Cardano, Girolamo, De subtilitate, 1663

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000250">
                <pb pagenum="363" xlink:href="016/01/012.jpg"/>
              nimium comprimatur, aqua ſubſiſtit. </s>
              <s id="s.000251">Ea­
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                <arrow.to.target n="marg22"/>
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              dem ratione plumbea lamina lata aquæ ſu­
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              pernatat: nam deſcendendo partes, quæ in
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              medio ſunt, non habentes, quò diffugiant,
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              nimium comprimerentur: vel ſi antè di­
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              labantur, vacuum relinqui in medio ne­
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              ceſſe eſt: non poteſt igitur vllo pacto deſ­
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              cendere, niſi ad vnam partem priùs incli­
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              netur. </s>
            </p>
            <p type="margin">
              <s id="s.000252">
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              Situla aqua
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              plena
                <expan abbr="circũ-uoluta">circun­
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                uoluta</expan>
              cur
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              non effunda­
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              tur.</s>
            </p>
            <p type="margin">
              <s id="s.000253">
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              Plumbea, la­
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              mina lata ſi
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              æqualiter
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              aqua inſi­
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              ſtat, mergi
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              cur non poſ­
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              ſit.</s>
            </p>
            <p type="main">
              <s id="s.000254">Quòd igitur à raritate fiant hæc, & quo­
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              modo, oſtenſum eſt. </s>
              <s id="s.000255">Operæpretium autem
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              erit, vt demonſtremus, hos motus à vacuo
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              nulla ratione fieri poſſe. </s>
              <s id="s.000256">Hoc autem infrà per
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              exquiſitas rationes declarabitur. </s>
              <s id="s.000257">Nunc autem
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              ſufficiat tantum declaraſſe ſenſibili quodam
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              experimento, quantum ad rationem inſtru­
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              mentorum docendam ſufficiat. </s>
              <s id="s.000258">Nam ſi fatiſ­
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              cant rimis machinæ, iam nullus vacui metus
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              eſt, & tamen trahunt, ſed tantò debilius, &
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              maiore difficultate, quantò hiant magis.
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              </s>
              <s id="s.000259">Hócque fundamento machinæ omnes con­
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              ſtant, quæ alioquin ab indiuiſibili quadam
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              ratione pendêrent, eſſétque ob id omnes ſta­
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              tim inutiles, vel ſaltem non diuturnæ. </s>
              <s id="s.000260">In non
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              exactis ergo operibus atque vetuſtis manet
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              etiam vſus: fruſtatio verò pro erroris magni­
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              tudine. </s>
              <s id="s.000261">Attractio igitur à forma fit, quæ
                <expan abbr="dũ">dum</expan>
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              metuit aliam conſequi raritatem, ne pereat,
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              quantum poteſt, reſiſtit. </s>
              <s id="s.000262">Oſtendimur enim
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              ſuperiùs, mutata ſubſtantia atque denſitate,
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              mutari quoque formam. </s>
              <s id="s.000263">Quòd ſi metu vacui
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              fieret attractio, quaſi conſentiente vniuerſo,
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              eſſet hæc attractio infinita, ſed non eſt, ve­
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              rùm pro quantitate formæ, & elementi ac
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              inſtrumenti continentis. </s>
              <s id="s.000264">Nam canalis paruus
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              aquam modicam haurit, nec trahit plumbi
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              magnam molem. </s>
              <s id="s.000265">Indicio igitur hoc eſt, à
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              forma fieri
                <expan abbr="hãc">hanc</expan>
              attractionem, & pro viribus
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                <arrow.to.target n="marg23"/>
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              eius atque magnitudine. </s>
              <s id="s.000266">Eſt & tertia conie­
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              ctura, quòd plana quæ non fatiſcunt,
                <expan abbr="attamẽ">attamen</expan>
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              diſiunguntur. </s>
              <s id="s.000267">At hoc fieri nequiret, niſi ad­
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              miſſo vacuo. </s>
              <s id="s.000268">Inter plana igitur quæcunque
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              dum clauduntur, aër intercipitur, qui vetat
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              plana diſiungi quoad licet. </s>
              <s id="s.000269">Sed cum (vt dixi)
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              pro ſui robore ſolùm impediat, maiore nixu
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              vincitur. </s>
              <s id="s.000270">Solùm illud obiicies, quòd à minore
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              aëre minùs hæc diſiunctio impediretur, at
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              magis tamen impeditur. </s>
              <s id="s.000271">Vt enim magis pla­
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              na ad vnguem coierint, eò minùs aëris inter­
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              cipitur, & tamen eò difficilius diuelluntur.
