Cardano, Girolamo, De subtilitate, 1663

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      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000331">
                <pb pagenum="365" xlink:href="016/01/014.jpg"/>
              ex leuioribus: atque ideò ex mari, quàm ex
                <lb/>
              fluminibus, vel lacubus. </s>
              <s id="s.000332">Altera quòd cymbæ
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              in mari plus ſuſtinent ponderis: reliqua, quòd
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              nauigium in ea aqua minùs graue eſt. </s>
              <s id="s.000333">Opor­
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              tet
                <expan abbr="hãc">hanc</expan>
                <expan abbr="autẽ">autem</expan>
              ob cauſam animaduertere, cùm,
                <lb/>
              vt dictum eſt, nauigium grauius reddatur in
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              aquæ ſuperficie
                <emph type="italics"/>
              (
                <emph.end type="italics"/>
              quia partim eſt in aëre)
                <lb/>
              quàm in imo, vt quantò magis eleuatur à
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              cymbis, eò plures ac maiores cymbæ alligen­
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              tur, ne decepti hac ratione non ſolùm denuò
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              mergatur, ſed & impetu adiecto omnes
                <expan abbr="ſecũ">ſecum</expan>
                <lb/>
              cymbas in profundum trahat. </s>
              <s id="s.000334">Dubitabit au­
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              tem aliquis, cur exoneratis cymbis B, imple­
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              tis autem aliis, per A, ſignificantur, non deſ­
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              cendat nauis, quæ eleuata fuit ab A, cymbis
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              vacuis? </s>
              <s id="s.000335">Non enim plenæ poſſunt ſuſtinere
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              pondus. </s>
              <s id="s.000336">Cauſa eſt, quia factis iam funibus
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              æqualibus cymbarum A, & B, cùm iam va­
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              cuum ſeu inane, vel aër, qui in cymbis con­
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              tinetur potentior ſit nauis pondere, plus tra­
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              het inane cymbarum B, quàm remittet gra­
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              uitas aucti poderis cymbarum A. </s>
              <s id="s.000337">Itaque hac
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              ratione perpetuò nauis aſcendet: hoc dunta­
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              xat obſeruato, vt plenarum cymbarum funes
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              eò ſint vacuarum cymbarum funibus breuio­
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              res, quantò pondus lapidum eas cymbas de­
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              primit. </s>
              <s id="s.000338">Sed de ſimplici leuis motu ſurſum ſa­
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              tis, nunc de motu, qui ex graui & leui com­
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              ponitur, dicendum erit. </s>
              <s id="s.000339">Pro cuius exemplo
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              mirificè ſe offert Heronis machina, quam
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              nos ſæpè tractauimus. </s>
              <s id="s.000340">Ea ſic ſe habet: A, la­
                <lb/>
                <arrow.to.target n="marg28"/>
                <lb/>
                <figure id="id.016.01.014.1.jpg" xlink:href="016/01/014/1.jpg" number="9"/>
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              brum aqua plenum: ſub quo vas B, & ipſum
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              aqua plenum, ſit iunctum A, vt ex altero in
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              alterum aqua permeare non poſſit. </s>
              <s id="s.000341">Sub B, vas
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              aliud, quod vocetur C, inane. </s>
              <s id="s.000342">Fiſtula D, fera­
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              tur ex B, in C, cuius ſummum os fermè ad
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              labrum perueniat. </s>
              <s id="s.000343">Fiſtula alia E, quæ ſuper
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              labrum non parùm aſcendat, & inſerta labro,
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              in medio penetret vſque ad imum primi va­
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              ſis, non tamen ipſi imo iungatur. </s>
              <s id="s.000344">Alia fiſtula
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              F, cuius ſupremum in imo labri oſculum
                <expan abbr="ſitũ">ſitum</expan>
                <lb/>
              ſit, inferiùs os in ipſo ſepto inter duo vaſa fi­
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              niatur, ita
                <expan abbr="tamẽ">tamen</expan>
              vt aqua ex labro per ſuperius
                <lb/>
              os in vas C, deferatur. </s>
              <s id="s.000345">Tunc verò videmus
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                <expan abbr="aquã">aquam</expan>
              , quę eſt in B, vaſe, per E, fiſtulam emitti,
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              ac eò donec finiatur labri aqua vſque perſe­
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              uerare. </s>
              <s id="s.000346">Id quomodo fiat ex duobus motibus
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              compoſitis demonſtrandum. </s>
              <s id="s.000347">Aqua deſcen­
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              dens per F, fiſtulam, cùm aër in C, non poſſit
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              ſubſiſtere, aſcendit per D, fiſtulam in vas B,
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              ſuperiùs. </s>
              <s id="s.000348">At verò cum ibi locus aqua plenus
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              ſit, cogitur aqua aſcendere per E, fiſtulam
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              preſſa ab aëre, atque ſic effunditur. </s>
              <s id="s.000349">Manife­
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              ſtum eſt igitur hîc duos eſſe motus: vnum ſe­
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              cundum naturam aquæ deſcendentis ex labro
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              in C, vas per F, fiſtulam, alterum aëris aſcen­
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                <arrow.to.target n="marg29"/>
                <lb/>
              dentis ex vaſe C, in vas B, quod
                <emph type="italics"/>
