Cardano, Girolamo, De subtilitate, 1663

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              <s id="s.000411">
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              ab ea, quæ eſt eſt in L, ideo tranſit ad C,
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              & non redit: reliqua Geometrica, oſtendens
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              partem mediam inter L, & B, in conuer­
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              ſione altiorem eſſe, quàm ſit pars media in­
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              ter B, & O. </s>
              <s id="s.000412">Indicio etiam eſt, quòd plum­
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              bea ſphærula impoſita, cùm à nulla alia re
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              prematur, aſcendit tamen in K. </s>
              <s id="s.000413">Et demon­
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              ſtratio hæc eſt: Sit tignum A B, in plano
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              A C, eleuatio partis A D, tigni ſit D C,
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              eius partis cochleæ pars correſpondens AE,
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              & altitudo DE, ſit gratia exempli ſeſquial­
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              tera DC, & ducatur recta AE, erunt igitur
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              omnes lineæ inter A D, & A C, minores
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              lineis è directo conſtitutis inter AD, & AE,
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              ex demonſtratis in ſexto elementorum Eu­
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              clidis:
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                <figure id="id.016.01.016.1.jpg" xlink:href="016/01/016/1.jpg" number="13"/>
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              </s>
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            <p type="margin">
              <s id="s.000414">
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              Aliquid per­
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              petuò
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                dit</expan>
              , quod in
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              fine erit al­
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              tius.</s>
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            <p type="margin">
              <s id="s.000415">
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              Demonſtratio
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              oſtendens
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              quod cochlea
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              verſa graue
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              aſcendit.</s>
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            <p type="main">
              <s id="s.000416">Circumuertatur igitur AB, ita vt quando
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              E, erit in humillimo loco, pondus rotun­
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              dum in A, poſitum ſit in directo D. </s>
              <s id="s.000417">Quia
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              igitur D E, longior eſt D C, igitur ſi E,
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              erit in oppoſito ſui loci, erit infrà C: ſed
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              C, eſt in directo A, igitur pondus erit in­
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              feriùs quàm ab initio: ſed omnes lineæ ſer­
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              uant eandem rationem, & ſunt longiores
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              etiam in circumferentia A E, quàm in re­
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              cta A E, à linea A D, quia pars eſt minor
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              toto: igitur conuerſo A B, pondus deſcen­
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              det in AE. </s>
              <s id="s.000418">Sed omne graue liberum in mo­
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              tu deſcendit, igitur pondus perueniet ad E.
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              </s>
              <s id="s.000419">Sed quum erit in E, circumactum deſcen­
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              det verſus F, non verſus A, tum ob impe­
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              tum, tum quia pars quæ eſt inter A, & E,
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              aſcendit, nam in priore motu deſcenderat:
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              pars autem E F, adhuc deſcendit, igitur
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              pondus perueniet ex H, in A, quare ex A, in
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              B, multis conuerſionibus eadem ratione fa­
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              ctis. </s>
              <s id="s.000420">Facilè autem ligula circumdata calamo
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              hoc, quod tibi perdifficile forſan videtur, ex­
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              perieris. </s>
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            <p type="main">
              <s id="s.000421">Sed ad rem reuertor. </s>
              <s id="s.000422">Cochlea quam Vi­
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              truuius docet, alieno indiget auxilio, hæc
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              autem noſtra ſeipſam circunducit: ſed eò
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              faciliùs, quò ſpiræ canalis frequentiores
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              fuerint, & machina mollius aſcenderit. </s>
              <s id="s.000423">Quò
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              verò faciliùs circumagetur, eò ſerius: hoc
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              enim fermè generale eſt in omnibus machi­
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              nis. </s>
              <s id="s.000424">Ita contrariis rationibus celeriter aquam
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              tranſmittet, ſed difficiliùs reuertetur. </s>
              <s id="s.000425">Por­
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              rò difficultas facit vt machinæ magis atte­
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              rantur, & aquarum multitudine ac impetu
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              indigeamus. </s>
              <s id="s.000426">Verùm celeritatem cum diffi­
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              cutate eligemus, vbi torrens fuerit, & ripa­
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              rum altitudo immodica. </s>
              <s id="s.000427">Nam ſi inſtrumen­
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              ti aſcenſus mollis fuerit, reddetur inſtrumen­
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              tum ob longitudinem grauiſſimum. </s>
              <s id="s.000428">Eadem
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              in magnitudine & prauitate ratio. </s>
              <s id="s.000429">Nam par­
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              uum facilè circumagitur, ſed ſerò irrigat.
