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="id000565">
                <pb pagenum="40 [=30]" xlink:href="015/01/049.jpg"/>
              tur aſcendere, maximum eſſe uidetur, adeò ut ægrè à pluribus fera­
                <lb/>
              tur, à quibuſdam non omnino feratur.</s>
            </p>
            <p type="head">
              <s id="id000566">SCHOLIVM.</s>
            </p>
            <p type="main">
              <s id="id000567">Ob hoc natura fecit, ut non quemadmodum in fidibus uoces ex
                <lb/>
              breuitate intenderentur, ſed ex conſtrictione ligulæ, ut dicunt, ſu­
                <lb/>
              per aſperam arteriam uox ad diapaſon acueretur addito impetu
                <lb/>
              proportione, ut ex conſtrictione, & impetu
                <expan abbr="cõſurgeret">conſurgeret</expan>
              dupla pro­
                <lb/>
              portio. </s>
              <s id="id000568">Hoc autem manifeſtè experimur in elymis in quibus nullæ
                <lb/>
              prorſus facta mutatione inſtrumenti conſtantibus digitis omni­
                <lb/>
              bus præter pollicem ſiniſtræ uocem exacuimus ad diapaſon, inde
                <lb/>
              etiam ad bis diapaſon: ſicut declarauimus in commentarijs Epi­
                <lb/>
              demiorum.</s>
            </p>
            <p type="main">
              <s id="id000569">Propoſitio trigeſima ſexta.</s>
            </p>
            <p type="main">
              <s id="id000570">Si proportio per proportionem minorem æquali ducatur, pro­
                <lb/>
              portio minor producetur. </s>
              <s id="id000571">Vnde manifeſtum eſt duas proportio­
                <lb/>
              nes minores æqualitate inuicem ductas proportionem minorem
                <lb/>
              unaquaque illarum producere.</s>
            </p>
            <p type="main">
              <s id="id000572">
                <arrow.to.target n="marg92"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000573">
                <margin.target id="marg92"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <figure id="id.015.01.049.1.jpg" xlink:href="015/01/049/1.jpg" number="44"/>
            <p type="main">
              <s id="id000574">Proportio a b ad c, qualiſcunque ſit, duca­
                <lb/>
              tur in proportionem minorem æqualitate
                <lb/>
              f ad g, dico quod producta proportio erit
                <lb/>
              minor ea, quæ eſt a b ad c fiat d ad a b, ut f
                <lb/>
              ad g, et erit per ſecundam huius d ad c pro­
                <lb/>
              ducta ex proportionibus a b ad c, & f g. </s>
              <s id="id000575">Itemque per decimam quar­
                <lb/>
                <arrow.to.target n="marg93"/>
                <lb/>
              tam quinti
                <expan abbr="Elementorũ">Elementorum</expan>
              erit d minor a b, igitur maior a b ad c, quàm
                <lb/>
              d ad c. igitur quàm proportio a b ad c in proportionem f ad g. </s>
              <s id="id000576">Sit
                <lb/>
              autem utraque minor æqualitate ea, quæ a b ad c, & ea quæ f ad g, di­
                <lb/>
              co productam unaquaque earum eſſe minorem. </s>
              <s id="id000577">Quod enim (manen
                <lb/>
              tibus his, quæ dicta ſunt) minor ſit d ad c, quam a b ad c ex prima
                <lb/>
              parte oſtenſum eſt. </s>
              <s id="id000578">Quòd uerò etiam minor ſit d ad c, quàm d ad
                <lb/>
              a b, & ex conſequenti quàm f ad g demonſtratur ſic. </s>
              <s id="id000579">Quia enim mi­
                <lb/>
              nor eſt a b ad c, æqualitate erit a b minor c, fiat ergo h æqualis a b,
                <lb/>
              erit ergo d ad h, ut d ad a b per ſeptimam quinti Elementorum, at d
                <lb/>
              ad c minor quàm d ad h per octauam eiuſdem, igitur minor d ad c,
                <lb/>
              quàm d ad a b, igitur patet propoſitum.</s>
            </p>
            <p type="margin">
              <s id="id000580">
                <margin.target id="marg93"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              10. P
                <emph type="italics"/>
              et.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000581">Propoſitio trigeſima ſeptima.</s>
            </p>
            <p type="main">
              <s id="id000582">Si plures homines, quorum nulli per ſe nauim mouere poſsint,
                <lb/>
              aut pondus ferre ſimul iuncti eam moueant, aut pondus ferant,
                <lb/>
              erunt illæ proportiones coniunctæ non productæ.
                <lb/>
                <arrow.to.target n="marg94"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000583">
                <margin.target id="marg94"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000584">Cùm enim primus non poſsit mouere nec ſecundus, erunt pro­
                <lb/>
              portiones minores æqualitate, Ideò per ſecundam partem præce­
                <lb/>
              dentis multo minus mouerent duo, quàm unus. </s>
              <s id="id000585">Et ſi quatuor </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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