              (
                <emph.end type="italics"/>
              vt dictum
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              eſt) ab aqua ſursùm impellatur. </s>
              <s id="s.000350">Ab his igitur
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              duobus motibus naturalibus violentius im­
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              petus fit quo aqua ex vaſe B, per fiſtulam
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              aſcendit. </s>
              <s id="s.000351">Verùm motus grauis dum repetit
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              alternatim folles mouet, aut alias machinas,
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              quòd in machina Cteſibica demonſtrare
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              oportunum erat, vt emboli maſculi viciſſim
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              in modiolis aſcendere, deſcenderétque poſ­
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              ſent. </s>
              <s id="s.000352">Id autem ſic fit: Rota cum pinnis iux­
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              ta aquæ delabentis caſum ( vt ſolet fieri) ſta­
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              tuatur, vt ex aquæ perpetuo defluxu ſuper
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              pinnas rota circumuoluatur, in qua ſit axis
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              A, quem palàm eſt neceſſe fore, vt & ipſe
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              circumagatur. </s>
              <s id="s.000353">Rotæ deſcriptionem, vt rem
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              notiſſimam ac in molis omnibus conſpi­
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              cuam, prætermitto. </s>
            </p>
            <p type="margin">
              <s id="s.000354">
                <margin.target id="marg27"/>
              Nauigia fa­
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              ciliùs ex ma­
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              ri, extrahi,
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              quàm flumi­
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              nibus vel la­
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              cubus.</s>
            </p>
            <p type="margin">
              <s id="s.000355">
                <margin.target id="marg28"/>
              Machina
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              Heronis.</s>
            </p>
            <p type="margin">
              <s id="s.000356">
                <margin.target id="marg29"/>
              De motu al­
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              lernante.</s>
            </p>
            <figure id="id.016.01.014.2.jpg" xlink:href="016/01/014/2.jpg" number="10"/>
            <p type="main">
              <s id="s.000357">Trabs ſuperiacens tignis atque incluſa fo­
                <lb/>
              raminibus rotundis vocetur B, ita vt mobilis
                <lb/>
              ſit, ac vt in cardinibus circumuolui poſſit.
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              </s>
              <s id="s.000358">Iuxta huius extremum E, annulus infixus, cui
                <lb/>
              alter annulus cum ferrea virga F: hæ rurſus
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              in annulum finiatur, quem excipiat alter an­
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              nulus G, virga H, annexus: in extremo H, an­
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              nulus iunctus eſt, qui vnco ita annectitur in
                <lb/>
              ſummitate axis A, vt ſecum moueatur, ſed
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              redeunte axe, redit & annulus ad priſtinum
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              locum ac ſitum. </s>
              <s id="s.000359">Ex altera trabis parte duo
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              annuli ex aduerſo collocantur C, & D. </s>
              <s id="s.000360">Licet
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              & bis duos & tria paria ſic ex aduerſo collo­
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              care. </s>
              <s id="s.000361">Si igitur emboli aut folles alter C, fune
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              iungatur, alter D, circumuoluto axe, trahitur
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              primum trabs verſus D, túncque eleuatur
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              follium alter ex C, altero cadente D. </s>
              <s id="s.000362">Quum
                <lb/>
              verò rota dimidium axis circumuertit, annu­
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              lus in imo H, redit ad locum ſuperiorem &
                <lb/>
              impellit E, propter virgas, & trabs flectitur
                <lb/>
              verſus C, atque ſic mutata vice folles mo­
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              uentur. </s>
              <s id="s.000363">Nutat enim trabs dextra ac ſiniſtra
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              viciſſim, ſed non circumuoluitur. </s>
              <s id="s.000364">Ergo licet
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              multa paria follium annulis multis in trabe
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              ex aduerſo collocatis mouere, ſed robuſta vi
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              aquæ opus eſt. </s>
              <s id="s.000365">Licet & eidem axi alteram
                <lb/>
              trabem, quod fabri facere ſolent à ſiniſtra
                <lb/>
              iungere,
                <expan abbr="atq;">atque</expan>
              ſic numerus
                <expan abbr="folliũ">follium</expan>
              duplicabitur.
                <lb/>
              </s>
              <s id="s.000366">Nec alio opus eſt auxilio, aliáve
                <expan abbr="quã">quam</expan>
              quæ in
                <lb/>
              vno patefacta eſt induſtria, ſed ſola maiore vi. </s>
            </p>
            <p type="main">
              <s id="s.000367">Sed motuum tranſlatio, quæ ſolet in vſu
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              eſſe, tùm in molendinis, tum horologiis,
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              quamvis vulgata, tamen ſubtiliori conſtat
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              ratione.
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                <figure id="id.016.01.014.3.jpg" xlink:href="016/01/014/3.jpg" number="11"/>
                <lb/>
                <arrow.to.target n="marg30"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.000368">
                <margin.target id="marg30"/>
              Motuum
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              tranſlatio.</s>
            </p>
            <p type="main">
              <s id="s.000369">Sit igitur rota AB, quæ circumagi poſſit </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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