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              </s>
              <s id="s.000430">Vſus eius vbi modica terra eſt irriganda, &
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              flumen profundum, & leniter currit, & ripæ
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              altiores. </s>
              <s id="s.000431">In contrariis cauſis magnis vtemur
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              machinis.
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              </s>
            </p>
            <p type="margin">
              <s id="s.000432">
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              Machina
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              Auguſtana.</s>
            </p>
            <p type="main">
              <s id="s.000433">Eſt & alius machinæ modus ( vt intelli­
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              go ) Auguſtæ, qui tamen ſub hoc genere
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              comprehenditur. </s>
              <s id="s.000434">Columna verſatilis A B,
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              rota cum paxillis vertitur à flumine, iuxta
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              rationem à nobis ſuperiùs declaratam, dum
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              de motuum tranſlatione ageremus. </s>
              <s id="s.000435">In ea
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              curriculi pro numero cochlearum, gratia
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              exempli, CDEFGHK, & cochleæ pro nu­
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              mero vaſorum, & vaſa pro altitudine: vaſa
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              autem LMNOPQR, fixa in columna ST.
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              </s>
              <s id="s.000436">Verſa A B, vertuntur in curriculis cochleæ
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              omnes, quarum infima C, haurit aquam
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              ex ſubiecto flumine, & transfundit eam in
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              vas L, à quo haurit cochlea D, transfun­
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              dens aquam in vas M, atque ita vno motu
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              columnæ A B, C in L, D in M, E in N,
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              F in O, G in P, H in Q, K in R, aquam
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              fundunt, haurientes è ſubiectis vaſis. </s>
              <s id="s.000437">R, au­
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              tem transfert aquam per os V, in locum de­
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              ſtinatum. </s>
              <s id="s.000438">Contingit rurſus dubitatio: quia
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              cochleæ ore ſuperiore aſcendente, aquam
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              mittere haud debent. </s>
              <s id="s.000439">Quamobrem primam
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              triplicem fecimus. </s>
              <s id="s.000440">Sed videntur ſubſultem
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              effundere dum aſcendunt: quia ( vt demon­
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              ſtratum eſt) partes deſcendunt, & aqua tota
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              deſcendit, quam ob cauſam compreſſa exi­
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              lit: ſed non quemadmodum ore cochleæ
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              deſcendente, ſed pluribus circa eundem axem
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              cochleis poſitis, fit continua non ſolùm,
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              ſed æqualis aquarum effuſio. </s>
              <s id="s.000441">Atque hæc de
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              machinis iuxta prima genera, & ſpecies di­
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              cta ſint. </s>
              <s id="s.000442">Sed poſtquàm de motibus natura­
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              libus ſermonem habuimus, qui in loco
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              fiunt, par eſt vt quid ſit locus intelligamus.
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              </s>
              <s id="s.000443">Nam & hoc eſſe quintum naturalium rerum
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              principium ſuppoſitum eſt: ſuppoſitones au­
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              tem hæ, ſecundùm ſenſum demonſtrationi­
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              bus ipſis ſunt firmiores. </s>
              <s id="s.000444">Quid igitur ſit locus,
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              ſciendum eſt. </s>
              <s id="s.000445">Eſt igitur locus, vltima corpo­
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              ris ſuperficies, corpus contentum ambiens.
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              </s>
              <s id="s.000446">Manet autem recedente corpore, quia ad cœ­
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              li ambitum comparata eſt. </s>
              <s id="s.000447">Manifeſtum eſt
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              igitur, locum quemlibet æqualem eſſe cor­
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              pori in eo contento ad vnguem: & quòd om­
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              ne corpus eſt in loco, & quòd in omni loco
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              aliquod corpus eſt. </s>
              <s id="s.000448">Nam omne corpus ſuam
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              habet extremam ſuperficiem, & illa vbi nul­
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              lum aliud ſit corpus à quo contineatur vt vl­
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              timum, cœlum eſt ei locus: alia autem cor-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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