Cardano, Girolamo
,
De subtilitate
,
1663
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016/01/019.jpg
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æquales: ſed vt demonſtratum eſt, pondus
<
lb
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in C, plus diſtat tam à meta, quàm à trutina,
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lb
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quam in E, ideo ratio anguli ibi non tenet:
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ſed quum comparamus pondera in F & R,
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iam illa æqualiter diſtant tam à trutina,
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quod à meta: ideo tunc anguli ratio ſpectan
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da eſt. </
s
>
<
s
id
="
s.000542
">Generalis igitur ratio hæc ſit: pon
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dera quò plus diſtant à meta ſeu linea deſ
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lb
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cenſus per rectam, aut obliquum, id eſt, per
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lb
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angulum, eò ſunt grauiora. </
s
>
<
s
id
="
s.000543
">Sed primò rectæ
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lb
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lineæ magnitudo ſpectanda eſt: vbi rectæ li
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neæ æquales ſint, tunc angulus quòd maior
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lb
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erit, eò pondus reddetur grauius. </
s
>
<
s
id
="
s.000544
">Si igitur
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lb
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BC ſinuetur verſus QC, eleuabitur, & mi
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<
arrow.to.target
n
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marg43
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<
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nus diſtabit à B puncto, ideoque reddet pon
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lb
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dera leuiora, aureuſque iuſti ponderis defi
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cere videbitur, & ex aduerſa parte poſitus
<
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/>
qui deficit, bonus videbitur. </
s
>
<
s
id
="
s.000545
">Sed vacua libe
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lb
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ra delegitur fraus, aut commutatis viciſſim
<
lb
/>
numo & indice. </
s
>
<
s
id
="
s.000546
">Sed cur pondera quærunt
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lb
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verſus medium moueri? </
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>
<
s
id
="
s.000547
">Hoc facilè diſſolui
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lb
/>
tur, ſi quis, quæ diximus mente teneat. </
s
>
<
s
id
="
s.000548
">Nam
<
lb
/>
pondus in F, dum peruenit ad C, propin
<
lb
/>
quius redditur mundi centro ad quod natu
<
lb
/>
ra fertur linea PB: & dum ex C in Q linea
<
lb
/>
BQ & ita intentum ponderis eſt rectà ferri
<
lb
/>
ad centrum quia vinculo prohibetur, moue
<
lb
/>
tur eo modo, quo moueri poteſt, atque ita à
<
lb
/>
dextra, vel ſiniſtra verſus perpendiculum, &
<
lb
/>
medium. </
s
>
<
s
id
="
s.000549
">Sed dices, cur igitur libra vacua C,
<
lb
/>
non mouetur verſus Q? Reſpondeo, quòd
<
lb
/>
tunc D moueretur verſus A: ſed vt viſum eſt
<
lb
/>
ratione rectæ linæ poſito C in Q & D in A,
<
lb
/>
adhuc tantum eſſet amiſſum ex parte D,
<
lb
/>
quantum acquiſitum ipſi C: ſed quod eſſet
<
lb
/>
amiſſum ex parte D, eſſet magis contra na
<
lb
/>
turam quam illud quod eſſet acquiſitum ipſi
<
lb
/>
C ſecundum naturam: igitur maius eſſet de
<
lb
/>
trimentum quam iuuamentum. </
s
>
<
s
id
="
s.000550
">Quare pari
<
lb
/>
bus ponderibus in C & D, non ſolum non
<
lb
/>
remouebuntur ab eo ſitu ſpontè, ſed vi amo
<
lb
/>
ta redibunt. </
s
>
<
s
id
="
s.000551
">His rationibus conſideratis, poſ
<
lb
/>
ſumus facere libram quæ vacua ponderibus
<
lb
/>
æqua videbitur, iuſtiſque notis ponderum
<
lb
/>
maius rerum ipſarum pondus repræſentet.
<
lb
/>
</
s
>
<
s
id
="
s.000552
">Sic enim vt Ariſtoteles refert, purpuram
<
lb
/>
vendentes imponebant emptoribus. </
s
>
<
s
id
="
s.000553
">Cuius
<
lb
/>
ratio ſic conſtat:
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id
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Cur libra
<
lb
/>
vacua redit
<
lb
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ſpontè ad ſi
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lb
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tum rectum,
<
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vel ſi pon
<
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dera æqua
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lia fuerint.</
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>
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type
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id
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s.000555
">
<
margin.target
id
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"/>
Vt aurei iu
<
lb
/>
ſti ponderis
<
lb
/>
leuiores vi
<
lb
/>
deantur, &
<
lb
/>
leues iuſti.
