Cardano, Girolamo, De subtilitate, 1663

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            <p type="main">
              <s id="s.001685">
                <pb pagenum="394" xlink:href="016/01/043.jpg"/>
              per ſe, quòd validiſſimo ictu excutietur
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              verſus D, quia ſimul impetu iacientis, &
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              natura feretur in D. </s>
              <s id="s.001686">Par autem erat, quòd
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              debiliſſimus ictus eſſet illi contrarius, id
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              eſt, verſus C, validiſſimus autem ſuperio­
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              rum verſus D, quorum neutrum experi­
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              mento conſtat: ſed validiſſimus eſt ſupe­
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              riorum FE, mediocris FC, & debiliſſi­
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              mus FA. </s>
              <s id="s.001687">Cur ita? </s>
              <s id="s.001688">Sanè quoniam aër rectà
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              magis, quàm ad latera fertur, igitur debi­
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              liſſimus eſt ictus ex F in A. </s>
              <s id="s.001689">Debuerat iuxta
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              hanc rationem validiſſimus eſſe ex F in C,
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              ſed quia tota grauitas obſtat ponderis, ideò
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              vbi aër maximè mouetur, & pondus mi­
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              nus grauitatis habet, hoc autem eſt in linea
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              FE, ibi validiſſimè torquetur pila. </s>
              <s id="s.001690">Reli­
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              quum eſt igitur vt mediocriter ex F in C
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              feratur, id eſt, rectà in ſublime. </s>
              <s id="s.001691">Ne tamen
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              erres in ſagittis, quæ ob longitudinem &
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              alas velociùs quandoque feruntur ex F in
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              A, quàm in C, nunquam autem magis,
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              quàm in E: ob id qui muros quatiunt, ma­
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              chinas ad ſemiorthon, id eſt, ad libellam
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              FE collocant: nam tertia fermè parte ictus
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              augetur. </s>
              <s id="s.001692">Cùm verò pila ad ſupremum re­
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              ctà peruenerit, non per circulum, nec
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              rectà ſurſum illicò deſcendit, ſed media
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                <arrow.to.target n="marg175"/>
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              quaſi linea, quæ parabolæ fermè imita­
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              tur circum ambientem lineam, vt BC eſt,
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              demùm ex C in D motu grauis rectà ad vn­
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              guem.
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                <figure id="id.016.01.043.1.jpg" xlink:href="016/01/043/1.jpg" number="26"/>
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                <arrow.to.target n="marg176"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.001693">
                <margin.target id="marg174"/>
              Ratio motus
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              grauium
                <expan abbr="cũ">cum</expan>
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              violenter
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              mouentur.</s>
            </p>
            <p type="margin">
              <s id="s.001694">
                <margin.target id="marg175"/>
              Modus quo
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              grauia poſt
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              ictum deſ­
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              cendunt.</s>
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            <p type="margin">
              <s id="s.001695">
                <margin.target id="marg176"/>
              Cur vix vl­
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              lus feriatur
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              à plumbeis
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              pilulis, quæ
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              maximo nu­
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              mero in al­
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              tum mit­
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              tuntur.</s>
            </p>
            <p type="main">
              <s id="s.001696">Quæ igitur proiiciuntur, tribus ex moti­
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              bus conſtant, primo violento, vltimo ex­
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              quiſitè naturali, & medio ex vtroque mi­
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              ſto: propter tam multiplicem motus ratio­
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              nem metiri ad vnguem talia planè eſt im­
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              poſſibile, coniectura tamen aſſequi licet.
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              </s>
              <s id="s.001697">Debiliſſimi planè motus ex B in C: vnde
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              plumbeæ pilæ calore diſſipatæ, ob hoc etiam
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              minùs lædunt, vt vix vnum aut alterum,
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              ob ictus in ſublime deſtinatos, quum tamen
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              frequenter aut auium cauſa, aut exoneran­
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              dæ machinæ, emitti ſoleant pilæ ſemiuncia
                <arrow.to.target n="marg177"/>
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              grauiores, vulneratos aut grauiter percuſſos
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              videas inter tot millia. </s>
              <s id="s.001698">Sed quum per æqui­
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              diſtantem finitori lineam tam difficulter
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              grauia moueantur, cur eſt quòd ſuſpenſa
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              facilè adeò impelluntur, vt annulus filo ſuſ­
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              penſus ſpontè videatur moueri, atque ob id
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              etiam præcantationis præſe fert imaginem?
