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="id000758">
                <pb pagenum="40" xlink:href="015/01/059.jpg"/>
              per numerum reuolutionum d, & partem reuolutionis exibit tem­
                <lb/>
              pus unius reuolutionis.</s>
            </p>
            <p type="margin">
              <s id="id000759">
                <margin.target id="marg129"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              10. P
                <emph type="italics"/>
              et.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000760">
                <margin.target id="marg130"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              11. P
                <emph type="italics"/>
              et.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id000761">Exemplum primi in re paulò obſcuriore: ſit f 4 & b 2 1/2 & a c 4/5, du
                <lb/>
              cemus 4 in 2 1/2 fit 10, adde 4/5 6 quod eſt 2 fit 12, diuide per 4/5 ſeu mul­
                <lb/>
              tiplica per 5/4 quod idem eſt, fit 15 circuitus e, in quatuor ergo circui­
                <lb/>
              tibus, & 4/5 qui ſunt duodecim anni perueniet a ad c, & in duodecim
                <lb/>
              annis e perueniet ad c, nam 12 ſunt 4/5 ipſius 15. Similiter in ſecundo
                <lb/>
              caſu ſit f 4 ut prius b 2 1/3 a c 1/7, ducemus 4 in 2 1/3 fit 9 1/3, addemusque h
                <lb/>
              portionem b qualis a c eſt totius circuitus, id eſt 1/7, eſt autem 1/7 2 1/3, 1/3
                <lb/>
              fient 9 1/3, ſimiliter ponatur d 5, & quia a c eſt 1/7 erunt 36/7, diuide ergo
                <lb/>
              9 2/3 id eſt 29/3 per 36/7 exeunt 203/108 tempus reuolutionis e. </s>
              <s id="id000762">Quin que ergo
                <lb/>
              reuolutiones e erunt 1015/108 addita ſeptima parte, quæ eſt 29/108 fient 2044/108
                <lb/>
              ſeu 261/27, & ſunt anni 9 18/27 ſeu 9 2/3, ergo in tanto tempore a faciet qua­
                <lb/>
              tuor circuitus, & ſeptimam partem, & e quinque circuitus, & ſe­
                <lb/>
              ptimam.
                <lb/>
                <arrow.to.target n="marg131"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000763">
                <margin.target id="marg131"/>
              C
                <emph type="italics"/>
              om./>
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000764">Ex hoc patet, quod non coniungentur in alio loco, neque alio tem
                <lb/>
              pore ante prædictum tempus.</s>
            </p>
            <p type="main">
              <s id="id000765">Propoſitio quinquageſima.</s>
            </p>
            <p type="main">
              <s id="id000766">Omnes circuituum portiones in eiuſdem temporibus
                <expan abbr="repetunt̃">repetuntur</expan>
              .</s>
            </p>
            <p type="main">
              <s id="id000767">Sint in circulo a b c d e f g: a & b iuncta, & in primo congreſſu
                <lb/>
              iungantur in c, in ſecundo in d, in tertio in e, in quarto in f, in quinto
                <lb/>
              in g, in ſexto in h, in ſeptimo in k, in octauo in l. </s>
              <s id="id000768">Et ſic deinceps
                <expan abbr="cũquetempora">cuique
                  <lb/>
                tempora</expan>
              ſint æqualia, erunt & circuitus totidem numero, & exceſ­
                <lb/>
              ſus æquales etiam a c, c d, d e, e f, f g, g h, h k,
                <lb/>
                <figure id="id.015.01.059.1.jpg" xlink:href="015/01/059/1.jpg" number="55"/>
                <lb/>
              k l. </s>
              <s id="id000769">Et ſi aggregatum a ſcilicet circulorum,
                <lb/>
              & portionis fuerit commenſum circulo, &
                <lb/>
              ita de b erunt omnia
                <expan abbr="cõmenſa">commenſa</expan>
              ad circulum, </s>
            </p>
            <p type="main">
              <s id="id000770">
                <arrow.to.target n="marg132"/>
                <lb/>
              & etiam inter ſe. </s>
              <s id="id000771">Et ſi inter ſe aggregata, uel
                <lb/>
              portiones erunt, & eodem modo reliqua.
                <lb/>
              </s>
              <s id="id000772">Et quoniam circuli circulis commenſi ſunt:
                <lb/>
              ſi portiones erunt inuicem commenſæ
                <expan abbr="erũt">erunt</expan>
              ,
                <lb/>
              & toti circuitus cum partibus commenſi, &
                <lb/>
              ſi non commenſi, neque erunt inter ſe, neque ad circulum. </s>
              <s id="id000773">Et ſi totum
                <lb/>
              ſpatium cum circuitibus erit unius generis, erunt duplicata, & tri­
                <lb/>
              plicata, & quadruplicata eiuſdem generis: quare cum ſpatia ipſa
                <lb/>
              detractis circuitibus uelut rhete habeant naturam reciſi, & ſpatia
                <lb/>
              ipſa tota ſint eiuſdem generis, erunt ſpatia, quæ relinquuntur eiuſ­
                <lb/>
              dem generis. </s>
              <s id="id000774">Erunt tamen incommenſa neceſſariò, ſi partes fuerint
                <lb/>
              incommenſæ toti. </s>
              <s id="id000775">Ponatur a c incommenſa toti circulo dico, quod
                <lb/>
              a k
                <expan abbr="etiã">etiam</expan>
              eſt incommenſa toti circulo: &
                <expan abbr="etiã">etiam</expan>
              a k, & k c. </s>
              <s id="id000776">Quia enim a c
                <lb/>
              eſt incommenſa circulo, & k a cum toto circulo ſemel eſt </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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