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              </s>
              <s id="s.000272">Sed cauſa eſt, quia magis neceſſe eſt aërem
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              illum à propria forma recedere, quò magis
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              rareſcit. </s>
              <s id="s.000273">
                <expan abbr="Cõſequitur">Conſequitur</expan>
              enim, vt dictum eſt, alia
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              ſubſtantia quædam, & noua generatio, quæ
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              vt à priore magis recedit, eò maiore labore
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                <expan abbr="cõficitur">conficitur</expan>
              . </s>
              <s id="s.000274">At dices: Aëre rarefacto, quid aliud
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              poteſt generari quàm ignis? </s>
              <s id="s.000275">Ignis autem ca­
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              lidiſſimus: at inter plana nulla eſt manifeſta
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              caliditas, imò frigus. </s>
              <s id="s.000276">Sed non eſt ignis ſeu
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              æther calidus: hoc enim inferiùs declarabi­
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              tur. </s>
              <s id="s.000277">Quod enim humidum eſt, ſi attenuetur,
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              non in ignem, ſed in ætheris tranſit natu­
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              ram: aër autem humidus, & æther minimè
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              calidus eſt. </s>
              <s id="s.000278">Confeſtim verò alio in ingredien­
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              te aëre, fit mixtio. </s>
            </p>
            <p type="margin">
              <s id="s.000279">
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              Plana iun­
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              cta quomodo
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              diſiungi poſ­
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              ſint.</s>
            </p>
            <p type="main">
              <s id="s.000280">Hæc ſatis ſint de his motibus duobus prio­
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              ribus, tum quiete, quæ ab eis fit, exempla,
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              cùm hîc non ſit præſentis inſtituti de ma­
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              chinis loqui, ſed in duodecimo libro de
                <expan abbr="Rerũ">Rerum</expan>
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              varietate. </s>
              <s id="s.000281">His ad vnguem tot exempla ex­
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              plicaſſe ſufficiat, quot etiam modos: ſex enim
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              modis ſena ſufficiunt exempla. </s>
              <s id="s.000282">Ergo grauia
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              deorſum moueri, leuia ſursùm, palàm eſt.
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              </s>
              <s id="s.000283">Sed ſuperaddunt quidam ne hoc contenti,
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              leuia grauibus velle ſupereſſe, vnde etiam
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              aër ſi ſub aqua exiſtat, quamvis in propria
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              regione, ſuperiùs tamen emergere nititur: vt
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              in vrceis manifeſtum eſt, cum ſemipleni ver­
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              tuntur: & in veſica aëre plena, quæ aquæ im­
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              merſa eſt. </s>
              <s id="s.000284">Sed non eſt hic motus alius à pri­
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              mo: nam aqua ipſa cum ſit in ſublimi, cona­
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              tur, deſcendere, & ad illius deſcenſum aër ne
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              nimium conſtringatur, aſcendit. </s>
              <s id="s.000285">Sed in ve­
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              ſica, quæ in flumine eſt, cum aër ſit in loco
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              aquæ, aſcendere nititur: igitur ſufficiet vna
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              ratio motus in elementis ad locum ſunum.
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              </s>
              <s id="s.000286">Quòd autem aqua veſicam impellat ſursùm,
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              non aër aſcendat, patet, quoniam veſica ſub
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              terra poſita non aſcendit. </s>
            </p>
            <p type="main">
              <s id="s.000287">Quod verò dubitatione magis dignum eſt,
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              id eſt: Quomodo aqua tantùm aſcendat,
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              quantùm deſcendere poteſt, dum à motu ra­
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              ritatis adiuuatur: id ipſum plenius exemplo
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              patebit.
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              </s>
            </p>
            <p type="margin">
              <s id="s.000288">
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              Quomodo
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              aqua
                <expan abbr="tantũ">tantum</expan>
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              aſcendat,
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              quantum
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              poteſt deſ­
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              cendere.</s>
            </p>
            <p type="main">
              <s id="s.000289">Vas ſit aqua plenum, cuius ſupremum E,
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              imum F, in quo canalis A B C. </s>
              <s id="s.000290">Sit autem
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              CD, linea æqualiter à finitore diſtans, ſecun­
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              dùm quem libella ducitur. </s>
              <s id="s.000291">Impleatur autem
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              canalis ABC, aqua, & emittetur aqua per
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              C, dico, quòd exhauriet quicquid eſt aquæ
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              ſupra C D, lineam: nihil autem eius quod
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              eſt infra C D, lineam, ſed canalis plenus
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              pendebit, & vas vſque ad CD, aqua plenum
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              conſpicietur. </s>
              <s id="s.000292">Hoc itaque ſic eſſe, declarat
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              exemplum. </s>
              <s id="s.000293">Forſan quis dicat, hæc ad aquæ
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              tractationem debuiſſe transferri: ſed non
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              oportuit, quandoquidem ſeu aqua, ſeu vino,
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              oleo, lactéve vas plenum fuerit, nihil inter­
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              ſit. </s>
              <s id="s.000294">Itaque huius experimenti potiùs ratio
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              reddenda eſt. </s>
              <s id="s.000295">Aqua igitur quæ ſupra C D,
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              eſt, quum tanta ad vnguem ſit, quæ aſcendit,
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              quanta eſt illa, quæ ex C, effunditur, ſeu ca­
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              nalis latior ſit in C, quàm in A, ſeu arctior,
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              quia ſemper totus canalis ad vnguem ple­
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              nus eſt, leuior eſt aqua, quæ effunditur
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              per C. </s>
              <s id="s.000296">Quòd verò leuior ſit aqua in parte
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              ſupra C D, quàm in C, cauſa eſt, quia
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              aqua ſupra C D, deſcendere appetit, vt ſit
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              inferior illa, quæ eſt in C, igitur compri­
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              mit aquam, & in canalem impellit. </s>
              <s id="s.000297">Quæ
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              autem eſt infra C D, non appetit eſſe in C,
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              altiùs eſt loco eius, ideo non vult aſcende­
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              re. </s>
              <s id="s.000298">Sed aqua, quæ effluit ex C, non præ­
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              bet conſiderandi cauſam, cùm tamen ſit hu­
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              milior ipſa aqua, quæ in vaſe continetur:
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              quia attractio illa non fit, niſi continuita­
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              tis ratione: continuitas pendet ex ratione ra­
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              ritatis, quæ nulla eſſe poteſt, aqua iam
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              egrediente os canalis C. </s>
              <s id="s.000299">Denique tota hæc
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              contemplatio abſoluitur hoc argumento, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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