<
lb
/>
</
s
>
<
s
id
="
s.000556
">Cur pondera
<
lb
/>
verſus me
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lb
/>
dium mo
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uentur.</
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>
</
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<
p
type
="
margin
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<
s
id
="
s.000557
">
<
margin.target
id
="
marg44
"/>
Modus fa
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lb
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ciendi
<
expan
abbr
="
librã
">libram</
expan
>
,
<
lb
/>
quæ pondera
<
lb
/>
rerum maio
<
lb
/>
ra quàm
<
lb
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ſint oſtendat.</
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>
</
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<
figure
id
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xlink:href
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number
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<
p
type
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main
">
<
s
id
="
s.000558
">Volenti libram quæ pro vndecim vnciis
<
lb
/>
duodecim præſeferat, virga AB ſumatur
<
lb
/>
metallica, quæ in partes viginti tres æquas
<
lb
/>
( nam totidem conſurgunt iunctis vndecim
<
lb
/>
ac duodecim ) diuidatur. </
s
>
<
s
id
="
s.000559
">In fine vndecimæ
<
lb
/>
& initio duodecimæ partis figatur lingua li
<
lb
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bramenti & agina. </
s
>
<
s
id
="
s.000560
">Conſtat igitur DC vnde
<
lb
/>
cima parte maiorem eſſe AD: quumque CD
<
lb
/>
paulò maior ſit AD & grauior, leuiorem li
<
lb
/>
ma vel terebratione reddemus, aut lancem
<
lb
/>
leuiorem adiiciemus ipſi C quàm A, adeò vt
<
lb
/>
dum lances vacuæ ſunt longitudinis AC, te
<
lb
/>
nuitatis penſata ratione, trutina ſub agina
<
lb
/>
iaceat, nullam in partem libra pendente: cui
<
lb
/>
tamen cùm ex parte C pondus vnciarum
<
lb
/>
vndecim adiunxerimus, & nota duodecim
<
lb
/>
vnciarum in lance A, libra æquilibrium de
<
lb
/>
monſtrabit. </
s
>
<
s
id
="
s.000561
">Quum ergo nec adulterinæ ſint
<
lb
/>
ponderum notæ, nec lancibus vacuis libra
<
lb
/>
videatur vitioſa, fraus mutatis mercibus ac
<
lb
/>
notis hinc inde, vt notæ ſunt in C, merces in
<
lb
/>
A, manifeſtè depræhenditur. </
s
>
<
s
id
="
s.000562
">Nam C latus
<
lb
/>
infrà deſcendet duplici cauſa, & quia maius
<
lb
/>
lanci ſuæ pondus ineſt, & quia CD, ipſa DA
<
lb
/>
longior eſt. </
s
>
<
s
id
="
s.000563
">Difficilior ac obſcurior eſt ſtate
<
lb
/>
ræ ratio, de qua in Arithmeticis diximus.
<
lb
/>
</
s
>
<
s
id
="
s.000564
">Nunc autem quum affinis ſit huic conſide
<
lb
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rationi, quantum neceſſarium eſt huic pro
<
lb
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poſito, adiicere optimum erit. </
s
>
<
s
id
="
s.000565
">Ergo tota in
<
lb
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tribus conſtat, quorum primum eſt Archi
<
lb
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medis in Parabolis: & eſt vbi regula ſtate
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ræ, nullius ponderis cenſeatur. </
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</
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figure
id
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number
="
18
"/>
<
p
type
="
main
">
<
s
id
="
s.000566
">Stantium in æquilibrio ponderum ratio
<
lb
/>
<
arrow.to.target
n
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marg45
"/>
<
lb
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eſt, vt diſtantiarum à trutina mutua. </
