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="id004473">
                <pb pagenum="263" xlink:href="015/01/282.jpg"/>
              ſemper. </s>
              <s id="id004474">Et orbes ſuperiores
                <expan abbr="nõ">non</expan>
              indigebant lumine Solis, quod ap­
                <lb/>
              paret in nocte ſerena, cum etiam adeò à nobis diſtent. </s>
              <s id="id004475">Vnde ſi cani­
                <lb/>
              cula eſſet in cœlo Lunæ, plus luminis afferret centuplo quàm Lu­
                <lb/>
              na, cùm diſtantia ſit quingentupla diſtantiæ Lunæ à terra. </s>
              <s id="id004476">Et ſi Sol
                <lb/>
              eſſet factus adeo maior, ut in orbe Saturni conſiſtens calefaceret ter
                <lb/>
              ram æqualiter, ut non exureretur in æſtate, hyeme neceſſe eſſet, ut ni
                <lb/>
              mium gelaſceret. </s>
              <s id="id004477">Sin autem æquale eſſet frigus in hyeme, exurere­
                <lb/>
              tur terra per æſtatem, quando quidem nec ſic illam pati poſsint, qui
                <lb/>
              in torrida plaga habitant. </s>
              <s id="id004478">Et ſi Sol eſſet ubi eſt Luna, & eo minor
                <lb/>
              non illuminarentur orbes ſuperiores. </s>
              <s id="id004479">Ideo nobilitas non eſt in or­
                <lb/>
              bibus ob altitudinem, ſed ob ſubſtantiam incorpoream quæ illi do
                <lb/>
              minatur. </s>
              <s id="id004480">Et eſt in loco congruenti toti corpus, uita autem non eſt
                <lb/>
              in loco.</s>
            </p>
            <p type="margin">
              <s id="id004481">
                <margin.target id="marg899"/>
              P
                <emph type="italics"/>
              rop.
                <emph.end type="italics"/>
              171.</s>
            </p>
            <p type="head">
              <s id="id004482">LEMMA.</s>
            </p>
            <figure id="id.015.01.282.1.jpg" xlink:href="015/01/282/1.jpg" number="282"/>
            <p type="main">
              <s id="id004483">Et proponantur a & b in proportione dupla alti­
                <lb/>
              tudinum & magnitudinum, &
                <expan abbr="cõparentur">comparentur</expan>
              ad d, erit
                <lb/>
              ergo angulus a d c maior b d c, quare ſi ſunt æquales
                <lb/>
              uires in a b, refrigerabitur magis d ab a quam b, &
                <lb/>
              ita patet utraque pars dicti in fine propoſitionis.</s>
            </p>
            <p type="main">
              <s id="id004484">Propoſitio ducenteſima trigeſima prima.</s>
            </p>
            <p type="main">
              <s id="id004485">Tres eſſe mundos, atque inter ipſos nullam eſſe proportionem:
                <lb/>
              nec numero eos definiri.</s>
            </p>
            <p type="main">
              <s id="id004486">Cum palam ſit eſſe corporeum mundum ut elementa, & incor­
                <lb/>
                <arrow.to.target n="marg900"/>
                <lb/>
              poreum ut Dei, & medium eſſe neceſſe eſt uitarum & hominum ac
                <lb/>
              cœleſtium, quòd primum ſenſu patet, ut cœli, hominum & anima­
                <lb/>
              lium, atque plantarum, & ratione etiam, quoniam extrema contraria
                <lb/>
                <expan abbr="nõ">non</expan>
              propriè medio copulantur, ut incorporeum ac corporeum. </s>
              <s id="id004487">Di­
                <lb/>
              co igitur nullam eſſe inter hos proportionem atque numerum face­
                <lb/>
              re: nam de numero conſtat, quoniam non ſunt tres, quia ſint in ordi
                <lb/>
              ne numerorum, ſed ut principium, medium, finis, & perfectum, per­
                <lb/>
              fectius, perfectiſsimum: ſcilicet poſitiuum, comparatiuum & ſuper­
                <lb/>
              latiuum. </s>
              <s id="id004488">Et quoniam ſunt extrema cum medio, ideò ſunt in propor
                <lb/>
              tione ſublimi etiam & non propria. </s>
              <s id="id004489">Quod ſi eſſent maximè mun­
                <lb/>
              di uitalis ad corpora, ſed corpora
                <expan abbr="nõ">non</expan>
              mouentur niſi iuxta finem ui­
                <lb/>
              tæ, & non uim: ipſa enim ſi poſſet habere uoluntatem infinitam mo
                <lb/>
              ueret in inſtanti: quia corpora non reluctantur animabus ſuis, ſed
                <lb/>
              quantus eſt actus in animabus & uitis, tanta eſt
                <expan abbr="potẽtia">potentia</expan>
              ad unguem
                <lb/>
              in corporibus, ergo non contingit proportio in mundo uitarum
                <lb/>
              uera niſi illa ſublimis. </s>
              <s id="id004490">Neque enim finita eſt quæ nullis circumſcribi­
                <lb/>
              tur terminis, neque infinita quo finitam pręſupponit, ſed neque inter
                <lb/>
              mundum & incorporeum & uitarum cùm mentes non moueant, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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