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="id000776">
                <pb pagenum="41" xlink:href="015/01/060.jpg"/>
              ſa a c, quia multiplex ei. </s>
              <s id="id000777">igitur cum circulus, & a k diuidantur in cir­
                <lb/>
                <arrow.to.target n="marg133"/>
                <lb/>
              culum et a k, & circulus ſit incommenſus circulo, cum a k erit aggre
                <lb/>
              </s>
              <s id="id000778">gatum ex circulo, & a k incommenſum ipſi a k, & a k pariter incom
                <lb/>
                <arrow.to.target n="marg134"/>
                <lb/>
              menſa circulo. </s>
              <s id="id000779">Rurſus quia a k eſt incommenſa circulo cum a k, &
                <lb/>
              circulus cum a k ſit multiplex ad a c, erit a k incommenſa a c, quare
                <lb/>
                <arrow.to.target n="marg135"/>
                <lb/>
              erit c k incommenſa a k & a c, & circulo ad dita a k. </s>
              <s id="id000780">Si ergo a c ſit
                <lb/>
              commenſa circulo, erunt omnes portiones e genere numeri, & ſi
                <lb/>
                <arrow.to.target n="marg136"/>
                <lb/>
              potentia rhete erunt omnes, uel potentia rhete, uel circulis detra­
                <lb/>
              ctis, ut a k & a l reciſa: & a c ſit potentia ſecunda rhete, id eſt radix cu
                <lb/>
              bica erunt omnes c d, d e, e f, potentia ſecunda rhete, et radices cubi­
                <lb/>
              cæ numeri, ſeu latera corporum rhete, a k uero & a l, & huiuſmodi
                <lb/>
              in infinitum reciſa potentia rhete.
                <lb/>
                <arrow.to.target n="marg137"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000781">
                <margin.target id="marg132"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.
                <lb/>
                <emph type="italics"/>
              præcedentis.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000782">
                <margin.target id="marg133"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              14.
                <emph type="italics"/>
              deci
                <lb/>
              mi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lement.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000783">
                <margin.target id="marg134"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              17.
                <lb/>
                <emph type="italics"/>
              eiuſdem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000784">
                <margin.target id="marg135"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              14.
                <lb/>
                <emph type="italics"/>
              rurſus.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000785">
                <margin.target id="marg136"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              17.
                <lb/>
                <emph type="italics"/>
              rurſus.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000786">
                <margin.target id="marg137"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000787">Ex hoc patet, quod cum circulus poſsit diuidi in infinita gene­</s>
            </p>
            <p type="main">
              <s id="id000788">
                <arrow.to.target n="marg138"/>
                <lb/>
              ra quantitatum, quæ non ſunt inuicem commenſæ cumque coniun­
                <lb/>
              ctiones hæ ſemper in eodem genere maneant, quod infinita pun­
                <lb/>
              cta, & infinitis in ſpeciebus quantitatum remanebunt in quibus a
                <lb/>
              & b in perpetuum nunquam conuenient. </s>
              <s id="id000789">Velut ſi coniunctio pri­
                <lb/>
              ma fiat in <02> cu. </s>
              <s id="id000790">1/2 alicuius circuli, nunquam conuenient, neque in me­
                <lb/>
              dietate, neque in quarta parte, nec octaua, nec tertia, nec ſexta, nec no­
                <lb/>
              na, nec quinta, nec decima, & ſic de ſingulis in genere commenſa­
                <lb/>
              rum toti circulo. </s>
              <s id="id000791">Neque in <02> quadrata 1/2 uel 1/3 uel 1/5 neque <02> 1/6 uel 1/20,
                <lb/>
              neque in <02> 3 m: 1, nec 2 m: <02> 3 nec in <02> <02> 2 aut 3 aut 7 nec in <02> rela­
                <lb/>
              ta alicuius numeri, nec in 2 m: <02> <02> cub. </s>
              <s id="id000792">3 nec 2 m: <02> cub. </s>
              <s id="id000793">4, & ſic
                <lb/>
              de alijs.</s>
            </p>
            <p type="margin">
              <s id="id000794">
                <margin.target id="marg138"/>
              P
                <emph type="italics"/>
              er penulti­
                <lb/>
              mam uigeſi­
                <lb/>
              mi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lement.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000795">Propoſitio quinquageſima prima.</s>
            </p>
            <p type="main">
              <s id="id000796">Operationes dictas exemplo declarare.
                <lb/>
                <arrow.to.target n="marg139"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000797">
                <margin.target id="marg139"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000798">Supponamus in circulo prædicto a c <02> 7 conſtat, quod eſſe non
                <lb/>
              poteſt, quia <02> 7 eſt maior monade, ideo toto circulo, quare non po
                <lb/>
              terit eſſe pars circuli, ſed referetur ad
                <expan abbr="quantitatẽ">quantitatem</expan>
              certam, uelut quod
                <lb/>
              circulus ſit 10. ſemper ergo diuidemus <02> 7, ſeu eam portionem per
                <lb/>
              10 quantitatem circuli & exibit <02> 7/100, & hæc erit portio circuli, & ita
                <lb/>
              ſi portio ſit <02> cub. </s>
              <s id="id000799">16, diuidemus <02> cub. </s>
              <s id="id000800">16 per 10 exibit <02> cu 2/125, &
                <lb/>
              ita de alijs.</s>
            </p>
            <p type="main">
              <s id="id000801">Sed cum ex repetitione creſcat portio illa, donec exuperet mo­
                <lb/>
              nadem, aut aliquem quemuis numerum detracta monade aut nu­
                <lb/>
              mero circuituum habebit rationem reciſi. </s>
              <s id="id000802">Velut <02> 7/100 quater ſum­
                <lb/>
              pta efficit <02> 112/100. Et hoc eſt potentia rhete, ſed ſi quis auferat mona­
                <lb/>
              dem fiet <02> 112/100 m: 1, & hoc eſt reciſum 1, ſcilicet 1 p: <02> v: 23/25 m: <02> 28/25, ſed ta
                <lb/>
              men uerè eſt linea media.</s>
            </p>
            <p type="main">
              <s id="id000803">Quod uerò non contingat coniungi in alio loco, neque tem­
                <lb/>
              pore ſit, ut a b iungantur in c, & ſit reuolutio a triplex integra, & b </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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