Cardano, Girolamo, De subtilitate, 1663

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000369">
                <pb pagenum="366" xlink:href="016/01/015.jpg"/>
              alia rota cum paxillis, vt in molendinis fieri
                <lb/>
              ſolet aut manubrio C, dentes verò in eius
                <lb/>
              exteriore ſuperficie reſpicientes cylindrum
                <lb/>
              ſeu columnam FG, erectam ad perpendicu­
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              lum plani F H. </s>
              <s id="s.000370">In quo plano etiam rota ſu­
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              perſtans fixum habet palum, cui axis infi­
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              gitur. </s>
              <s id="s.000371">In FG, autem columna, DE, cur­
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              riculum dentatum eſt. </s>
              <s id="s.000372">Itaque quum rota
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              A B, circumuertitur ſuper axe CK, motu
                <lb/>
              ex A, in B, ſeu A, ſurſum deorſum, F G,
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              cylindrus circumuertitur ex D E, verſus
                <lb/>
              K, ſeu ex dextro in ſiniſtrum, quare con­
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              tingit tranſlatio motus, quæ erit eò velo­
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              cior, quò numerus dentium A B, rotæ,
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              plures continebit dentes circuli D E. </s>
              <s id="s.000373">His
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              autem vtemur ad machinæ Auguſtanæ in­
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              tellectum. </s>
            </p>
            <p type="main">
              <s id="s.000374">His modò viſis, poſtquam ſermonem de
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              motibus omnibus generalibus fermè abſol­
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              uimus, quarto exemplo in libramento aqua­
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              rum declarato, Heronis autem machina in
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              compoſitis elementorum motibus ſatisfa­
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              ciente, vt in vniuerſum pro decem modis
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              decem exempla ſubiecerim, colligere illa in
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              vnum breuiter operæ pretium erit. </s>
              <s id="s.000375">Quieti
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              ob raritatem lucernæ exemplum appoſui­
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              mus. </s>
              <s id="s.000376">Motui à raritate fiſtulam in vaſe col­
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              locatam, vbi de aquæ deſcenſu egimus.
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              </s>
              <s id="s.000377">Quieti ob denſitatem plumbi laminam, tum
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              coria ſuper aquam ſparſa. </s>
              <s id="s.000378">Motui ob denſi­
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              tatem impulſum bellicarum machinarum.
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              </s>
              <s id="s.000379">Motui attractionis ob raritatem, & impul­
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              ſus ob denſitatem, in Cteſibica machina.
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              </s>
              <s id="s.000380">Vtriuſque verò motus, tum etiam quietis
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              ob raritatem, Brambilica machina exem­
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              plum erit. </s>
              <s id="s.000381">Motus leuis elementi, nauigij re­
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              cuperationem: grauis verò, ſimplicis horo­
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              logiorum motum ſubiecimus. </s>
              <s id="s.000382">Grauis, ſed
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              ſæpiùs repetiti, follium alternam iactatio­
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              nem. </s>
              <s id="s.000383">Grauis ac leuis ſimul ad vnum finem
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              tendentium, Heronis machinam. </s>
            </p>
            <p type="main">
              <s id="s.000384">Ergo ſic poterat videri tractatio hæc ab­
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              ſoluta: ſed non omnia ſumpſimus genera.
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              </s>
              <s id="s.000385">Decem enim hæc exempla duobus conti­
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              nentur generibus: altero, quòd vnum tan­
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              tùm habet motorem, vt Heronis machina:
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              reliquo, quod duos, ſed diuerſos habet mo­
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              tores, vt Brambilica. </s>
              <s id="s.000386">Supereſt tertium ge­
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              nus, in quo illæ continentur machinæ, quæ
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              plures habent motores, ſed non diuerſos:
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              quod quidem videtur eſſe nobiliſſimum, quia
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              motui principali, ſeu
                <foreign lang="grc">αὐτοκινέτῳ</foreign>
              magis aſſi
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              milatur. </s>
              <s id="s.000387">Contingit is motus, quum aqua,
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              gratia exempli, rotam, qua aqua effunditur
                <arrow.to.target n="marg31"/>
                <lb/>
              verterit. </s>
              <s id="s.000388">Atque hoc in genere primum eſt
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              Archimedis inuentum Cochlea appellata,
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              cuius meminit Diodorus Siculus in antiqua
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              hiſtoria bis, dicens Ægyptum ſiccatam
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              beneficio cochleæ ab Archimede inuentæ.
