Cardano, Girolamo
,
De subtilitate
,
1663
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<
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369
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xlink:href
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Quomodo
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pondera fa
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cile mouean
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tur.</
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id
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xlink:href
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<
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type
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<
s
id
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">Adiecimus hoc, quia pleraque inſtrumen
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n
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ta hauriendis aquis idonea, hominum aut
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iumentorum viribus aguntur. </
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<
s
id
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s.000510
">Sed etſi ipſa
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rum aquarum rapido impetu agitentur ma
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chinæ, rurſus addita manubriis pondera fa
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ciliorum efficiunt motum. </
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<
s
id
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s.000511
">Licet itaque ſolo
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impetu aquarum defluentium, aquas ipſas in
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ſuprema loca impellere, atque ægros humi
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lioribus aquis irrigare. </
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<
s
id
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s.000512
">Sed hoc tantùm in
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his quæ decurrunt, & impetum labendo ha
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bent. </
s
>
<
s
id
="
s.000513
">Aptetur enim à latere vno Cteſibica,
<
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aut Brambilica, aut alterius generis machi
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na: nam ( vt dixi ) innumeri poſſunt eſſe
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modi earum, quanquam hæ omnibus aliis,
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coclea excepta, ſint elegantiores: & ( vtiam
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docuimus ) alternus manubrij motus rota
<
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cum pinnis agitata perficiatur, ſic fiet vt
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ſpontè aqua ſeipſam ſurſum impellat: nam
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que ars contra ſua inſtituta eam facere co
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git. </
s
>
<
s
id
="
s.000514
">Quod exemplum nonnullæ ciuitates quæ
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editioribus à flumine locis poſitæ ſunt, ſe
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quuntur.
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marg41
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</
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type
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<
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id
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">
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Quomodo
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aqua
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abbr
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ſeipsã
">ſeipsam</
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>
<
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impellat ſur
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ſum.</
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>
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type
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<
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id
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De libra &
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illius ratio
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ne.</
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main
">
<
s
id
="
s.000517
">Poſt hæc videndum eſt de ponderibus
<
lb
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quæ in libra conſtituuntur. </
s
>
<
s
id
="
s.000518
">Sit igitur libra,
<
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/>
cuius trutina ſit appenſa in A, & finis vbi
<
lb
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iunguntur latera lancis B, & lanx CD, &
<
lb
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manifeſtum eſt quòd CD mouetur circa B,
<
lb
/>
velut centrum quoddam, quia CD non po
<
lb
/>
teſt ſeparari ab ipſo B: & ſit angulus ABC,
<
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& ABD rectus. </
s
>
<
s
id
="
s.000519
">Dico quòd pondus in C
<
lb
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conſtitutum erit grauius, quàm ſi lanx collo
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/>
cetur in quocunque alio loco, vt puto quòd
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<
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id
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id.016.01.018.2.jpg
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xlink:href
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number
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16
"/>
<
lb
/>
conſtitueretur lanx in F. </
s
>
<
s
id
="
s.000520
">Vt autem cognoſ
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camus quòd C ſit grauius in eo ſitu, quam
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in F, neceſſarium eſt vt in æquali tempore
<
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/>
moueatur per maius ſpatium verſus cen
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/>
trum. </
s
>
<
s
id
="
s.000521
">Videmus enim grauiora pari ratione
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in reliquis, velociùs ad centrum ferri. </
s
>
<
s
id
="
s.000522
">Quòd
<
lb
/>
autem hoc contingat magis pondere & li
<
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bra in C collocata quàm in F, oſtendo dua
<
lb
/>
bus rationibus. </
s
>
<
s
id
="
s.000523
">Prima, quòd ſi in aliquo
<
lb
/>
tempore moueatur ex C in E, & ſit arcus
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CE æqualis FG, quod tardius deſcendet ex
<
lb
/>
F in G, quàm ex C in E, & ita erit leuiùs
<
lb
/>
in F, quàm in C. Secundò, quòd poſito
<
lb
/>
quòd in æquali ſpatio temporis moueretur
<
lb
/>
ex C in E, ex & F in G, adhuc per arcum
<
lb
/>
CE æqualem FG, magis appropinquaret
<
lb
/>
centro quàm per motum factum in arcu
<
lb
/>
FG. </
s
>
<
s
id
="
s.000524
">Ideò ergo duplici ratione magis gra
<
lb
/>
uabit pondus lance poſita ad perpendicu
<
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lum cum trutina, quàm in quoque alio
<
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/>
loco. </
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>
</
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type
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main
">
<
s
id
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s.000525
">Primùm igitur ſic declaratur. </
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>
<
s
id
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s.000526
">Manife
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ſtum eſt in ſtateris, & in his, qui pondera
<
lb
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eleuant, quòd quantò magis pondus à tru
<
lb
/>
tina, eò magis graue videtur: ſed pondus
<
lb
/>
in G diſtat à trutina quantitate BC lineæ,
<
lb
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& in F quantitate FP, ſed CB eſt maior FP,
<
lb
/>
ex decimaquinta, tertij elementorum Eu
<
lb
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clidis: igitur lance poſita in C, grauius pon
<
lb
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dus videbitur quàm in F, quod erat primum.
