Cardano, Girolamo
,
De subtilitate
,
1663
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Monſtrum
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mirabile.</
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<
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s.012908
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Nauim quo
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modo quot
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paſſuum M.
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exegerit, vel
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ploſtrum de
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prehenda
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mus.</
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id
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s.012909
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id
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Meteoroſco
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pium.</
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</
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<
p
type
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main
">
<
s
id
="
s.012910
">Sit igitur meridiei circulus AEBF, fixus
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lb
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ſuper pede AM. </
s
>
<
s
id
="
s.012911
">In eo poli fingantur KF, &
<
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vertex tuus E. </
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<
s
id
="
s.012912
">Alius circulus immobilis
<
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æquinoctij ACBD, fixus ſuper pedem AM,
<
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& ad rectos angulos ſecans priorem circu
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id
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xlink:href
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number
="
152
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<
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lum AKBF. </
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>
<
s
id
="
s.012913
">Sit alius circulus FGHK per
<
lb
/>
polos, & in ipſis polis F & K, per paxillos
<
lb
/>
verſatilis C E D L. </
s
>
<
s
id
="
s.012914
">Sit igitur diſtantia EN,
<
lb
/>
nota rectáque, numerentur autem diuiſis
<
lb
/>
ſingulis circulis ex his in partes ter mille
<
lb
/>
ſexcentas, partes illæ in C E D per EN, &
<
lb
/>
conſtituatur C N D, ſuper viam rectam ex
<
lb
/>
ciuitate tua in N locum, & vbi punctus N,
<
lb
/>
cadit, ducatur CKHF, circulus mobilis me
<
lb
/>
ridiei. </
s
>
<
s
id
="
s.012915
">Habebis igitur per arcum KN latitu
<
lb
/>
dinem loci, ſeu poli eleuationem, & per GC
<
lb
/>
differentiam longitudinis loci N à tua vr
<
lb
/>
be: cúmque longitudo vrbis tuæ iam nota
<
lb
/>
ſit, erit & longitudo N. </
s
>
<
s
id
="
s.012916
">Quòd ſi altitudo N
<
lb
/>
nota fuerit, & iter rectum EN, circumdu
<
lb
/>
ctis circulis CED & GNH, donec occurrant
<
lb
/>
extrema arcuum EN diſtantiæ rectæ, & KN
<
lb
/>
notæ altitudinis loci N in vnum, fiet arcus
<
lb
/>
tunc GC notus, differentia ſcilicet longitu
<
lb
/>
dinis loci N, à patria tua. </
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>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.012917
">Manifeſtum eſt autem, quòd contraria
<
lb
/>
ratione habitis longitudinibus, & latitudi
<
lb
/>
nibus locorum, diſtantia quoque cognita
<
lb
/>
erit. </
s
>
<
s
id
="
s.012918
">Quòd ſi velis, vt inſtrumentum vnicui
<
lb
/>
que ſeruiat regioni, facies paxillos EL, mo
<
lb
/>
biles in circulo meridiei, AKBF, vt ſub qua
<
lb
/>
cunque altitudine collocari vertex tuus poſ
<
lb
/>
ſit. </
s
>
<
s
id
="
s.012919
">Porrò diuiſiones in ſingulas denas con
<
lb
/>
ſpicuè, & in quinas minus, inde in quinqua
<
lb
/>
genas aureo colore, vt diſtinguantur dili
<
lb
/>
genter, velut in ſtateris. </
s
>
<
s
id
="
s.012920
">Numerus autem ne
<
lb
/>
ceſſarius non eſt, quia vbique principium
<
lb
/>
ſtatuere oportet. </
s
>
<
s
id
="
s.012921
">Aſſequimur etiam & iſta
<
lb
/>
demonſtratione, ſed difficiliori modo: atque
<
lb
/>
hæc ad amuſſim omnia. </
s
>
<
s
id
="
s.012922
">Quòd verò ſemper
<
lb
/>
licet melius aſſequi, eſt proportio periferiæ
<
lb
/>
circuli ad diametrum, ab Archimede mira
<
lb
/>
bili ingenio inuenta: quæ cùm facillima ſit,
<
lb
/>
eam quatuor verbis ſubſcribere placuit. </
s
>
<
s
id
="
s.012923
">Tri
<
lb
/>
bus indiget illa ſuppoſitis: primùm, quòd
<
lb
/>
circuli periferia maior eſt aggregato late
<
lb
/>
rum inſcriptæ figuræ, & minor circumſcri
<
lb
/>
<
arrow.to.target
n
="
marg1768
"/>
<
lb
/>
ptæ. </
s
>
<
s
id
="
s.012924
">De inſcripta patet ex rectæ lineæ diffi
<
lb
/>
nitione: de circumſcripta, licet apud aliquos
<
lb
/>
videatur per ſe manifeſtum, à nobis tamen
<
lb
/>
in libris Elementorum per antiparalogiſ
<
lb
/>
mum demonſtratur. </
s
>
<
s
id
="
s.012925
">Secundum eſt, quòd no
<
lb
/>
ta quacunque linea in circulo collocata, il
<
lb
/>
lius arcus per medium diuiſi, linea recta ſub
<
lb
/>
tenſa cognita erit. </
s
>
<
s
id
="
s.012926
">Hæc licet à Ptolemæo de
<
lb
/>
monſtretur, vt tamen quiſque rationem
<
lb
/>
habeat inueniendæ propoſitæ proportio
<
lb
/>
nis, duobus verbis rem cum operatione de
<
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/>
clarabo. </
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>
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type
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id
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margin.target
id
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Quomodo
<
lb
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ſciamus pro
<
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portionem
<
lb
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periferiæ cir
<
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culi ad dia
<
lb
/>
metrum.</
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>
</
p
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<
p
type
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main
">
<
s
id
="
s.012928
">Sit A B nota in proportione ad BC, &
<
lb
/>
diuidatur arcus AB, per æqualia in D, & du
<
lb
/>
catur AD, dico eam eſſe notam. </
s
>
<
s
id
="
s.012929
">Nam ducta
<
lb
/>
DCK, erit ex demonſtratis ab Euclide EA,
<
lb
/>
media proportione inter KE & ED, & qua
<
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/>
dratum DA, æquale quadratis A E & E D.
