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="id000743">
                <pb pagenum="39" xlink:href="015/01/058.jpg"/>
              circuitus c, & relinquentur 3 3/4 ſequetur igitur, ut ſit proportio 17 ad
                <lb/>
              13, & 2 1/2 ad 1/2 & 3 1/3 ad 3 eadem, & ita 17/13, 5/2 & 10/9 eadem ſi iam ſupponi
                <lb/>
              mus 17 & 10 eſſe primos inuicem, ut in ſecunda demonſtratione./>
                <lb/>
              </s>
              <s id="id000744">Igitur ſequuntur eadem corrolaria, quæ dicta ſunt.</s>
            </p>
            <p type="main">
              <s id="id000745">Propoſitio quadrageſima nona.</s>
            </p>
            <p type="main">
              <s id="id000746">Propoſito mobilis in circulo circuitus tempore, dataque ratione
                <lb/>
              diſtantiæ ab illo mobilis circuitum inuenire, quod ex eodem pun­
                <lb/>
              cto diſcedens cum alio mobili in dato puncto conueniat ſub quo­
                <lb/>
              cunque numero circuituum tempus quoque coniunctionis.</s>
            </p>
            <p type="main">
              <s id="id000747">
                <arrow.to.target n="marg128"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000748">
                <margin.target id="marg128"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <figure id="id.015.01.058.1.jpg" xlink:href="015/01/058/1.jpg" number="54"/>
            <p type="main">
              <s id="id000749">Sit in circuli peripheria a
                <expan abbr="pũctus">punctus</expan>
              , qui cir
                <lb/>
              cuat æquali motu (hoc enim ſemper intel­
                <lb/>
              ligitur) in b tempore: & ſit datus punctus c
                <lb/>
              in quo diſcedens e mobile ex coniunctio­
                <lb/>
              ne cum a poſt certos circuitus proprios,
                <lb/>
              aut etiam. </s>
              <s id="id000750">ſine ulla circuitione perfecta de­
                <lb/>
              beat conuenire. </s>
              <s id="id000751">Volo ſcire tempus circui­
                <lb/>
              tionis e: & etiam tempus coniunctionis.
                <lb/>
              </s>
              <s id="id000752">Sit ergo primum ut abſque circuitione ulla e, a debeat comprehen­
                <lb/>
              dere e in c poſt numerum circuitionum ipſius a, qui ſit f. </s>
              <s id="id000753">nam ſi a o c
                <lb/>
              currit e in prima circuitione ipſius e, igitur a mouetur uelocius
                <lb/>
              quàm e, cum ergo debeat attingere ipſum e, neceſſe eſt ut a pertran­
                <lb/>
              ſeat prius per punctum ex quo diſceſsit antequam redeat ad con­
                <lb/>
              iunctionem e: ergo perficiet ſaltem unam circuitionem. </s>
              <s id="id000754">Ducemus
                <lb/>
              ergo f in b, & fiet g tempus circuitus aut circuituum a, & quia ſpa­
                <lb/>
              tium a c datum eſt, ſit b temporis circuitus a ad h, uelut circuli to­
                <lb/>
                <arrow.to.target n="marg129"/>
                <lb/>
              tius ad a c, & iungatur g cum h & fiat k. </s>
              <s id="id000755">Fiat quoque, ut monadis
                <lb/>
              ad h, ita l ad monadem, & ducatur l in k, & fiat m: dico m eſſe tem­
                <lb/>
              pus circuitus e. </s>
              <s id="id000756">Conſtat enim ex ſuppoſito, quod k eſt tempus to­
                <lb/>
              tum in quo a peruenit poſt b circuitiones in c, ſi ergo e moueretur
                <lb/>
              per m tempus totum ex ſuppoſito perficeret circuitum, at quia cir­
                <lb/>
              cuitus ad a c, ut monadis ad h, igitur etiam ut l ad monadem, ergo
                <lb/>
              proportio circuitus ad a c, ut m ad monadem: ergo ſi in m tranſit to
                <lb/>
              tum circuitum in monade tranſit a c: ſed monas ducta in k facit k,
                <lb/>
              igitur e in tempore k perueniet in c, quod erat demonſtrandum.
                <lb/>
              </s>
              <s id="id000757">Proponatur modo tempus reuolutionum e ipſum d: eodem mo­
                <lb/>
                <arrow.to.target n="marg130"/>
                <lb/>
              do agemus ducendo fin b fit g, addatur h & fiat k, diuidatur k per
                <lb/>
              aggregatum d & a e, & exeat m, (idem enim eſt diuidere per aggre­
                <lb/>
              gatum d & h, & multiplicare per l) dico ergo ut in demonſtratione
                <lb/>
              priore, quod m eſt tempus circuitus e. </s>
              <s id="id000758">Nam cum k ſit tempus, in
                <lb/>
              quo a poſt circuitus f peruenit ad c, ergo diuiſo ipſo toto tempore </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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