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