Cardano, Girolamo
,
De subtilitate
,
1663
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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. </
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<
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">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. </
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<
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">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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Aliquid per
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petuò
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dit</
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, quod in
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fine erit al
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tius.</
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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.</
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<
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id
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">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. </
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<
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id
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">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. </
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<
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id
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">Sed omne graue liberum in mo
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tu deſcendit, igitur pondus perueniet ad E.
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</
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<
s
id
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">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. </
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<
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id
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">Facilè autem ligula circumdata calamo
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hoc, quod tibi perdifficile forſan videtur, ex
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perieris. </
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<
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id
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">Sed ad rem reuertor. </
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<
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id
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">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. </
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<
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id
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">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. </
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>
<
s
id
="
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">Ita contrariis rationibus celeriter aquam
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tranſmittet, ſed difficiliùs reuertetur. </
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>
<
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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. </
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>
<
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id
="
s.000426
">Verùm celeritatem cum diffi
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/>
cutate eligemus, vbi torrens fuerit, & ripa
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rum altitudo immodica. </
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>
<
s
id
="
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">Nam ſi inſtrumen
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ti aſcenſus mollis fuerit, reddetur inſtrumen
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tum ob longitudinem grauiſſimum. </
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>
<
s
id
="
s.000428
">Eadem
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in magnitudine & prauitate ratio. </
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<
s
id
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">Nam par
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uum facilè circumagitur, ſed ſerò irrigat.
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</
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<
s
id
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s.000430
">Vſus eius vbi modica terra eſt irriganda, &
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flumen profundum, & leniter currit, & ripæ
<
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altiores. </
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<
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id
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">In contrariis cauſis magnis vtemur
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machinis.
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Machina
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Auguſtana.</
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<
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">Eſt & alius machinæ modus ( vt intelli
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go ) Auguſtæ, qui tamen ſub hoc genere
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comprehenditur. </
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<
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id
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">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. </
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<
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id
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">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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</
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<
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id
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">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. </
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<
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id
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">R, au
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tem transfert aquam per os V, in locum de
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ſtinatum. </
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<
s
id
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">Contingit rurſus dubitatio: quia
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cochleæ ore ſuperiore aſcendente, aquam
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mittere haud debent. </
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<
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id
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">Quamobrem primam
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triplicem fecimus. </
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<
s
id
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">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. </
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>
<
s
id
="
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">Atque hæc de
<
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machinis iuxta prima genera, & ſpecies di
<
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cta ſint. </
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>
<
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id
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">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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</
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<
s
id
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">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. </
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>
<
s
id
="
s.000444
">Quid igitur ſit locus,
<
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ſciendum eſt. </
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<
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id
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">Eſt igitur locus, vltima corpo
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ris ſuperficies, corpus contentum ambiens.
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</
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<
s
id
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s.000446
">Manet autem recedente corpore, quia ad cœ
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li ambitum comparata eſt. </
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>
<
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. </
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>
<
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-</
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