, erit pa­
                <lb/>
              rallelipedum ex latere mediæ partis in totum ſuperficiem maius ag
                <lb/>
                <figure id="id.015.01.260.1.jpg" xlink:href="015/01/260/1.jpg" number="261"/>
                <lb/>
              gregato parallelipedorum ex par­
                <lb/>
              tibus inæqualibus, in latera alte­
                <lb/>
              rius partis mutuo in eo, quod fit
                <lb/>
              ex differentia lateris minoris par­
                <lb/>
              tis a mediæ latere in differentiam
                <lb/>
              maioris partis ſuperficiei à media
                <lb/>
              ſuperficie bis, & ex differentia am­
                <lb/>
              borum laterum inæqualium iun­
                <lb/>
              ctorum ad ambo latera æqualia
                <lb/>
              iuncta in minorem partem ſuperficiei.</s>
            </p>
            <p type="main">
              <s id="id004124">Proponatur a g diuiſa in duo quadrata æqualia a h, h b, & late­
                <lb/>
                <arrow.to.target n="marg814"/>
                <lb/>
              ra erunt a c, c b, & in duo inæqualia a d d g, quarum latera ſint b c,
                <lb/>
              a f, dico quod parallelipeda a c in c g, & c b in c k, & ſunt æqualia pa
                <lb/>
              rallelipedo ex a c in a g, excedunt
                <lb/>
                <figure id="id.015.01.260.2.jpg" xlink:href="015/01/260/2.jpg" number="262"/>
                <arrow.to.target n="table30"/>
                <lb/>
              parallelipeda ex a f in d g, & b c
                <lb/>
              in d k, in duplo f c in d h, cum eo
                <lb/>
              quod fit ex f e in d k ſemel. </s>
              <s id="id004125">Quia
                <lb/>
              ergo parallelipedum ex a e in a g
                <lb/>
              eſt æquale parallelipedis a f & f c
                <lb/>
              in a h, h d, h k, quare parallelipe­
                <lb/>
              dis a f in a h, h d, d k, & f c in d k, &
                <lb/>
              c e in d k, & f e in d k, & f e in d h
                <lb/>
              bis. </s>
              <s id="id004126">Ad parallelipedum a fin d g,
                <lb/>
              eſt æquale parallelipedis a fin a h, h d. </s>
              <s id="id004127">Et parallelipedum b e in d k,
                <lb/>
              parallelipedis a f, f e, c e in d k. </s>
              <s id="id004128">Detractis ſimilibus relinquetur f c in
                <lb/>
              d l, l e, e h bis, quod eſt f c in d h bis, cum eo quod fit ex e f in d k ſi­
                <lb/>
              mul, quod eſt propoſitum.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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