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="187 [=193]" xlink:href="015/01/212.jpg"/>
            <p type="margin">
              <s id="id003318">
                <margin.target id="marg612"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              20.
                <emph type="italics"/>
              ter
                <lb/>
              tij
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id003319">Ex hoc patet quòd quando b
                <lb/>
                <figure id="id.015.01.212.1.jpg" xlink:href="015/01/212/1.jpg" number="206"/>
                <lb/>
                <arrow.to.target n="marg613"/>
                <lb/>
              erit in c peracta quarta circuli, ut in
                <lb/>
              ſecunda figura erit per motum l e
                <lb/>
              in a: nam cum d a ſit dupla c b, igi­
                <lb/>
              tur in eodem tempore l perueniet
                <lb/>
              ad a, in quo b perueniet ad c.</s>
            </p>
            <p type="margin">
              <s id="id003320">
                <margin.target id="marg613"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              _{m}. 1.</s>
            </p>
            <p type="main">
              <s id="id003321">Dico etiam, quod
                <expan abbr="quãdo">quando</expan>
              b per­
                <lb/>
                <arrow.to.target n="marg614"/>
                <lb/>
              ueniet ad fin prima figura, d perue­
                <lb/>
              niet ad g, quia permeabit totum cir
                <lb/>
              culum, & a b d ſunt in una recta li­
                <lb/>
              nea. </s>
              <s id="id003322">Et cum b perueniet ad m in ſe­
                <lb/>
              cunda figura, d rurſus perueniet ad a centrum.</s>
            </p>
            <p type="margin">
              <s id="id003323">
                <margin.target id="marg614"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              _{m}. 2.</s>
            </p>
            <p type="main">
              <s id="id003324">Ex hoc patet, quòd punctum d permeabit lineam rectam æqua­
                <lb/>
                <arrow.to.target n="marg615"/>
                <lb/>
              lem duplo diametri unius circuli, id eſt, quantum eſt linea a g in pri
                <lb/>
              ma figura.</s>
            </p>
            <p type="margin">
              <s id="id003325">
                <margin.target id="marg615"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 3.</s>
            </p>
            <p type="main">
              <s id="id003326">Sequitur etiam, quòd d punctum meabit et remeabit per rectam
                <lb/>
                <arrow.to.target n="marg616"/>
                <lb/>
              lineam ag, peragendo bis eam in uno circuitu circuli b c, ſeu duo­
                <lb/>
              bus circuitibus d e.</s>
            </p>
            <p type="margin">
              <s id="id003327">
                <margin.target id="marg616"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 4.</s>
            </p>
            <p type="main">
              <s id="id003328">Oſten damus modo, quod pun
                <lb/>
                <figure id="id.015.01.212.2.jpg" xlink:href="015/01/212/2.jpg" number="207"/>
                <lb/>
              ctum d extra lineam centrorum, ſci
                <lb/>
              licet in linea d c a f tranſibit per
                <expan abbr="re­ctã">re­
                  <lb/>
                ctam</expan>
              eandem, ut in tertia figura pro­
                <lb/>
              ducatur c d uſque ad k, ita ut c k ſit
                <lb/>
              æqualis c a, erit ergo punctus d pri
                <lb/>
              mæ figuræ m è regione k tertiæ, &
                <lb/>
              dum c mouetur ad e, d perueniat
                <lb/>
              ad g, erit ergo e g æqualis ea, & ſe­
                <lb/>
              cet circulus g h rectam a d in h, &
                <lb/>
              ducatur c h. </s>
              <s id="id003329">Et erit ut prius angu­
                <lb/>
              lus h e g duplus h a g, ergo arcus
                <lb/>
              g h duplus e c, ergo g remeauit in
                <lb/>
              h in tempore quo c feretur in e,
                <lb/>
              quare d deſcendit per rectam in h.</s>
            </p>
            <p type="main">
              <s id="id003330">Dico rurſus, quòd quanto ma­
                <lb/>
              gis d erit propinquum lineæ d g,
                <lb/>
              tanto minus deſcendet in recta,
                <lb/>
              quanto magis propinquum longi
                <lb/>
              tudinibus medijs,
                <expan abbr="tãto">tanto</expan>
              celerius mo
                <lb/>
              uebitur, adeò ut in ſecunda figura
                <lb/>
              apparet motum ex d in g, non deſcendit niſi per d n, & motum ex g
                <lb/>
              in l deſcendit ex n in a centrum fixum. </s>
              <s id="id003331">Deſcendat ergo ex e in h & h </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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