<
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/>
</
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<
s
id
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s.012930
">Per quintam igitur ſecundi Elementorum
<
lb
/>
Euclidis detraham quadratum A E notum,
<
lb
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quia AE eſt dimidium AB, ex quadrato CD
<
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<
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<
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cognito, & relinquatur quadratum CE co
<
lb
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gnitum: igitur CE. </
s
>
<
s
id
="
s.012931
">Quare detracta CE ex
<
lb
/>
CD, relinquetur E D cognita. </
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>
<
s
id
="
s.012932
">Iungam igi
<
lb
/>
tur quadrata AE & E D, & per penultimam
<
lb
/>
primi Elementorum habebo quadratum AD
<
lb
/>
cognitum. </
s
>
<
s
id
="
s.012933
">Tertium ſuppoſitum eſt, quòd co
<
lb
/>
gnito latere figuræ inſcriptæ circulo, co
<
lb
/>
gnoſcam & latus circumſcribentis. </
s
>
<
s
id
="
s.012934
">Hoc li
<
lb
/>
cet colligatur ab Euclide in quarto Ele
<
lb
/>
mentorum, vt tamen habeamus demonſtra
<
lb
/>
tionem cum operatione, vno eam verbo hîc
<
lb
/>
ſubiungam. </
s
>
<
s
id
="
s.012935
">Sit latus AB inſcriptæ figuræ, &
<
lb
/>
FG circumſcriptæ, ſub eodem enim angulo
<
lb
/>
continentur centri, ducantúrque A F &
<
lb
/>
CBG. </
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>
<
s
id
="
s.012936
">Quia igitur nota eſt AB, nota eſt AE,
<
lb
/>
ideóque K E & E D, vt demonſtratum eſt.
<
lb
/>
</
s
>
<
s
id
="
s.012937
">Sed vt CE ad CD, ita AB ad FG. </
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>
<
s
id
="
s.012938
">Ducta igi
<
lb
/>
tur AB in CD, & quod producitur diuiſo
<
lb
/>
per CE, exit FG cognita. </
s
>
<
s
id
="
s.012939
">Suppoſito igitur
<
lb
/>
AB latere hexagoni, quod per demonſtrata
<
lb
/>
ab Euclide eſt æquale dimidio diametri, per
<
lb
/>
ſecundum ſuppoſitum habebo latus figuræ
<
lb
/>
duodecim baſium, & per eandem figuræ 24.
<
lb
/>
baſium, inde 48. inde 96. inde 192. & 384. &
<
lb
/>
768. & poſſum procedere abſque errore, imò
<
lb
/>
abſque extractione radicum. </
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>
</
p
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<
p
type
="
main
">
<
s
id
="
s.012940
">Sit igitur gratia exempli ſtatus in latere
<
lb
/>
figuræ 768. laterum, habebo igitur per ter
<
lb
/>
tium ſuppoſitum latus figuræ 768. circum
<
lb
/>
ſcriptæ: duces vtrunque per numerum late
<
lb
/>
rum, id eſt, per 768. & habebis ambitum in
<
lb
/>
terioris, & exterioris figuræ, & proportio
<
lb
/>
nem illorum ad diametrum circuli. </
s
>
<
s
id
="
s.012941
">Sed peri
<
lb
/>
feria circuli maior eſt ambitu inſcriptæ figu
<
lb
/>
ræ, & minor circumſcriptæ, ex primo ſup
<
lb
/>
poſito igitur habebo proportionem perife
<
lb
/>
riæ circuli ad diametrum, inter quas pro
<
lb
/>
portiones debent collocari, & tamen nun
<
lb
/>
quam ad perfectam cognitionem, & metam
<
lb
/>
peruenire poteſt. </
s
>
<
s
id
="
s.012942
">Ex quo patet, Archimedem
<
lb
/>
non indiguiſſe inuentis à Ptolemæo, nec
<
lb
/>
tabulis ſinuum, exquiſitiúſque ac purius ſine
<
lb
/>
illis, quàm cum illis geometram ad hanc </
s
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archimedes
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