Cardano, Girolamo, De subtilitate, 1663

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.012527">
                <pb pagenum="634" xlink:href="016/01/281.jpg"/>
              quid hæc nunc ſcriptura ab intellectu meo
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              differt? </s>
              <s id="s.012528">Intellectus verò meus eſt, quicquid
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              in me boni eſt. </s>
              <s id="s.012529">Sic igitur qui hæc leget, an­
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              nos poſt bis mille, intellectum meum vide­
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              bit, & aſſequetur. </s>
              <s id="s.012530">Atque hæc eſt vniuſcuiuſ­
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              que intellectus perpetuitas, non autem æter­
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              nitas. </s>
              <s id="s.012531">Manet ergo poſt fata quod optimum
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              eſt in nobis, etiam præter ſcripta, audiéntque
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              ſecula loquentem me: ita ex mortali homine
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              fit aliquid, quod ſemper manet: intellectus,
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              autem, & quod intelligitur vnum ſunt, &
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              ſubſtantia æterna. </s>
              <s id="s.012532">Dictum eſt autem de hoc
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              aliàs. </s>
            </p>
            <p type="margin">
              <s id="s.012533">
                <margin.target id="marg1715"/>
              Qui pauca
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              ſcripſerunt,
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              nullius au­
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              ctoritatis eſ­
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              ſe debent,
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              præterquam
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              in Poëſi, &
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              Mathemati­
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              ca.
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              </s>
              <s id="s.012534">Gloria cur
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              expectatur.</s>
            </p>
            <p type="main">
              <s id="s.012535">In Poëſi tamen, qui parùm ſcribit, cùm
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              furore agatur, iudicium habere poteſt. </s>
              <s id="s.012536">Et
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              in Mathematicis, quia ſolum probantur,
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              quæ finem habent, & qua ad demonſtran­
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              dum finem ſunt neceſſaria: cùm tamen ob
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              id etſi multò plura ſcirent Euclides, & Ar­
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              chimedes, quàm ſcripſerint, laudantur
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              magis, & in his atque probantur, qui plu­
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              ra ſcripſerunt, vt Homerus, Virgilius,
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              Naſo, Archimedes, Euclides, Ptolomæus:
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              quàm qui pauca, vt Theocritus, Perſius,
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              Catullus aut Nicomachus, Diocles, & Ar­
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              chitas.
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                <arrow.to.target n="marg1716"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.012537">
                <margin.target id="marg1716"/>
              Theonis
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              laus.
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              </s>
              <s id="s.012538">Sphæræ ad
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              aliorum cor­
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              porum capa­
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              citatem pro­
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              portio.</s>
            </p>
            <p type="main">
              <s id="s.012539">Im verò & inter celebres authores repo­
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              natur Theon, qui Euclidis elementa, &
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              Ptolemæi magnam expoſuit compoſitionem.
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              </s>
              <s id="s.012540">Hic inter cætera inuenta demonſtrandi
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              ſphæram, omnium corporum eſſe capaciſ­
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              ſimam. </s>
              <s id="s.012541">Ea ratio vt demonſtrat, ita etiam
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              arte verum hoc eſſe deprehendimus: etſi non
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              ad amuſſim, qualis ſit ratio capacitatis ſphæ­
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              ræ ad reliqua corpora. </s>
              <s id="s.012542">Si igitur cubi latus
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              ſit quatuor, corpus ipſum erit 64. & am­
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              bitus omnium ſuperficierum 96. at ſphæra,
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              cuius ambitus eſt 96. habet ex Archimede
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              maiorem circulum 24. ad vnguem: igi­
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              tur demetiens erit ex Archimede cùm
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              area ſit 24. fermè quinque & dimidium
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              Igitur cylindrus ſuper maiorem circulum
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              erit quaſi 122. fit enim ex dimetiente in ba­
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              ſin: at cylindrus ſuper circulum maximum
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              ſphæræ ex Archimede eſt ſeſquialter illi:
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              igitur cùm cylindrus ſit 132. fermè, erit
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              ſphæra quaſi 88. igitur cùm vbi ambitus eſt
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              96. ipſe cubus ſolidus eſt 64. cum autem
                <arrow.to.target n="marg1717"/>
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              ſphæræ ambitus eſt 96. ipſa ſphæra eſt. </s>
              <s id="s.012543">88.
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              igitur proportio ſphæræ ad cubum, cùm am­
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              bitus eſt, idem erit fermè, & propinquiſ­
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              ſima ei, quæ eſt 11. ad 8. Faciliùs demon­
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              ſtrantur hæc in plano, corpora enim ſolida
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              omnia, quæ ſphæra includi poſſunt, cer­
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              ta ratione in libris de Varietate rerum,
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              qualiter in plano poſſent deſcribi, docui­
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              mus. </s>
              <s id="s.012544">Nunc ſphæram leui labore, & par­
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              uo errore ex ambitu conficere, propoſitum
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              eſt. </s>
              <s id="s.012545">Typographicæ enim arti, ſeu cœleſtem,
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              ſeu terrenam conficere velimus, vtiliſſimum
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              hoc eſt. </s>
              <s id="s.012546">Proponamus ſphæram, cuius æqui­
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              noctij circulus ſit 44. & diuidatur ſex circu­
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              lis maioribus, per polos ductis in duode­
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              cim partes æquales: ſeparentúrque duode­
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              cim illæ zonæ, dico eas in plano extendi
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              poſſe, vt non lædantur. </s>
              <s id="s.012547">Quamobrem ex ſo­
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              lido ad planum, & ex plano rurſus ad ſoli­
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              dum, abſque errore notatu digno, tranſi­
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              tus mutuus fiet: vt quæ in ſolido ratione
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              inuenta ſunt, poſſint in plano fingi: & in
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              plano ficta, ad ſolidum redigi. </s>
              <s id="s.012548">Maximum
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              enim, ſi quod erit diſcrimen, in medio erit.
