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="id001167">
                <pb pagenum="61" xlink:href="015/01/080.jpg"/>
              dit: linea uerò tangens uerticem hyperbolis ad quam ordinatæ
                <lb/>
                <arrow.to.target n="marg240"/>
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              poſſunt, Recta appellabitur. </s>
              <s id="id001168">Data recta linea poſitione, aliaque ma
                <lb/>
              gnitudine data & angülo parabolen, & hyperbolen, & ellipſim,
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              & contra poſitas circa datam poſitione tanquàm diametrum de­
                <lb/>
              ſcribere tanquàm cono erecto, ut angulus ad uerticem ſectionis
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              comprehenſus ſit, & per rectam rectangulum æquale comprehen­
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              datur quadrato datæ lineæ magnitudine. </s>
              <s id="id001169">Si linea in duas partes
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                <arrow.to.target n="marg241"/>
                <lb/>
              diuidatur, eique utrinque æquales lineæ adiun­
                <lb/>
                <figure id="id.015.01.080.1.jpg" xlink:href="015/01/080/1.jpg" number="76"/>
                <lb/>
              gantur erit rectangulum ex partibus totius æ­
                <lb/>
              quale rectangulis partium prioris lineæ, & ex
                <lb/>
              priore linea cum una adiecta in eam, quæ adiecta eſt. </s>
              <s id="id001170">Si hyperbo
                <lb/>
                <arrow.to.target n="marg242"/>
                <lb/>
              len recta linea in uertice contingat, & utrinque abſcindatur, quan­
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              tum eſt, quod poteſt in quartam partem rectanguli ex diametro
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              tranſuerſa hyperbolis, quæ exterius adiacetin eam, quæ recta dici­
                <lb/>
              tur, ad quam, quæ ordinatim ducuntur, ſunt æquidiſtantes lineæ,
                <lb/>
              quæ à ſectionis centro ad terminos contingentis ducuntur ſemper
                <lb/>
              ipſi ſectioni magis appropinquabunt, nec unquam conuenient: &
                <lb/>
              ob id aſymptoton appellantur. </s>
              <s id="id001171">Nec ullæ aliæ intra
                <expan abbr="angulũ">angulum</expan>
              illum
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                <arrow.to.target n="marg243"/>
                <lb/>
              inueniri poterunt. </s>
              <s id="id001172">Vnde etiam intra
                <expan abbr="datũ">datum</expan>
              angulum deſcribere do­
                <lb/>
              cemur hyperbolen cuius anguli latera ſint aſymptota. </s>
              <s id="id001173">Aſymptotis
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                <arrow.to.target n="marg244"/>
                <lb/>
              duabus propoſitis uni hyperboli, in finitas alías eidem aſymptotas
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              inuenire. </s>
              <s id="id001174">Duabus rectis aſymptotis infinitas ſubijci poſſe hyperbo
                <lb/>
              les illis rectis, & inter ſe aſymptotas. </s>
              <s id="id001175">Cum in duabus ſuperficie­
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                <arrow.to.target n="marg245"/>
                <lb/>
              bus æquidiſtantibus duo circuli æquales, quorum linea per cen­
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              tra non eſt ad perpendiculum earum infinitis planis ſecantur, fiunt
                <lb/>
              in ipſis lineæ à peripheria in peripheriam rectæ quæ corpus cylin­
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              dricum claudunt quod ſcalenus cylindrus appellatur: longè alius
                <lb/>
              ab eo, qui fit recto cylindro per duo plana æquidiſtantia, ſed non
                <lb/>
              ad perpendiculum poſita diſſecto. </s>
              <s id="id001176">nam eius extremæ ſuperficies
                <lb/>
              non circuli, ſed ellipſes ſunt. </s>
              <s id="id001177">Si ſcalenus cylindrus plano non æ­
                <lb/>
                <arrow.to.target n="marg246"/>
                <lb/>
              quidiſtanti baſi, ſed ita ut angulos interiores æquales faciat angu­
                <lb/>
              lis baſis ſectio circulus erit: uocaturque hæc ſectio ſub contraria: nec
                <lb/>
              ulla præter hanc & baſi æquidiſtantem ſectio circulus eſſe poteſt:
                <lb/>
              ſed ſunt ellipſes. </s>
              <s id="id001178">Super eundem circulum, & ſub eadem altitudi­
                <lb/>
                <arrow.to.target n="marg247"/>
                <lb/>
              ne ellipſes ſimiles in cono & cylindro eſſe poſſunt, quæ ab eodem
                <lb/>
              plano fiant, docetque uel baſi uel cono uel cylindro, aut cono pro­
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              poſito reliqua facere, quod eſt ualde admirabile: cum ellipſis cylin­
                <lb/>
              drica ſemper æqualis ſit in utraque parte à diametro tranſuerſa
                <lb/>
              utrinque æqualiter diſtante, conica uerò minor neceſſariò ſit in ſu­
                <lb/>
              periore parte uerſus coni uerticem latior in inferiore, ubi partes a
                <lb/>
              diametro tranſuerſa æqualiter diſteterint: ipſę autem non ſolum </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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