Cardano, Girolamo, De subtilitate, 1663

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        <body>
          <chap>
            <p type="main">
              <s id="s.011952">
                <pb pagenum="622" xlink:href="016/01/269.jpg"/>
              tena ponderi iniecta, quæ ipſum interim
                <lb/>
                <arrow.to.target n="marg1644"/>
                <lb/>
              ſuſtineat, ab alio verò tigno iuxta AB fixo,
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              rurſus AD trabe remiſſa, H in quamcunque
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              volueris altitudinem trahi. </s>
              <s id="s.011953">Refert Munſte­
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              rus, in Alſatia rotis bigalibus, curribúſque è
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              bubali corio, è profundiſſimis puteis tanto
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              impetu aquam exhauriri, vt rotæ quamuis li­
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              gneæ ſint & madidæ, ignem tamen excu­
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              tiant. </s>
              <s id="s.011954">Videtur igitur inſtrumentum illud
                <lb/>
              tria egregia amplecti, altitudinem, capaci­
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              tatem, atque celeritatem.
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                <arrow.to.target n="marg1645"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.011955">
                <margin.target id="marg1643"/>
              Oleum illi­
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              tum ferro,
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              vel chalybi
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              duplicem
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              præſtat vti­
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              litatem.
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              </s>
              <s id="s.011956">Quæ maxi­
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              mè labi fa­
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              ciant.</s>
            </p>
            <p type="margin">
              <s id="s.011957">
                <margin.target id="marg1644"/>
              Rotæ quib.
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              </s>
              <s id="s.011958">maxima
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              aqua hauri­
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              tur.</s>
            </p>
            <p type="margin">
              <s id="s.011959">
                <margin.target id="marg1645"/>
              Curruum
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              ratio.</s>
            </p>
            <p type="main">
              <s id="s.011960">Sed his relictis, ad plauſtra & currus tran­
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              ſeundum eſt. </s>
              <s id="s.011961">Quæcunque igitur rotis maio­
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              ribus innituntur, in molli ſolo facillimè, ac
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              celerrimè mouentur, quòd hærens lutum
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              rotarum minimam occupet partem, atque
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              ideò parum impediat. </s>
              <s id="s.011962">Semper etiam maior
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              rota celerius ſpatium ſuperat vbi ferendo
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              ſufficiat oneri. </s>
              <s id="s.011963">Quantò etiam pauciores, eò
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              perficitur celerius iter. </s>
              <s id="s.011964">Nam plures ſi paruæ
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              ſunt, minore ambitu minus conficiunt ſpatij:
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              ſi magnæ, addunt vi grauitatem, nec tamen
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              plus amplectuntur ſpatij, ob id igitur ſe­
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              gnius mouentur. </s>
              <s id="s.011965">Quamobrem Imperatores
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              Romani eſſedo, id eſt, curru duarum magna­
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              rum rotarum vehebantur. </s>
              <s id="s.011966">Nam vbi pondus
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              haud admodum graue eſt, aut pluribus equis
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              trahitur, celerrimè perficitur iter. </s>
              <s id="s.011967">Eſſedis
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              hac de cauſa bellica immodici ponderis
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              tormento deferuntur. </s>
              <s id="s.011968">Rurſus facilitatis ra­
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              tio huic eſt ad vnguem exquiſitè contraria.
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              </s>
              <s id="s.011969">In ſolido enim ſolo plures paucis, & paruæ
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              magnis, ad facilitatem præſtant. </s>
              <s id="s.011970">Nam pon­
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              dus quaſi per rotas diſtribuitur: vnde fit
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              additio proportionum illarum, non multi­
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              plicatio. </s>
              <s id="s.011971">Exemplum: Sex duplæ inuicem du­
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              ctæ, ſexaginta quatuor ad vnum reddunt ra­
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              tionem. </s>
              <s id="s.011972">Eædem iunctæ faciunt duodecu­
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              plam. </s>
              <s id="s.011973">Tantum intereſt inter additionem &
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              multiplicationem. </s>
              <s id="s.011974">Quòd igitur vna rota
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              pondus refert librarum 60. ſex in rotis, 10.
