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="id000803">
                <pb pagenum="42" xlink:href="015/01/061.jpg"/>
              ſexcuplex, & tempus totum decem annorum: ita ut a c ſit tertia
                <lb/>
              pars circuitus, & a circuitus tres anni, & quia circuitus b ſunt ſex
                <lb/>
              cum tertia, diuidemus decem per 6 1/3 exit
                <lb/>
              1 11/29, dico quod non prius, neque in alio
                <lb/>
                <figure id="id.015.01.061.1.jpg" xlink:href="015/01/061/1.jpg" number="56"/>
                <lb/>
              puncto. </s>
              <s id="id000804">Si enim primùm in eodem pun­
                <lb/>
              cto, &, gratia exempli, in quatuor annis
                <lb/>
              congruit enim, & b dicamus quod per­
                <lb/>
              egerit duas reuolutiones cum tertia, hoc
                <lb/>
              enim eſt neceſſarium, ſi debet perueni­
                <lb/>
              re ad c, & erunt anni tres, & 23/19, non ergo
                <lb/>
              anni quatuor. </s>
              <s id="id000805">Cum enim tempora di­
                <lb/>
              uerſa diuiduntur per numeros haben­
                <lb/>
              tes proportionem erunt, qui prodeunt
                <lb/>
                <arrow.to.target n="table13"/>
                <lb/>
              numeri in eadem ratione. </s>
              <s id="id000806">Diuiſo ergo
                <lb/>
              10 per 1 11/19 exit 6 2/3, & diuiſo 4 per 1 11/19 exit
                <lb/>
              2 8/15, igitur 6 1/3 ad 2 8/15, ut 10 ad 4, igitur 8/25
                <lb/>
              non poteſt eſſe æquale 1/3. Si enim per
                <lb/>
              præcedentem repetuntur, ergo non poſ­
                <lb/>
              ſunt redire, donec iterum coniungantur in ipſo a. </s>
              <s id="id000807">Si enim aliter ſit
                <lb/>
              ut ex e, igitur e c eſt æqualis a c pars toti, quod contingere non po­
                <lb/>
              teſt. </s>
              <s id="id000808">Sin uerò coniunctio fiat in d, igitur per præcedentem d e eſt
                <lb/>
              pars a c ſubmultiplex quomodolibet, quare non fuerunt aſſum­
                <lb/>
              pti primi numeri. </s>
              <s id="id000809">Veluti in exemplo conſtituimus, quod a, & b
                <lb/>
              conueniunt in c in decem annis, & a c eſt tertia pars circuitus: er­
                <lb/>
              go in triginta annis conueniunt in a, & in quadraginta rurſus in c.
                <lb/>
              ſi ergo quis aſſumpſiſſet quadraginta annos ab initio pro con­
                <lb/>
              greſſu, & diuiſiſſet per 1 12/19 exiret 25 1/3, & ſi per 3 exiret 13 1/3, & mani­
                <lb/>
              feſtum eſt, quod uterque numerus poteſt diuidi per eundem nu­
                <lb/>
              merum, utpote 4 & exit numerus cum eadem parte ſcilicet 6 1/3 &
                <lb/>
              3 1/3 ergo conuenient ante, non ergo aſſumpſiſti minimos in ea pro­
                <lb/>
              portione. </s>
              <s id="id000810">Illi autem nequaquam amplius diuidi non poſſunt eo­
                <lb/>
              dem modo.</s>
            </p>
            <table>
              <table.target id="table13"/>
              <row>
                <cell>Decem</cell>
                <cell/>
                <cell>Quatuor</cell>
                <cell/>
              </row>
              <row>
                <cell>3</cell>
                <cell>3 1/3</cell>
                <cell>1 11/19</cell>
                <cell>2 8/15)</cell>
              </row>
              <row>
                <cell>1 11/19</cell>
                <cell>6 1/3</cell>
                <cell/>
                <cell/>
              </row>
            </table>
            <p type="main">
              <s id="id000811">Propoſitio quinquageſima ſecunda.</s>
            </p>
            <p type="main">
              <s id="id000812">Tria mobilia coniuncta in eodem puncto, quorum duo, & duo
                <lb/>
              conueniant in partibus in commenſis inter ſe, in perpetuum in nul­
                <lb/>
              lo unquam puncto conuenient.</s>
            </p>
            <p type="main">
              <s id="id000813">
                <arrow.to.target n="marg140"/>
              </s>
            </p>
            <p type="margin">
              <s id="id000814">
                <margin.target id="marg140"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id000815">Sint a b c iuncta, & primo iungantur a & b, iterum in d & b, &
                <lb/>
              c in e, & ſint a d, a e incommenſæ, dico quòd a b c nunquam con­
                <lb/>
              uenient in aliquo puncto, ſeu primo, ſeu alio à primo: ſi non con­</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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