Cardano, Girolamo, De subtilitate, 1663

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000602">
                <pb pagenum="372" xlink:href="016/01/021.jpg"/>
              poſita angulo coni. </s>
              <s id="s.000603">Cum itaque fuerit poſita
                <lb/>
              virga æqualis CL ponderis vnciarum 7, &
                <lb/>
              librile in B, ita quod KL ſit 10. & KC, 4. & G
                <lb/>
              libra vna, ſic conſtituemus ſtateram. </s>
              <s id="s.000604">Ducam
                <lb/>
              pondus LK, quod eſt 5, in ſe, fit 25, diuido
                <lb/>
              per pondus KC, quod eſt 2, fit 12 1/2, cui ad­
                <lb/>
              do vncias 5, LK, fit 17 1/2: ponam igitur CD
                <lb/>
              vinculum ferreum vncias 5 1/2, & relinque­
                <lb/>
              tur pondus LK vnius libræ. </s>
              <s id="s.000605">Cùm igitur po­
                <lb/>
              ſuerimus G in K ęquabitur librę, & aliam
                <lb/>
              libram oportebit addere in D propter LK,
                <lb/>
              igitur in K oſtendemus duas libras, & ſic ſcri­
                <lb/>
              bemus, deinde S 3, in T 4, in F 5. in V 6, in L,
                <lb/>
              quis ſpatiis. </s>
              <s id="s.000606">Ex hoc patet quòd omnia hæc
                <lb/>
              ſpatia per vncias diſtribui poterunt, præter
                <lb/>
              primum BK. </s>
              <s id="s.000607">Poſſemus tamen & ipſum di­
                <lb/>
              uidere, vt in B libra intelligatur, & AB in
                <lb/>
              K vncię per æqua ſpatia additę
                <expan abbr="ſignificabũt">ſignificabunt</expan>
              ,
                <lb/>
                <arrow.to.target n="marg50"/>
                <lb/>
              prima 13. ſecunda 14. tertia 15. & ita de aliis. </s>
            </p>
            <p type="margin">
              <s id="s.000608">
                <margin.target id="marg50"/>
              Cur libræ
                <lb/>
              ſunt plerum­
                <lb/>
              que exactio­
                <lb/>
              nes ſtateris.</s>
            </p>
            <p type="main">
              <s id="s.000609">Patet autem cauſa ex his, quare librę tri­
                <lb/>
              bus cauſis ſtateris ſint exactiores. </s>
              <s id="s.000610">Hoc au­
                <lb/>
              tem ab initio propoſitum fuit. </s>
              <s id="s.000611">Nam in ſta­
                <lb/>
              tera difficile eſt virgulam adeò exactam in
                <lb/>
              magnitudine conſtituere: & ſi etiam ſit in
                <lb/>
              magnitudine, non erit in pondere: vix enim
                <lb/>
              hoc aſſequi poſſumus. </s>
              <s id="s.000612">Secundò difficillimum
                <lb/>
              eſt per æqualia interualla omninò ad amuſ­
                <lb/>
              ſim diuidere LB. </s>
              <s id="s.000613">Tertiò pondus rarò in ex­
                <lb/>
              tremo C appendi ſolet, quod cùm citra
                <lb/>
              appenditur, confuſionem parit. </s>
            </p>
            <p type="main">
              <s id="s.000614">
                <expan abbr="Sũt">Sunt</expan>
              & additamenta multa quæ
                <expan abbr="vitiãt">vitiant</expan>
              ſtate­
                <lb/>
              ram, horum nullum in libra eſt. </s>
              <s id="s.000615">Ob id præ­
                <lb/>
              cioſa non in ſtatera ſed libra ſolent exami­
                <lb/>
              nari. </s>
              <s id="s.000616">Multum autem refert ad exactam ſta­
                <lb/>
              terę ſtructuram, vt G leue ſit, tum etiam
                <lb/>
              LC, & quod LB tripla ſit BC. nam ſic LK
                <lb/>
              æqualis erit KC, & quòd vincula CD in ex­
                <lb/>
              tremo ſint LC, & ęqualis ponderis cum LK.
                <lb/>
                <arrow.to.target n="marg51"/>
                <lb/>
              Hoc enim ſtaterę genus, librę
                <expan abbr="proximũ">proximum</expan>
              erit. </s>
            </p>
            <p type="margin">
              <s id="s.000617">
                <margin.target id="marg51"/>
              Vtres quan­
                <lb/>
              tum ponderis
                <lb/>
              in aqua ſu­
                <lb/>
              ſtineant.
                <lb/>
              </s>
              <s id="s.000618">Quomodo
                <lb/>
              homo aquæ
                <lb/>
              immobilis ac
                <lb/>
              ſupinus ſu­
                <lb/>
              perſtet.</s>
            </p>
            <p type="main">
              <s id="s.000619">Quantum verò ponderis vtres in aqua
                <lb/>
              ſuſtineant pro pontibus conſtruendis, expe­
                <lb/>
              rimentum docet. </s>
              <s id="s.000620">Nam veſica plena aëre,
                <lb/>
              quę capax fuit quinque librarum aquę &
                <lb/>
              vncię, pondus librarum quatuordecim ac ſe­
                <lb/>
              mis laterum ſuſtinebat: quo fit vt in flumi­
                <lb/>
              num aqua triplum fermè ponderis aquæ,
                <lb/>
              cuius ſunt capaces vtres, continere poſſint.
