Cardano, Girolamo, De subtilitate, 1663

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              <s id="s.010904">
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              quidem per conum rectum, conum ſolùm
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              intelligi volo) diuidetur plano ſuper tri­
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              gonum A B C, ad perpendiculum ſtanti,
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              ita quòd tranſeat per aliquem punctum con­
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              ſtitutum extra verticem, puta G, tunc vel
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              axis, ſeu dimetiens figuræ intra conum clau­
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              ſæ æquidiſtabit baſi ſecans ambo latera
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              trianguli, & tunc figura illa erit neceſſariò
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              circulus, vt in prima figura circulus GH. </s>
              <s id="s.010905">De­
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              ſcripſi autem tam baſim, quàm ſuperficiem
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              ſecantem circulos perfectos in prima figura,
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              vt illos agnoſceres. </s>
              <s id="s.010906">In aliis autem ſequen­
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              tibus figuris circuli longiores, quàm pro
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              latitudine ſcribentur, vt conus, & ſectiones
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              ex plano ad ſolidi imaginem tranſlati me­
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              liùs repræſentari poſſint. </s>
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            <p type="margin">
              <s id="s.010907">
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              Creatio
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              quinque fi­
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              gurarum in
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              cono.</s>
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            <figure id="id.016.01.241.1.jpg" xlink:href="016/01/241/1.jpg" number="96"/>
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              <s id="s.010908">Quòd ſi planum illud per G tranſiens, &
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              ad perpendiculum ſupra triangulum ſtans
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              conum ſecans bifariam, nam hoc ſemper eſt
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              neceſſarium, ſecet, & ambo latera trigoni
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              ABC, illius autem figuræ dimetiens non
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              æquidiſtet baſi coni, ſed quaſi inclinetur,
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              fiet ſecunda figura, quæ vocatur Ellipſis. </s>
              <s id="s.010909">Ve­
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              lut ſit conus ABCE, cuius triangulus per
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              axem ſit ABC, in coni ſuperficie & latere
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              trianguli punctus præter verticem, quem
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              ſuper G voco, ſicut & planum per G pun­
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              ctum, & ad perpendiculum ſtans ſuper trian­
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              gulum ABC, & conum in duas partes di­
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              uidens ſemper dicatur K. </s>
              <s id="s.010910">Si igitur GH, quæ
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              intra conum clauditur, eſtque pars plani
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              K, habeat axem GH, vt in ſecunda figura,
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              qui ambo latera AB, & A C diuidat, nec
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              tamen æquidiſtet plano baſis BCE, ſed vel
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              ſuprà, vel infra inclinetur, fit figura vocata
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              Ellipſis, ideſt, defectio, quia non vt duæ ſe­
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              quentes poteſt in infinitum extendi. </s>
            </p>
            <p type="main">
              <s id="s.010911">Si verò plano K per punctum G, ducto,
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              ſecantéque conum fiat figura, cuius axis
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              æquidiſtet tertio lateri, vocabitur figura il­
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              la Parabole. </s>
              <s id="s.010912">Veluti is tertia figura plano K
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              diuidente conum figura incluſa in cono,
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                <figure id="id.016.01.241.2.jpg" xlink:href="016/01/241/2.jpg" number="97"/>
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              quæ eſt G H D F, habeat axem G æquidi­
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              ſtantem AB, tertio lateri trigoni, tunc ve­
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              cabitur figura illa Parabulæ, id eſt, è regione,
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              quia quantumcunque cum cono ipſo pro­
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              ducatur, ſemper eſt è regione alterius lateris.
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              </s>
              <s id="s.010913">Cùm igitur duæ præcedentes figuræ ſecent
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              ambo latera trigoni ABC, hæc & ſequens
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              non ſecant latus AB aduerſum, vt vides. </s>
              <s id="s.010914">Si
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              igitur planum ad perpendiculum ſtans ſuper
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              triangulum A E C, (quod ſemper intelligi
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              volo, ſicut etiam quòd tranſeat per pun­
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              ctum extra verticem (non ſecuerit latus
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              illi contrapoſitum, ſecando conum, & ta­
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              men illius figuræ, quæ intra conum clau­
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              ditur axis, non æquidiſtet tertio lateri, ſic
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              enim eſſet Parabole, nec ſecet latus, vt di­
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              xi, contrapoſitum intra conum, quia eſſet
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              Ellipſis, vt dictum eſt, ſed illud latus con­
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              trapoſitum ſecet extra conum, tunc dice­
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              tur Hyperbole, id eſt exceſſus: quià angu­
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              lus axe figuræ, & latere trigoni conten­
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              tus, in Hyperbole maior eſt, quàm in Para­
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              bule. </s>
              <s id="s.010915">Sit igitur planum ſecans conum bi­
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              fariam, & ad perpendiculum ſtans ſupra
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              trigonum A B C, & fiat figura GHF, vt
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              in quarta deſcriptione, & huius figuræ di­
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              mittens GD, non ſecet latus AB, intra co­
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              num, nec ab illo æquidiſtet, ſed protra­
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              ctum occurrat illi extra conum in E, quòd
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              neceſſarium eſt, quandoquidem nec illi
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              æquidiſtat, nec occurrit intra conum, tunc
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              hæc figura vocabitur Hyperbole, quia an­
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              gulus AGD, in ea maior eſt, quàm in Pa­
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              rabole. </s>
              <s id="s.010916">Ex his iam patet in cono perfe­
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              ctionem plani ad perpendiculum ſuper tri­
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              gonum conum per axem diuidentis erecti,
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              & per datum punctum præter verticem
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                <figure id="id.016.01.241.3.jpg" xlink:href="016/01/241/3.jpg" number="98"/>
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              tranſeuntis, quatuor fieri figuras, ſcilicet
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              circulum, Ellipſim, Parabolem, & Hyber­
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              bolem, nec poſſe ex vno cono plura gene­
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              ra inueniri: nam quintum habet plano
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              diuidente duos conos æquiangulos contra
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              ſe poſitos ad verticem (in quinta figura
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                <figure id="id.016.01.241.4.jpg" xlink:href="016/01/241/4.jpg" number="99"/>
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              exemplum habes) & tunc fiunt neceſſa­
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              riò duæ hyperboles: hæ duæ ab Apol­
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              lonio vocantur contrapoſitæ: vt ſi ſint
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              duo coni verticibus iuncti A B C, &
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              A D E, ſic vt lineæ B A E, & C A D, </s>
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