<
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</
s
>
<
s
id
="
s.000527
">Ex hac etiam demonſtratione manifeſtum
<
lb
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eſt, libram quantò magis diſcendit verſus
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lb
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C ex A, tantò grauiùs pondus reddere, & eò
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velociùs moueri: at ex C verſus Q, contra
<
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ria ratione pondus reddi leuius, & motum
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ſegniorem, quod & experimentum docet.
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</
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<
s
id
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s.000528
">Secundum verò ſic demonſtratur. </
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>
<
s
id
="
s.000529
">Quia enim
<
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CE eſt æqualis FG, ſumatur CH æqualis
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CE, eritque æqualis CH ipſi FG, quare re
<
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cta ſubtenſa CH, æqualis rectæ ſubtenſæ
<
lb
/>
FG. </
s
>
<
s
id
="
s.000530
">Igitur ex octaua primi elementorum
<
lb
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angulus BFG, æqualis erit angulo BCH. </
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>
<
s
id
="
s.000531
">Igi
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tur ductis ad perpendiculum rectis FL &
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lb
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HK, minor eſt angulus FGL. qui & ipſe
<
lb
/>
eſſet pars coæqualis BFG, ex quinta primi
<
lb
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elementorum, angulo KCH. </
s
>
<
s
id
="
s.000532
">Igitur latus
<
lb
/>
HK, maius latere FL: nam rectæ FG & HC
<
lb
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æquales fuerunt, & trigoni orthogonij ſeu
<
lb
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rectanguli: igitur BN maior OF, & ideo
<
lb
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BM maior OP. </
s
>
<
s
id
="
s.000533
">Dum igitur libra mouetur ex
<
lb
/>
C in E pondus deſcendit per BM lineam, ſeu
<
lb
/>
propinquius centro redditur quàm eſſet in
<
lb
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C, & dum mouetur per ſpatium arcus FG,
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lb
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deſcenditque per OP, & BM, maior eſt OP.
<
lb
/>
</
s
>
<
s
id
="
s.000534
">Igitur ſuppoſito etiam quod in æquali tem
<
lb
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pore tranſiret ex C in K, & ex F in G, adhuc
<
lb
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velociùs deſcendit ex C, quam ex F. </
s
>
<
s
id
="
s.000535
">Igitur
<
lb
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grauius eſt in C, quàm in F. </
s
>
<
s
id
="
s.000536
">Ex hoc autem
<
lb
/>
demonſtratur quod dicit Philoſophus, quòd
<
lb
/>
ſi æqualia ſint pondera in F & R, libra ta
<
lb
/>
men ſpontè redit ad ſitum CD, vbi trutina
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lb
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ſit AB. </
s
>
<
s
id
="
s.000537
">Nec hoc demonſtrat Iordanus, nec
<
lb
/>
intellexit. </
s
>
<
s
id
="
s.000538
">Similiter cur trutina QB poſita,
<
lb
/>
atque infrà libram ipſam, velut accidit con
<
lb
/>
uerſa libra, vt manu trutinam teneas ſuper
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n
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"/>
<
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incumbente libra pondus quod iam deſcen
<
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derat tractum ad R, vbi æquale aliud ad
<
lb
/>
conſtitutum in F, vel lances omninò vacuæ
<
lb
/>
ſint, non ſolùm non reuertuntur ad ſitum
<
lb
/>
CD, ſeu perpendiculi, imò magis R deſcen
<
lb
/>
dit verſus Q & F aſcendit verſus A. vt expe
<
lb
/>
rimento patet. </
s
>
<
s
id
="
s.000539
">Hoc etiam Iordanus non de
<
lb
/>
monſtrauit. </
s
>
<
s
id
="
s.000540
">Ariſtoteles dicit hoc contingere,
<
lb
/>
quum trutina eſt ſupra libram, quia angu
<
lb
/>
lus QBF metæ, maior eſt angulo QBR, Et ſi
<
lb
/>
militer quum trutina fuerit QB, erit meta
<
lb
/>
AB, & tunc angulus RBA, maior erit angu
<
lb
/>
lo FBA, ſed maior angulus reddit grauius
<
lb
/>
pondus: igitur dum trutina ſuperius eſt F,
<
lb
/>
erit grauius R, ideo F trahet libram verſus
<
lb
/>
C, & dum fuerit inferius R, erit grauius
<
lb
/>
quàm F, ideo trahet libram verſus
<
expan
abbr
="
q.
">que</
expan
>
Quòd ſi
<
lb
/>
quis obiiciat, igitur pondus in F, erit gra
<
lb
/>
uius quàm in C, trutina in A appenſa cuius
<
lb
/>
tamen oppoſitum iam eſt demonſtratum.
<
lb
/>
</
s
>
<
s
id
="
s.000541
">Reſpondemus, quòd latior angulus à meta,
<
lb
/>
facit pondus grauius, quum rectæ fuerint </
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>
</
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</
chap
>
</
body
>
</
text
>
</
archimedes
>