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              </s>
              <s id="s.000389">Quod ſi ita eſt, cùm Archimedes ſecundi
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              belli Punici temporibus floruerit, neſcio
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              quo pacto antiquo tempore bene potuerit
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              Ægyptus habitari. </s>
              <s id="s.000390">Vtcunque tamen res ſe
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              habeat, inſtrumentum id nobiliſſimum pro­
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              culdubio eſt, atque tali artifice haud indi­
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              gnum. </s>
              <s id="s.000391">Meminit huius Vitruuius in fine ſui
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              operis. </s>
              <s id="s.000392">Sed Galeaz de Rubeis ciuis noſter,
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              fabérque ferrarius, cuius infrà mentionem
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              facturi ſumus, cùm iam olim inuentam ip­
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              ſe, quaſi primus auctor exiſtimaret reperiſſe,
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              præ lætitia inſaniuit. </s>
              <s id="s.000393">Vidimus illum verſan­
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              tem truſatilem machinam, ac paulò pòſt
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              mente excuſſum. </s>
              <s id="s.000394">Erat autem machina
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              talis: </s>
            </p>
            <p type="margin">
              <s id="s.000395">
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              Cochlea Ar­
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              chimedis.</s>
            </p>
            <figure id="id.016.01.015.1.jpg" xlink:href="016/01/015/1.jpg" number="12"/>
            <p type="main">
              <s id="s.000396">Lignum A H, ſolidum, rectum, rotun­
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              dum, æqualéque, ac tam longum vt incli­
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              natum ad ſuperficiem aquæ, infixúmque
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              alueo quantum opus eſt, ſupra ipſam aquam
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              promineat, canali ( vt vides ) metallico
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              ſimplici, ad cochleæ imaginem fabricato,
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              circumtegatur. </s>
              <s id="s.000397">Sunt qui multiplici vtantur:
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              tres mihi neceſſarij eſſe videntur, quique
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              adeò ſenſim aſcendant, vt omnia ſpatia com­
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              pleantur. </s>
              <s id="s.000398">Duo ora habet canalis, inferius
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              quidem latius, anguſtius quod ſuperius eſt.
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              </s>
              <s id="s.000399">Vocetur autem illud K. </s>
              <s id="s.000400">Demonſtrandum
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              eſt igitur, quòd vbi terminis A & H ti­
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              gnum claudatur, ita vt circumuerti poſſit,
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              quod motu aquæ circumuertetur. </s>
              <s id="s.000401">Secundò,
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              quòd vbi circumagatur aqua aſcendet, ef­
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              fundeturque per K. </s>
              <s id="s.000402">Nam pinnæ quæ additæ
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              ſunt B C D E F G, ſeu inter ſpatia alter­
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              utrinque, ſeu in coniunctionibus tigni cum
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              canali, occurrentes aquæ, neceſſariò ver­
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              tent illud inſtrumentum: quia augeri poſſunt
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              longitudine ac latitudine: pondus verò AH,
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              paruum eſt, & longè minus etiam factum
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              ob inclinationem, & axes in annulis poſi­
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              tos, ita vt circumagi poſſint. </s>
              <s id="s.000403">Oſtendunt id
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              etiam molæ in fluminibus Pado atque Tici­
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              no, vbi quanquam leniſſimè fluant aquæ,
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              hoc tamen ingenio lapides molares circum­
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              acti terunt, ac molunt triticum. </s>
              <s id="s.000404">Sed quòd
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              aqua ipſa aſcendat ex L, in K, patet: quum
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              enim L, eleuatur, pars quæ ſuccedit fit humi­
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              lior, igitur aqua deſcendet, qua aſcendente
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              iterum pars ſuccedens deſcendit: eadémque
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              ratio ſemper oſtendit
                <expan abbr="aquã">aquam</expan>
              verſus K, tendere:
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              hócque experimento pulcherrimè congruit,
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              & nos non ſemel periculum de hoc fecimus.
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              </s>
              <s id="s.000405">Conuerſo igitur axe ſeu tigno in fœmineis
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              cardinibus A, & H, in quibus intruditur,
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              donec aqua canalis impletus fuerit, effun­
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                <arrow.to.target n="marg32"/>
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              deretur per K, ſuper planum ripæ. </s>
              <s id="s.000406">Ex quo
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              non videtur hæc ratio concludere, aqua
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              perpetuò deſcendit, igitur in fine erit in hu­
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              miliore loco, quàm in initio. </s>
              <s id="s.000407">Sed tamen non
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              ſemper deſcendit, verùm pars quæ deſcen­
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              dit maior, impellit minorem, cogitque aſ­
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              cendere. </s>
              <s id="s.000408">At cùm effundi cœperit, tunc tam
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              machina faciliùs vertetur, & aqua quaſi
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              ſponte effluet, propter ea, quæ de aquæ deſ­
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              cenſu iam demonſtrauimus. </s>
              <s id="s.000409">Sunt qui canali
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              tabulas affigant, nectántque omnia ſimul,
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              vt machina robuſtior ac firmior euadat, pa­
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              xillos tabulis, non tigno, ob commodita­
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              tem maiorem inſerentes. </s>
              <s id="s.000410">Dubitabit autem
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              meritò aliquis, cur aſcendente parte canalis
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              iuxta B, cùm tam L, quàm C, deſcendant,
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              aqua non non redeat in L, & rurſus effun­
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              datur ( nam L, humilior eſt quàm C, ) &
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              ex eadem parte. </s>
              <s id="s.000411">Duplex huius ratio eſt: al­
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              tera, quòd aqua quæ eſt in B, impellitur </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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