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              </s>
              <s id="s.012549">Pars ea 3 2/3 ex 44. in ſphæra habet. </s>
              <s id="s.012550">Sinus
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              igitur eius eſt quarta pars diametri, id eſt
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              3 1/2 duc in ſe fit 12 1/4 & tantùm debet produ­
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              ci ex 14. diuiſo in duas partes. </s>
              <s id="s.012551">Igitur partes
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              erunt fermè 13 1/16 & 15/15. hæc igitur eſt ſagit­
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              ta: quadrata igitur ſinus, & ſagittæ iuncta
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              ſunt 13 33/256. Igitur latus quod arcui par­
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              tium 3 2/3 ſubtenditur, parùm differt à 3
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              5/8. Igitur arcus à recta ſua diſcrimen eſt
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              1/24. Quare ad partem æquinoctij interceptam
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              1/88 inſenſibile prorſus. </s>
              <s id="s.012552">Et hæc ratio in om­
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              nibus parallelis eſt obſeruanda, vt ex his,
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              quæ in ſeptimo ſuper Euclidem demonſtra­
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              uimus, patet, in paruis quoque minùs con­
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              ſpicua erit. </s>
              <s id="s.012553">Quare ſeu in charta, ſeu in pa­
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              pyro, dum extenditur, nihil differt. </s>
              <s id="s.012554">Atque
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              eo modo ſenſu deprehendi etiam poteſt
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              proportio ſphæræ ad reliqua omnia corpo­
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              ra, quæ ambitum æqualem habent. </s>
              <s id="s.012555">Cùm
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              verò, vr ſuperiùs dictum eſt, leuis ſit ſphæ­
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              rica figura, & plus continet, omnia quaſi
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              quendam habent ſenſum: nam quò plus
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              continet, eò robuſtior redditur ad reſiſten­
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              dum: itaque elementa liquida, maximè vt
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              aër, & aqua, & obſcurius terra, in rotundam
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              formam ſpontè ſe vertunt, vt tutiſſimam ab
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              externa iniuria.
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              </s>
            </p>
            <p type="margin">
              <s id="s.012556">
                <margin.target id="marg1717"/>
              Sphæra quo­
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              modo ex pla­
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              nis fiat.</s>
            </p>
            <p type="margin">
              <s id="s.012557">
                <margin.target id="marg1718"/>
              Viuentium
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              facultates
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              tres princi­
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              pales, &
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              quatuor
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              ſeruientes.</s>
            </p>
            <p type="main">
              <s id="s.012558">Verùm viuentia ipſa præter hunc laten­
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              tem ſenſum alias habent facultates: princi­
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              pales tres, generationem, nutritionem, au­
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              gmentum. </s>
              <s id="s.012559">Quatuor his ſeruientes: attra­
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              ctionem, quæ fit à magno calore, & multo
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              humido: retentricem, quæ ſpecies attra­
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              ctionis leuis: nam quæ attrahit, retinet
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              etiam, ideò à maiore calore trahitur, & ca­
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              lore ille humido non indiget. </s>
              <s id="s.012560">Si verò calor
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              ſit paruus, & humidum abundet, expellitur:
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              cum verò calor, & humidum maxima ſunt,
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              concoquitur. </s>
              <s id="s.012561">Maximus igitur calor aut cum
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              maximo humido eſt, & concoquit: aut cùm
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              mediocri, & trahit: mediocris calor cum
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              multo humido expellit, abſque humido
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              retinet. </s>
              <s id="s.012562">Sunt & tria genera cauſarum,
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              trium virtutum in animalibus præter has:
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              nam cùm quæ retinet, trahit, expellitve,
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              non tamen quæ concoquit, fieri poſſint à
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              villis ſeu fibris: fiunt etiam à muſculis vo­
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              luntati obedientibus: tertio a vacuo, vt in
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              corde. </s>
              <s id="s.012563">De his verò aliàs dictum eſt. </s>
              <s id="s.012564">Expul­
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              tricis in plantis: indicia, & exemplum à la­
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              chrymis earum, ſumendum eſt: nam odiſſe
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              videntur, quod expellunt, & fugiunt, quan­
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              tum licet. </s>
              <s id="s.012565">Verùm cum inſtrumentis ad fu­
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              gam aptis careant, expellunt potiùs. </s>
              <s id="s.012566">At ani­
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              malium nonnulla genera, vt grues ac hirun­
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              dines, verno tempore ad nos veniunt, æſtuo­
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              ſam regionem fugientes: autemno timen­
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              tes hyemem, in calidas regiones caternatim
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              commigrant, vnde videntur in Alexandria.
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              </s>
              <s id="s.012567">Iam infinitum ſit, ſi velim artium omnium
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              mira inuenta explicare, ſed hæc pro exem­
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              plo ſunt. </s>
              <s id="s.012568">Animaduerti ſaltantes procul ma­
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              gis è ſublimi loco ſaltare: id qua ratione fo­
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              ret, quærere volui. </s>
              <s id="s.012569">Igitur planum AB, in
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              plano ex A in C, ſaltus fiat: ſit murus erectus
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              ſuper planum A D: dico quòd ex D, ſalta-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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