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              tantum æquiualet, ita & à paruitate auxi­
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              lium ſumitur, nam eò facilius quò tardius:
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              at dictum eſt tardius pondera vehi, ac ferri
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              in paruis rotis, quàm magnis, eò igitur vt
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              facilius. </s>
              <s id="s.011975">Additur & tertia ratio facilitatis,
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              quia axis non premitur, ideò liberius cir­
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              cumagitur. </s>
              <s id="s.011976">Ob id igitur in paruis, atque hu­
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              milibus plauſtris, quæ axibus plurium rota­
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              rum non inſident, maxima pondera in firmo
                <lb/>
              ſolo committuntur. </s>
              <s id="s.011977">At in vdo, cœnoſóque
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              magnæ ac paucæ rotæ non ſolùm celerius,
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              multóque, ſed etiam facilius pondera ve­
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              hunt. </s>
              <s id="s.011978">Cúmque fixi radij è directo axis cele­
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              rius, & facilius circumuertantur rotam, pau­
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              lò exterius prominentes melius pondus ſu­
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              ſtinent, & recuperationi ſunt habiliores.
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              </s>
              <s id="s.011979">Quæcunque verò rotas poſteriores maiores
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              habent anterioribus, quaſi incumbente one­
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              re facilius trahuntur: cùm onus ſemetip­
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              ſum impellat: & in aſcenſu redduntur æqua­
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              les: licet in his iuſto plus partes anteriores
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              premantur.
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              </s>
            </p>
            <p type="margin">
              <s id="s.011980">
                <margin.target id="marg1646"/>
              Ergatarum
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              ratio.</s>
            </p>
            <p type="main">
              <s id="s.011981">Diximus de axibus ergatarum, quòd lon­
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              giores eſſe debeant: nam iuxta longitudinis
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              rationem ſingula capita minuunt pondus.
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              </s>
              <s id="s.011982">Duplicati igitur ad dimidium etiam dedu­
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              cunt. </s>
              <s id="s.011983">Ita quatuor ad quartam partem: adeò
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              vt ſi vnico axe cubitali quatuor homines
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              centum libras vehant, aut trahant, quatuor
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              axibus ſenum cubitorum iidem libras b s
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              mille, & quadringentas vehent, deducta ta­
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              men additione ponderis axium, quod mini­
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              mum eſt. </s>
              <s id="s.011984">Hæc autem ratio ſuperius dum de
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              ſtatera loqueremur demonſtrata eſt. </s>
              <s id="s.011985">Ita fit
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              vt maximis rotis hominibus per gradus ſa­
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              lientibus, maxima pondera circa axem fune
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              circumacta trahantur. </s>
              <s id="s.011986">Vt enim dimetientis
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              rotæ ad axis dimetientem, ita ponderis fune
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              eleuati ad pondus ac robur hominum, qui
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              intrò rotam circumagunt. </s>
            </p>
            <p type="margin">
              <s id="s.011987">
                <margin.target id="marg1647"/>
              Rota & cur
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              quomodo
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              pondera ma­
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              xima eleuet.</s>
            </p>
            <p type="main">
              <s id="s.011988">Similis in ictibus conſideratio: nam ſe­
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                <arrow.to.target n="marg1648"/>
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              curis ictu ferit, maximo pondere preſſa non
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              diuiduntur, & tamen pondus maiorem ha­
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              bebit vim ictu. </s>
              <s id="s.011989">Cauſa eſt, quòd aër non po­
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              teſt in ictu effugere: quanquam enim acuta
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              cuſpide, momento tamen tam paruo tempo­
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              ris effugere nequit. </s>
              <s id="s.011990">Ne igitur nimis denſe­
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              tur, cogitur in poros ingredi ſubiecti ligni,
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              atque cunei vice diuidere illud. </s>
              <s id="s.011991">Indicio eſt,
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              quòd paulò tardior ictus, maximum in diui­
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              dendo diſcrimen affert
                <expan abbr="dilabẽte">dilabente</expan>
              aëre. </s>
              <s id="s.011992">Quòd ſi
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                <arrow.to.target n="marg1649"/>
                <lb/>
              ictus, rei latæ velox ſit ingrediente aëre, vbi­
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              que reſoluitur quod ſubiectum eſt, quaſi in
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              nihil: vt qui feriuntur pila machinæ, quam
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              bombardam vocant. </s>
              <s id="s.011993">Sed nix homo magnum
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              aliquid, etiamſi leuiſſimum ſit, celerrimè
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              mouere poterit: ob hanc cauſam quicquid
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              ferietur in aërem, & ſpiritum reſolui neceſſe
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              eſt. </s>
              <s id="s.011994">Sed cur enſis in vertice ferit maximè?
