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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      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id000713">
                <pb pagenum="37" xlink:href="015/01/056.jpg"/>
              guem. </s>
              <s id="id000714">Hoch declarato ponatur m spatium compositum ex circulis
                <lb/>
              pertranſitis a b a cum ſpatio b d, etenim ſpatium, quod pertranſit
                <lb/>
              b a coniunctione in a, ad coniunctionem primam in d, & erit ex de­
                <lb/>
              monſtratis horum differentia circulus qui uocetur o, & ſit p ſpa­
                <lb/>
              tium, quod pertranſit b in tempore eodem, in quo a pertranſit o, &
                <lb/>
              ſit q differentia o, & p quę in circulo eſt c d l b, quia igitur in eodem
                <lb/>
              tempore a pertranſit m & b, n, erit m ad n, ut a ad b, & eadem ratio­
                <lb/>
              ne a ad b, ut o ad p, igitur ex undecima quinti Euclidis m ad n, ut o
                <lb/>
              ad p, quare cum o ſit differentia m & n, & q, differentia o & p erit ex
                <lb/>
              decimanona quinti Euclidis, m ad o, ut o ad q, & ita circulus eſt ana
                <lb/>
              logus inter ſpatium pertranſitum à motore uelociori, & inter diffe­
                <lb/>
              rentiam ſpatij quæ accidit, dum uelocior motor pertranſit circu­
                <lb/>
              lum, id eſt quòd circulus a c d eſt analogus inter c d l b, & circulos
                <lb/>
              pertranſitos a b a cum portione b d. </s>
              <s id="id000715">Reuertor igitur ad propoſi­
                <lb/>
              tum, cum ſit m ad o, ut o ad q, & m ad o, ut n ad p, ex ſexta decima
                <lb/>
              quinti Euclidis, erit ex undecima eiuſdem n ad p, ut o ad q, quare ex
                <lb/>
              ſexta decima ſexti Elementorum ducto o, id eſt circulo, ſeu maiore
                <lb/>
              numero in p ſpatium pertranſitum a b, ſeu ducto fin g, & diuiſo per
                <lb/>
              q differentiam ſpatiorum, ſeu per h exibit n, ſeu ſpatium quod
                <lb/>
              pertranſit b ab una coniunctione ad aliam quod erat demon­
                <lb/>
              ſtrandum.</s>
            </p>
            <p type="main">
              <s id="id000716">
                <arrow.to.target n="marg123"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000717">
                <margin.target id="marg123"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000718">Ex hoc patet, quod proportio temporis coniunctionis ad tem­
                <lb/>
              pus tardioris motus circuitionis eſt ueluti temporis circuitus uelo
                <lb/>
              cioris motoris ad differentiam temporis motus tardioris, & uelo­
                <lb/>
              cioris motoris in uno circuitu.</s>
            </p>
            <p type="main">
              <s id="id000719">Propoſitio quadrageſima octaua.</s>
            </p>
            <p type="main">
              <s id="id000720">Si tria mobilia ex eodem puncto diſcedant, fuerintque duorum, ac
                <lb/>
              duorum coniunctiones in temporibus commenſis illa tria mobi­
                <lb/>
              lia denuò coniungentur in tempore producto ex denominatore di
                <lb/>
              uiſionis temporis maioris per minus in minus, aut numeratore
                <lb/>
              in maius.</s>
            </p>
            <p type="main">
              <s id="id000721">
                <arrow.to.target n="marg124"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000722">
                <margin.target id="marg124"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000723">Sint tria mobilia a, quod circuat in duobus annis b in quinque,
                <lb/>
              c in ſeptem. </s>
              <s id="id000724">Dico quod primum redibunt in numero producto ex
                <lb/>
              ſeptem quinque & duobus, qui ſunt numeri primi, & erit ille nume­
                <lb/>
              rus ſeptuaginta annorum. </s>
              <s id="id000725">Nam in ſeptuaginta annis a perficiet tri­
                <lb/>
              ginta quinque reuolutiones b quatuordecim, c decem: ergo
                <expan abbr="redibũt">redibunt</expan>
                <lb/>
              per perfectos circuitus ad idem punctum. </s>
              <s id="id000726">Oſtendo modo quod
                <lb/>
              non ante: nam ſi ſic: ſit, ut in triginta quinque annis igitur b & c per­
                <lb/>
              ficient perfectos circuitus, ergo
                <expan abbr="redibũt">redibunt</expan>
              ad idem punctum, a autem
                <lb/>
              non redibit, quoniam eius circuitus non numerat trigintaquinque
                <lb/>
              aliter non fuiſſet ſeptuaginta minimus numeratus ab a b c, cum </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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