s
>
<
s
id
="
s.000567
">Velut ſi
<
lb
/>
D appenſum ex lancula in C faciat æquili
<
lb
/>
brium cum G appenſo in F, & proportio FB
<
lb
/>
ad BC ſit quadrupla, erit etiam D quadru
<
lb
/>
plum ad G Secundum, cùm in parte breuiore
<
lb
/>
fuerit ſolùm appenſum pondus, & regula fue
<
lb
/>
rit ponderoſa, æqualis in magnitudine &
<
lb
/>
pondere, & fiat æquilibrium, erit proportio
<
lb
/>
ponderis appenſi ad pondus totius regulæ,
<
lb
/>
vt differentiæ partium regulæ ad duplum
<
lb
/>
ponderis minoris. </
s
>
<
s
id
="
s.000568
">Exemplum: D pondus in
<
lb
/>
C appenſum faciat æquilibrium
<
expan
abbr
="
cũ
">cum</
expan
>
BL virga
<
lb
/>
<
expan
abbr
="
abſq;
">abſque</
expan
>
alio pondere, & ſic BL & BC, vt axi,
<
lb
/>
fiat æqualis BK ipſi BC, tunc dico quòd pro
<
lb
/>
portio D ad pondus CL, eſt veluti ponderis
<
lb
/>
LK ad pondus KC. </
s
>
<
s
id
="
s.000569
">Sed ex hoc habetur re
<
lb
/>
gula: cognito pondere CL & CK ha
<
lb
/>
bendi pondus D, ducemus KL, quæ ſit 40,
<
lb
/>
gratia exempli in ſe, fit 1600, diuide per pon
<
lb
/>
dus CK, quod ſit 16, exit 100, huic adde
<
expan
abbr
="
põ-dus
">pon
<
lb
/>
dus</
expan
>
KL, quod eſt 40, fit
<
expan
abbr
="
põdus
">pondus</
expan
>
D, 140. Et ita
<
lb
/>
poterimus ad
<
expan
abbr
="
quancunq;
">quancunque</
expan
>
menſuram volueri
<
lb
/>
mus ſcire
<
expan
abbr
="
quantũ
">quantum</
expan
>
<
expan
abbr
="
põderis
">ponderis</
expan
>
refert ſtatera. </
s
>
<
s
id
="
s.000570
">Ter
<
lb
/>
tium habetur ex his duobus & eſt, ſi virgula
<
lb
/>
ſine pondere cenſeatur, à parte
<
expan
abbr
="
autẽ
">autem</
expan
>
quę dif
<
lb
/>
ferentia eſt
<
expan
abbr
="
longitudinũ
">longitudinum</
expan
>
ab agina, pondus æ
<
lb
/>
quale extendatur per
<
expan
abbr
="
totã
">totam</
expan
>
<
expan
abbr
="
virgã
">virgam</
expan
>
,
<
expan
abbr
="
æqualẽ
">æqualem</
expan
>
<
expan
abbr
="
gra-uitatẽ
">gra
<
lb
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uitatem</
expan
>
habebit cum
<
expan
abbr
="
eodẽ
">eodem</
expan
>
pondere appenſo in
<
lb
/>
puncto diſtante à librili per
<
expan
abbr
="
medietatẽ
">medietatem</
expan
>
totius
<
lb
/>
virgę. </
s
>
<
s
id
="
s.000571
">Sit vt virga CL nullius ſit ponderis, &
<
lb
/>
ſit BC æqualis BK, & coextenſum
<
expan
abbr
="
põdus
">pondus</
expan
>
æ
<
lb
/>
qualiter, vt ſub forma tetragoni faciat
<
expan
abbr
="
æqui-libriũ
">æqui
<
lb
/>
librium</
expan
>
<
expan
abbr
="
cũ
">cum</
expan
>
D
<
expan
abbr
="
appẽſo
">appenſo</
expan
>
in C, & ſumatur G
<
expan
abbr
="
ęqui-pondiũ
">ęqui
<
lb
/>
pondium</
expan
>
ęquale
<
expan
abbr
="
põderi
">ponderi</
expan
>
<
expan
abbr
="
coextẽſo
">coextenſo</
expan
>
, & ſit BM
<
expan
abbr
="
di-midiũ
">di
<
lb
/>
midium</
expan
>
totius CL, dico quòd G
<
expan
abbr
="
ſuſpensũ
">ſuſpensum</
expan
>
in M
<
lb
/>
faciet
<
expan
abbr
="
æquilibriũ
">æquilibrium</
expan
>
<
expan
abbr
="
cũ
">cum</
expan
>
D, & ita æqualiter gra
<
lb
/>
uabit vt
<
expan
abbr
="
coextensũ
">coextensum</
expan
>
toti KL. </
s
>
<
s
id
="
s.000572
">Sit igitur vt in M
<
lb
/>
faciat
<
expan
abbr
="
ęquilibriũ
">ęquilibrium</
expan
>
<
expan
abbr
="
cũ
">cum</
expan
>
D, igitur per
<
expan
abbr
="
primã
">primam</
expan
>
<
expan
abbr
="
harũ
">harum</
expan
>
<
lb
/>
proportio MB ad BC, vt D ad G.
<
expan
abbr
="
Itẽ
">Item</
expan
>
quia facit </
s
>
</
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</
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>
</
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</
text
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</
archimedes
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