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              </s>
              <s id="s.001699">Cauſa eſt, quòd tota vis integra impellen­
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              ti relinquitur: qui verò proiicit, duo facit,
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              ſuſtinet & impellit: at appenſo pondere,
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              quum ab alio iam ſuſtineatur: quicquid
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              virium eſt ad impulſum integrum manet.
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              </s>
              <s id="s.001700">At vero quum impellitur, tanta fermè vi
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              redit ad medium, quanta ab illo, depul­
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              ſum eſt: igitur quum ea vi iam depulſum
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              fit à medio, gratia exempli per cubiti ſpa­
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              tium, tantundem diſcedere in contrariam
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              partem neceſſarium erit, atque ita conti­
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              nuo ac alternato reditu tardiſſimè con­
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              quieſcere. </s>
              <s id="s.001701">Cùm igitur in annulo motus hic
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              vel occulta ſpirituum motione paululùm
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              iuuatur, adeò ſpontè augetur, vt verbis
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              vim fuiſſe credas. </s>
              <s id="s.001702">Quamobrem cùm pau­
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              lò concitatior eſt annuli motus, ipſo iam
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              ( vt dixi ) ſeipſum mouente, videtur annu­
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              lo dæmon ineſſe, qui annulum moueat. </s>
              <s id="s.001703">Eſt
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              autem motus hic etiam in filo longiore fa­
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              cilior, euidenti demonſtratione. </s>
              <s id="s.001704">Sit enim
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              annulus in F, & moueatur per BC, ſuſ­
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              penſus in A, & rurſus ſuſpenſus in A po­
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              natur in G, & moueatur per DHE, quæ ſit
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              æqualis BFC, & L centrum terræ: con­
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              ſtat igitur, quod dum eſt in F, mouebitur
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              contra naturalem motum per FG: & dum
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              eſt in H, per HK, ſed HK eſt breuior FG,
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              vt in primo de Circulis demonſtrauimus.
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              </s>
              <s id="s.001705">Igitur cùm potentia mouens eadem ſit, &
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              quod mouetur idem, & maius tranſeat
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              ſpatium in F quàm in H, à centro, ſeu ma­
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              gis aſcendat, tranſibit illud in longiori tem­
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              pore: igitur ſi in æquali tempore debent
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              moueri, minore impetu indiget H, quàm F,
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              & ideò quantò altiùs ſuſpenditur, eò faci­
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                <figure id="id.016.01.043.2.jpg" xlink:href="016/01/043/2.jpg" number="27"/>
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              liùs mouetur mobile, & minori labore.
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              </s>
              <s id="s.001706">Cùm igitur filum longum fuerit, initium
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              motus ducet, vel ab incauto manuum mo­
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              tu, vel ab aëre, vel à ſpiritibus ipſis, quo­
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              rum vis etiam per filum deſcendit. </s>
              <s id="s.001707">Ita adeò
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              facili motu illius, & tot cauſis mouenti­
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              bus, nil mirùm immotis digitis, & fili ini­
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              tio annulum moueri, quo moto vix ceſſa­
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              tionis, cùm graue ( vt dixi ) appenſum tam
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              pertinaciter ſeipſum moueat, initium pote­
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              rit inuenire: atque hoc modo præcantatio­
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              ne moueri videtur. </s>
            </p>
            <p type="margin">
              <s id="s.001708">
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              De motu
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              annuli.</s>
            </p>
            <p type="main">
              <s id="s.001709">Sed poſtquam hæc clara ſunt: dubitabit
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              aliquis, cur tenuia corpora non ſolum mo­
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              tum velocem admittunt, quòd rationi con­
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              ſonum eſt, ſed etiam faciunt, quod diſſonum
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              eſt? </s>
              <s id="s.001710">Nam impulſus aquæ minùs violentus
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              eſt, cum alicui rei intruditur, quàm aëris, &
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              aëris, quàm ignis, Indicio fuit inſtrumen­
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              tum, quod ( vt audio ) nam non vidi, Ger­
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              manus attulit, vlnas longum 20. ex cupreſ­
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              ſo, cuius foramen adeò anguſtum erat, vt
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                <arrow.to.target n="marg178"/>
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              cicerem etiamſi rotundus fuiſſet, non eſſet
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              admiſſurum. </s>
              <s id="s.001711">Craſſitudo vlna minor. </s>
              <s id="s.001712">Impel-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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