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>
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        <body>
          <chap>
            <p type="main">
              <s id="id003266">
                <pb pagenum="189" xlink:href="015/01/208.jpg"/>
              eſt, ſi uolo duos terminos ſemel, & dein de in minorem, & <02>
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              cubica producti eſt ſecundus terminus, idem facio de minore in
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              ſe in de in maiorem, & accipio <02> cu. </s>
              <s id="id003267">Exemplum, uolo duos termi­
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              nos inter 2 & 3, duco 3 in ſe fit 9, duco 2 in 9 fit 18, capio <02> cu. </s>
              <s id="id003268">18. hic
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              eſt unus terminus, & ita duco 2 in ſe fit 4, duco in 3 fit 12, capio <02> cu.
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              </s>
              <s id="id003269">12 pro ſecundo termino. </s>
              <s id="id003270">Et ſi uolo tres terminos, duco 3 in 3 fit 9, du
                <lb/>
              co 3 in 9 fit 27, duco 2 in 27 fit 54, & <02> <02> 54 eſt primus terminus.
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              </s>
              <s id="id003271">Item duco 2 in 2 fit 4, duco 3 in 3 fit 9, duco 4 in 9 fit 36, & <02> <02> 36, id
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              eſt, <02> 36 eſt ſecundus terminus, ſimiliter duco 2 ad ſuum cubum fit
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              8, duco 3 in 8 fit 24, & <02> <02> 24, eſt tertius terminus. </s>
              <s id="id003272">Similiter uolo
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              quatuor terminos medios, duco 3 in 3 fit 9, duco 9 in 9 fit 81, duco 2
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              in 81 fit 162, & <02> relata prima 162, eſt primus terminus, item duco 2
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              in 2 fit 4, & 4 in 4 fit 16, & 3 in 16 fit 48, & <02> relata prima 48 erit
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              quartus terminus, item ducendo 3 ad cubum fit 27, & 2 ad quadra­
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              tum, & fit 4, & 4 in 27 fit 108, & <02> relata prima 108, erit ſecundus
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              terminus, & ſimiliter ducendo 2 ad cubum fit 8, & 3 ad quadratum
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              fit 9, & 9 in 8 fit 72, & <02> relata prima 72 eſt tertius terminus. </s>
              <s id="id003273">Habe­
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              bis ergo terminos in continua proportione 2, id eſt, <02> relata pri­
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              ma 32, <02> relata prima 48, <02> relata prima 72, <02> relata prima 108, <02>
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              relata prima 172, & <02> relata prima 243, quod eſt 3, & ita de alijs in
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              infinitum.</s>
            </p>
            <p type="main">
              <s id="id003274">At pro muſica, ſi ſint exhibiti duo numeri minores utpotè 2 & 3,
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              uelim tertium terminum, diuido 2 per 1 differentiam exit 2, detraho
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              1 pro regula remanet 1, diuido 3 maiorem terminum per 1 exit 3, ad­
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              de 3 ad 3, fit 6 maior terminus. </s>
              <s id="id003275">Similiter capio 3 & 4, diuide 3 mino­
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              rem terminum per 1 differentiam exit 3, detrahe 1 pro regula, relin­
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              quitur 2, diuide 4 terminum medium per 2 exit 2, adde ad 4 fit 6 ma
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              ior terminus. </s>
              <s id="id003276">Stiphelius autem erat in ſua regula, nam ſic 12 4 & 3
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              eſſent in continua proportione muſica ex ſua regula. </s>
              <s id="id003277">Dico ergo,
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              quod ſi proponantur 5 & 7, & uelim muſicam proportionem con­
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              tinuare, detraho 5 de 7 relinquitur 2, diuido 5 per 2 exit 2 1/2, detra­
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              he 1 pro regula remanet 1 1/2, diuide 7 per 1 1/2 exit 4 & 2/3, adde ad 7
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              fit 11 2/3, reduc ad integra multiplicando omnia per 3, habebis
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              35, 21, & 15, in continua proportione muſica, nam 35 ad 15 eſt ut 7
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              ad 3, & 14 ad 6, eſt ut 7 ad 3, eſt autem 14 differentia 21 & 35, & 6 dif­
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              ferentia 21 & 15, & ita poſſes continuare inueniendo quartum,
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              quintum, ſextum, in infinitum. </s>
              <s id="id003278">Rurſus ſint propoſiti duo termini
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              maiores, uelut 6 & 4, detrahe 4 à 6 exit 2, diuide 6 per 2 exit 3, ad­
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              de 1 pro regula fit 4, diuide 4 minorem terminum per 4 exit 1, de­
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              trahe 1 ex 4, relinquitur 3 minor terminus, & ita propoſitis 6 & 3 </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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