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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              <s id="id002574">
                <pb pagenum="146" xlink:href="015/01/165.jpg"/>
              ſito igitur ut a h ad h b ita h b ad b l, ſed angulus a h b eſt æqualis
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              angulo h b l, ergo triangulus a h b eſt
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              ſimilis triangulo h b l, quare angulus
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              b h l eſt ęqualis angulo h a f, igitur du
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              orum triangulorum f a h, & fb h duo
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                <arrow.to.target n="marg506"/>
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              anguli unius a & f ſunt æquales duo­
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              bus angulis, alterius igitur propor­
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                <figure id="id.015.01.165.1.jpg" xlink:href="015/01/165/1.jpg" number="171"/>
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              tio a f ad fh reſpicientium angulos ę­
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              quales ut a h ad h b reſpicientium an­
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                <arrow.to.target n="marg508"/>
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              gulum f, ſed a h ad h b ut c ad d, ex ſup
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              poſito igitur a f ad f h, ut c ad d, ſed ut c ad d ita a f ad g, ex ſuppoſito
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              ergo h f eſt æqualis g.
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              quin­
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            <p type="margin">
              <s id="id002582">
                <margin.target id="marg509"/>
              C
                <emph type="italics"/>
              or
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              ^{m}. 1.</s>
            </p>
            <p type="main">
              <s id="id002583">Cum ergo hęc demonſtratio ſit ex ſenſu in uno puncto h, ideò ad
                <lb/>
              quælibet puncta traduci poteſt, quæ potero imaginari, & ita pri­
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              ma uocabitur ſenſus,
                <expan abbr="ſecũda">ſecunda</expan>
              imaginandi: Et
                <expan abbr="quoniã">quoniam</expan>
              in demonſtran­
                <lb/>
              do non aſſumimus aliquid, quod ſit proprium alicui puncto, niſi
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              proportionem h a ad h b ſimilem eſſe c ad d, ideo hoc pertinet ad
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              intellectum, & eſt tertium. </s>
              <s id="id002584">Et idem dico ſi k eſſet ultra h quod po­
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              teſt contingere. </s>
              <s id="id002585">modò k a ad k b ſit ut c ad d & k f ſit ęqualis g idem
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              ſequetur, & comprehenditur ſub tertio & pertinet ad intellectum,
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              & quoniam demonſtratur quod punctum k ubicunque ſumatur, eſt
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              in ęquali
                <expan abbr="diſtãtia">diſtantia</expan>
              à puncto f ſcilicet per g lineam, erit ſemper in peri­
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              pheria circuli, & hoc poteſt eſſe in infinitis locis ſimpliciter & extra
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              infinitum nihil eſt, igitur ſub hoc continetur conuerſum ſcilicet,
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              quod a quolibet puncto circuli ductis lineis ad a & b ipſę erunt in
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              proportione c ad d. </s>
              <s id="id002586">Et ita abſque principijs Geometricis concluditur
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              propoſitio Geometrica & hoc eſt
                <foreign lang="grc">περιλάμπουσιν</foreign>
              & fermè ſummum in­
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              tellectus humani. </s>
              <s id="id002587">Et poteſt demonſtrari Geometricè duobus uer­
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              bis. </s>
              <s id="id002588">Quia. n. </s>
              <s id="id002589">
                <expan abbr="fſupponit̃">f ſupponitur</expan>
              æqualis g eo quòd h eſt in peripheria circu­
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              li erit media inter a f & f b, quare cum angulus f ſit communis, erit
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              proportio a h ad h b, laterum reſpicientium angulum f in utroque </s>
            </p>
            <p type="main">
              <s id="id002590">
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              triangulo, uelut h f lateris in maiori ad f b latus in minori, quare
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                <arrow.to.target n="marg511"/>
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              cum ex ſuppoſito h f ad fb ſit ut c ad d, erit a ad b, ut c ad d. </s>
              <s id="id002591">Et uides
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              Apollonium, & Pappium quanta ſuperflua adijciant in hac ſecun­
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                <arrow.to.target n="marg512"/>
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              da parte demonſtrationis, quæ eſt prima apud illos, & ducunt
                <expan abbr="unã">unam</expan>
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              lineam non neceſſariam ex puncto b ad latus fh. </s>
              <s id="id002592">Vt
                <expan abbr="antiquorũ">antiquorum</expan>
              ple
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              rique non tantum potuerint Geometria & ingenio, quæ ferunt excel
                <lb/>
              lentiſsima in illis, quantum nos ex Dialectica
                <foreign lang="grc">πε̣ριλάμπουσιν</foreign>
              inducen
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              tes. </s>
              <s id="id002593">eſt enim ſingulare hoc exemplum.
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                <arrow.to.target n="marg513"/>
              </s>
            </p>
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              </s>
            </p>
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                <expan abbr="eiuſdẽ">eiuſdem</expan>
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              </s>
            </p>
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              I
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              n primo
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              C
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              o
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              nicor.
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              A
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              pol.
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              in
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              P
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              ræfat.
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              </s>
            </p>
            <p type="margin">
              <s id="id002597">
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              C
                <emph type="italics"/>
              or
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              ^{m}. 2.</s>
            </p>
            <p type="main">
              <s id="id002598">Ex hoc
                <expan abbr="etiã">etiam</expan>
              patet quod ſi circulus duceretur ſecundum f k tran­
                <lb/>
              ſiretque per m & n eſſet a m ad m b & a n ad b n, ut a h ad h b.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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