Cardano, Girolamo
,
De subtilitate
,
1663
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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. </
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<
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">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. </
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<
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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. </
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Creatio
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quinque fi
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gurarum in
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cono.</
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<
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">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. </
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<
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id
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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. </
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<
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id
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">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. </
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<
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">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. </
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<
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id
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">Veluti is tertia figura plano K
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diuidente conum figura incluſa in cono,
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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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</
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<
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">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. </
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<
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id
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">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. </
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<
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">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. </
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<
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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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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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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, </
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