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="id002829">
                <pb pagenum="161" xlink:href="015/01/180.jpg"/>
              ria & recta ſunt ex genere quantitatis continuæ, & quòd detur ma­
                <lb/>
              ius & minus & nunquam detur ęquale, uidetur abſurdum ne dum
                <lb/>
              admirabile. </s>
              <s id="id002830">Et maximè quod etiam anguli ex peripheria & recta
                <lb/>
              ſunt diuerſorum generum inter ſe & infinitorum. </s>
              <s id="id002831">Pręterea iſtud re­
                <lb/>
              pugnare uidetur ipſimet Euclidi, dicenti duabus magnitudinibus
                <lb/>
                <arrow.to.target n="marg547"/>
                <lb/>
                <arrow.to.target n="marg548"/>
                <lb/>
              propoſitis inæqualibus, ſi de maiore earum plus dimidio detraha­
                <lb/>
              tur, atque iterum de reſiduo maius dimidio, & rurſus de eo quod re­
                <lb/>
              linquitur plus dimidio, neceſſe erit ut tandem minor minore quan­
                <lb/>
              titas relinquatur. </s>
              <s id="id002832">Neque illud argumentum uidetur concludere an­
                <lb/>
              gulus contactus, ex recta, & circuli circumferentia non poteſt recta
                <lb/>
              diuidi, & rectilineus poteſt diuidi, ergo rectilineus ſemper eſt ma­
                <lb/>
              ior angulo contactus, quia hoc contingit in angulo contactus pro
                <lb/>
              pter modum anguli, non paruitatem: ſicut etiam non ualet de figu­
                <lb/>
                <figure id="id.015.01.180.1.jpg" xlink:href="015/01/180/1.jpg" number="189"/>
                <lb/>
              ra a lunari, & quadrangulo b. </s>
              <s id="id002833">nam poteſt b diuidi
                <lb/>
              ab angulo ad angulum recta & a non poteſt, &
                <lb/>
              tamen a maius eſt quam b, cum contineat ipſam.
                <lb/>
              </s>
              <s id="id002834">Proponantur ergo duo circuli a d e & a f g qui ſe contingant in a, &
                <lb/>
              eorum centra ſint b & c & ducantur rectæ a f d & a g e & conſtat
                <lb/>
              qui portiones a d & a f ſimiles ſunt,
                <lb/>
                <figure id="id.015.01.180.2.jpg" xlink:href="015/01/180/2.jpg" number="190"/>
                <lb/>
              itemque a e & a g, ducta enim a b c
                <lb/>
                <arrow.to.target n="marg549"/>
                <lb/>
              per centra circulorum ex contactu
                <lb/>
              tranſibit per illa: quare anguli h a g
                <lb/>
              & h a e ſunt ijdem & ſimiliter h a f
                <lb/>
              & h a d ijdem, portiones ergo af &
                <lb/>
              a d itemque a g & a e ſimiles ſunt: an­
                <lb/>
              gulus igitur g a e ex peripherijs &
                <lb/>
                <arrow.to.target n="marg550"/>
                <lb/>
              e a d ex rectis ſunt ijdem in puncto
                <lb/>
              a: ſed quod ad baſsim maior eſt ba­
                <lb/>
              ſis g e quam e d: hoc enim ſuppono
                <lb/>
              quod per ſe eſt manifeſtum toties
                <lb/>
                <expan abbr="diuidẽdo">diuidendo</expan>
              arcum d e ut fiat minor recta g e. </s>
              <s id="id002835">Quia ergo ſunt duę ma­
                <lb/>
              gnitudines, quarum ter mini ſunt ijdem ex una parte, ſcilicet pun­
                <lb/>
              ctum a, ex alia autem unus eſt maior altero, ſcilicet g e quam e f &
                <lb/>
                <arrow.to.target n="marg551"/>
                <lb/>
              a d e peripheria eſt maior recta a g e. </s>
              <s id="id002836">Ergo per regulam dialecti­
                <lb/>
              cam ſi ſub eadem proportione procederent, maius eſſet ſpatium
                <lb/>
              ſemper inter peripherias quàm rectas. </s>
              <s id="id002837">igitur angulus peripheria­
                <lb/>
              rum eſt maior angulo à rectis contento. </s>
              <s id="id002838">Cum angulus non ſit
                <lb/>
              niſi quidam habitus propinquitatis linearum, ſed angulus con­
                <lb/>
              tactus ex recta & peripheria maior eſt contento ex peripherijs cum
                <lb/>
              habeat rationem totius ad partem, igitur angulus contactus eſt
                <lb/>
              maior dato angulo rectilineo.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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