                <lb/>
              </s>
              <s id="s.000621">Illud etiam non prętermittendum, ex denſi­
                <lb/>
              tatis ratione oriri, vt homines cùm ita ſe
                <lb/>
              continuerint ſupini in aqua, vt velut iacula­
                <lb/>
              tores in funibus nullam penitùs in partem
                <lb/>
              flectantur immobiles, tum nequaquam mer­
                <lb/>
              gi. </s>
              <s id="s.000622">Hoc tamen cùm per ſe ſit difficillimum,
                <lb/>
              ob motum etiam & aquæ inęqualitatem
                <lb/>
              etiam redditur difficiliùs. </s>
              <s id="s.000623">Atque hacte­
                <lb/>
              nus de rerum mortalium principiis di­
                <lb/>
              ctum ſit. </s>
            </p>
            <figure id="id.016.01.021.1.jpg" xlink:href="016/01/021/1.jpg" number="20"/>
            <p type="main">
              <s id="s.000624">
                <emph type="center"/>
              LIBER SECVNDVS.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s id="s.000625">
                <emph type="center"/>
              De Elementis & eorum motibus &
                <lb/>
              actionibus.
                <emph.end type="center"/>
                <lb/>
                <arrow.to.target n="marg52"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.000626">
                <margin.target id="marg52"/>
              De elemen­
                <lb/>
              torum nu.</s>
            </p>
            <p type="main">
              <s id="s.000627">NVNC verò de Elementis aga­
                <lb/>
              mus, quæ forma & materia
                <lb/>
              prima conſtant, & animata
                <lb/>
              quaſi videntur: ea Græcis
                <lb/>
                <foreign lang="grc">σοιχεῖα</foreign>
              vocant. </s>
              <s id="s.000628">Perdiſcere au­
                <lb/>
              tem primum oportet, quot & quænam ſint.
                <lb/>
              </s>
              <s id="s.000629">Ariſtoteles quatuor exiſtimat, terram,
                <expan abbr="aquã">aquam</expan>
              ,
                <lb/>
              aërem, atque ignem. </s>
              <s id="s.000630">Primùm enim quatuor
                <lb/>
              qualitates primæ ſunt. </s>
              <s id="s.000631">Hæ ſolæ non conſti­
                <lb/>
              tuunt elementum, quia vim non haberent
                <lb/>
              agendi ac patiendi: nec pluſquam duæ ſi­
                <lb/>
              mul eſſe poſſunt, quin contraria ſimul ſint.
                <lb/>
              </s>
              <s id="s.000632">Nam calidi, frigidi, ſicci atque humidi, ſi
                <lb/>
              tria quomodolibet acceperis, contraria ac­
                <lb/>
              cipere neceſſe eſt. </s>
              <s id="s.000633">Sed nec calidum cum fri­
                <lb/>
              gido, nec ſiccum cum humido iungi poteſt.
                <lb/>
              </s>
              <s id="s.000634">Igitur binis iunctis qualitatibus neque con­
                <lb/>
              trariis, ſimul tantùm quatuor fient coniu­
                <lb/>
              gationes, quæ quatuor elementa conſti­
                <lb/>
              tuent. </s>
              <s id="s.000635">Inter imum etiam locum atque ſu­
                <lb/>
              premum, ſimpliciter duo loca intercidere
                <lb/>
              neceſſe eſt, imum non exquiſitè, atque ſu­
                <lb/>
              premum: atque eo totidem ſimplicia cor­
                <lb/>
              pora. </s>
              <s id="s.000636">Videmus etiam, & ſi quid probabilia
                <lb/>
              argumenta faciunt, in miſtis ipſis quatuor
                <lb/>
              elementa: nam de terra, aëre & aqua, nemo
                <lb/>
              dubitare poteſt ob magnitudinem, & maxi­
                <lb/>
              mas moles, vt mare aquarum, aëris & terræ
                <lb/>
              in vniuerſo: ignis verò incrementa, & po­
                <lb/>
              tentiam, ac ſimplicitatem, cuius etiam fons
                <lb/>
              in Lunæ concauo eſſe creditur. </s>
              <s id="s.000637">Plures etiam
                <lb/>
              exiſtimant in diſtilationibus hæc quatuor
                <lb/>
              videri: & humores totidem in animalibus
                <lb/>
              ſenſus depræhendi. </s>
              <s id="s.000638">Quinetiam multi arbi­
                <lb/>
              trantur ob hoc Cometes fieri, quòd ſub cœ­
                <lb/>
              lo ab ignis elemento vapores accendantur.
                <lb/>
              </s>
              <s id="s.000639">Sed certè ſub cœlo Lunæ nullus eſt ignis:
                <lb/>
              nam quum cœlum puriſſima res ſit, non
                <lb/>
              decuit ſub omnis qualitatis experte re, ar­
                <lb/>
              dentiſſimam collocaſſe. </s>
              <s id="s.000640">Natura enim ſem­
                <lb/>
              per extrema mediis iungit. </s>
              <s id="s.000641">Inter carnem
                <lb/>
              enim & os, membranam: inter os & liga­
                <lb/>
              menta, cartilagines: inter os & cerebrum,
                <lb/>
              quòd carne cerebrum eſſet mollius, dupli­
                <lb/>
              cem membranam, ac duriorem oſſi pro­
                <lb/>
              pinquiorem collocauit. </s>
              <s id="s.000642">Nec motus veloci­
                <lb/>
              tas, caloris aut cauſa, aut argumentum eſſe
                <lb/>
              poteſt. </s>
              <s id="s.000643">Nanque ea quæ conſtant, etſi motu
                <lb/>
              accendantur, vt lapides, plumbum & anima­
                <lb/>
              lia, quæ tamen diſſipantur, quò celerius mo­
                <lb/>
              uentur, eò fiunt frigidiora, vt aqua & aër:
                <lb/>
              venti enim validi omnes frigidi, & flumina
                <lb/>
              celeriter fluentia frigidiſſimas habent aquas.
                <lb/>
              </s>
              <s id="s.000644">Eſt etiam aliud non leue argumentum huius </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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