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              </s>
              <s id="s.011995">quia motus centrum eſt ipſa manus: perife­
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              ria in cuſpide, ita interuallo iſto etiam ar­
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              ma, & aſſides diuiduntur. </s>
              <s id="s.011996">Sic calcitroſis equis
                <lb/>
              proximi, ſecuriores ſumus quàm paulò re­
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              motiores. </s>
              <s id="s.011997">Addit ad vim attractio non pa­
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              rum: quoniam ſi non trahatur, quod diui­
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              ſum eſt, impedit ne diuidatur: dum trahi­
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              tur raptim, quòd impedit aufertur: & inca­
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              leſcit quod diuiditur: hocque modo triplici
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              ratione ictus cum attractione ſumma gladij
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                <arrow.to.target n="marg1650"/>
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              parte melius ſecant. </s>
              <s id="s.011998">Haſtæ quoque longio­
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              res magis concutiunt, & magis perforant
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              breuibus, quòd maius habeant pondus, &
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              maioribus viribus, quamvis nos fallat opi­
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              nio, impelluntur. </s>
              <s id="s.011999">Horum memoria in men­
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              tem illud reuocauit, quòd niſi quotidie oc­
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              curreret, parum à miraculo abeſſe videretur.
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              </s>
              <s id="s.012000">Nauis onerata quam vix quadraginta boum
                <lb/>
              iuga mouerent, ventus celerrimè impellit:
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              quódque maius eſt, tenuis carbaſus, quàm
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              digitus terebraret impulſu, ſinuata tantam
                <lb/>
              molem ducit, & non diſrumpitur. </s>
              <s id="s.012001">Cauſa
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              facilitatis motus eſt triplex: magnitudo car­
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              baſi quauis magna venti colligitur, & alti­
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              tudo, vt demonſtratum eſt, ac impetus prio­
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              ris motus: nam ab initio vix mouetur. </s>
              <s id="s.012002">Vn­
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              de dubitationem haberet Ariſtoteles, qui
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              motus violentos minui iuxta finem exiſti­
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              mat. </s>
              <s id="s.012003">Conſtat autem ab æquali vento, ſi paria
                <lb/>
              ſint reliqua, motum nauis ſemper fieri cele­
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              riorem. </s>
              <s id="s.012004">An non ſemper, ſed ad metam vſque?
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              </s>
              <s id="s.012005">Palam enim ab initio augeri. </s>
              <s id="s.012006">Sed cauſa eſt,
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                <expan abbr="quoniã">quoniam</expan>
              etiam ceſſante eo quod mouet motus
                <lb/>
              ipſe (vt diximus) violentus augetur, quantò
                <lb/>
              magis nam manente cauſa. </s>
              <s id="s.012007">Magis etiam in
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              aqua, ob maius impedimentum. </s>
              <s id="s.012008">Tripliciter
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              igitur naues concitato iam curſu velociùs
                <lb/>
              mouentur, quàm ab initio: cauſam autem </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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