Cardano, Girolamo
,
De subtilitate
,
1663
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A D ad latus A B. </
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<
s
id
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s.011045
">Atque ita etiam ratio
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ſubtenſæ quatuor lateribus & duobus, &
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ſubtenſæ ſex lateribus ac tribus, tum alia
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rum cum latere reſpiciente ſubtenſas. </
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<
s
id
="
s.011046
">Mul
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tiplex igitur ratio in figuris æquilateris cir
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culis inſcriptis, & quæ ex his compo
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nuntur.
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<
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id
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<
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id
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Ratio gene
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ralis
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expan
abbr
="
omniũ
">omnium</
expan
>
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figurarum
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æqualia ha
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bentium la
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tera circulo
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inſcripta
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rum.</
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>
</
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<
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Laterum
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heptagoni
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ratio.</
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>
</
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<
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type
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<
s
id
="
s.011049
">Sed nulla melius, quam heptagoni cir
<
lb
/>
culo inſcripti, & æquilateri. </
s
>
<
s
id
="
s.011050
">Si igitur he
<
lb
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ptagonus deſcriptus ABCDEFG, & duo
<
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bus lateribus ſubtenſa AF & B F ſubtenſa
<
lb
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A B, & AF, cumque vt demonſtratum eſt,
<
lb
/>
angulus F B A duplus ſit angulo A F B, &
<
lb
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arcus BCDEF duplus eiſdem rationibus ar
<
lb
/>
cui AGF, erit angulus BAF duplus angulo
<
lb
/>
ABF, quare ex demonſtrata proportione
<
lb
/>
BA, & BF ad AF vt AF ad AB: itémque per
<
lb
/>
<
expan
abbr
="
eandẽ
">eandem</
expan
>
AB & AF, ad BF vt BF ad AF. </
s
>
<
s
id
="
s.011051
">Refle
<
lb
/>
xa igitur hæc bis proportio vocabitur. </
s
>
<
s
id
="
s.011052
">Po
<
lb
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namus igitur A B nouem, poſita igitur AF
<
lb
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ſexdecim & BF viginti, ſi propoſitio viginti
<
lb
/>
nouem ad ſexdecim eſſet qualis ſexdecim ad
<
lb
/>
<
expan
abbr
="
nouẽ
">nouem</
expan
>
haberemus latera trigoni ABF. </
s
>
<
s
id
="
s.011053
">Sed
<
expan
abbr
="
cũ
">cum</
expan
>
<
lb
/>
maior ſit proportio vigintinouem ad ſexde
<
lb
/>
cim, quàm ſexdecim ad nouem, ponemus
<
lb
/>
AF ſexdecim, ac rem habebis prope A B
<
lb
/>
200. A F 359. BF 448. vel per Alizam
<
lb
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regulam poſita AF. 1. erit BF. </
s
>
<
s
id
="
s.011054
">R Mut. </
s
>
<
s
id
="
s.011055
">7/54 in
<
lb
/>
2 1/3 ( m 1/3. ex prima æſtimatione. </
s
>
<
s
id
="
s.011056
">Quibus
<
lb
/>
habitis, ſi ducatur ex B linea per centrum,
<
lb
/>
& vbi cadit in circuli periferia linea ad F
<
lb
/>
<
figure
id
="
id.016.01.246.1.jpg
"
xlink:href
="
016/01/246/1.jpg
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number
="
104
"/>
<
lb
/>
& ad A, habebis quadrilaterum cum duo
<
lb
/>
bus dimetientibus, cuius duo latera, & di
<
lb
/>
metientium vna erit cognita. </
s
>
<
s
id
="
s.011057
">Duos inſu
<
lb
/>
per trigonos orthogonios, quorum baſis
<
lb
/>
erit diameter circuli: vnde poſita reliqua
<
lb
/>
dimetientium re, cùm dimetientibus re
<
lb
/>
ctangulum æquale ſit rectangulis duobus
<
lb
/>
quæ fiunt ex lateribus quadranguli inuicem
<
lb
/>
oppoſitis per demonſtrata à Ptolomæo, erit
<
lb
/>
ex his, quæ docuimus in Arte magna,
<
lb
/>
compoſitis minoribus capitulis ratio dia
<
arrow.to.target
n
="
marg1552
"/>
<
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metri circuli ad A B latus heptagoni co
<
lb
/>
gnita. </
s
>
<
s
id
="
s.011058
">Ex his igitur conſtat methodi reſo
<
lb
/>
lutoriæ, cuius toties Galenus meminit, ex
<
lb
/>
quiſitiſſimum, cui non par eſt in medica
<
lb
/>
arte exemplum. </
s
>
<
s
id
="
s.011059
">Propoſitum in circulo co
<
lb
/>
gnitæ diametri heptagonum deſcribere: fa
<
lb
/>
ctum iam ſupponamus, & ſit ſuprà deſ
<
lb
/>
criptus: oportet igitur ſcire, qualiter de
<
lb
/>
ducta diametro deducenda ſit AB. </
s
>
<
s
id
="
s.011060
">Vt ve
<
lb
/>
rò hoc ſciamus, ratio A B ad diametrum
<
lb
/>
excogitanda eſt: vt verò hæc habeatur, ra
<
lb
/>
tio ad A F, & F B quærenda erit: vt
<
lb
/>
hanc habeas, excogitata eſt rurſus angu
<
lb
/>
lorum proportio, quæ ſola eſt manifeſta.
<
lb
/>
</
s
>
<
s
id
="
s.011061
">Inde ea habita quærendum, quòd hæc
<
lb
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proportio inter latera decernat. </
s
>
<
s
id
="
s.011062
">Atque hæc
<
lb
/>
bis reflexa proportio dicitur. </
s
>
<
s
id
="
s.011063
">Hanc cùm
<
lb
/>
ex reflexis ſimplicibus conſtet, diuiſam
<
lb
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demonſtrare oportet. </
s
>
<
s
id
="
s.011064
">Atque hic eſt finis
<
lb
/>
reſolutoriæ methodi. </
s
>
<
s
id
="
s.011065
">Ab hoc igitur fine,
<
lb
/>
compoſita methodus, quam præpoſuimus
<
lb
/>
in laterum heptagoni demonſtratione, ini
<
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tium ſumit. </
s
>
<
s
id
="
s.011066
">Sed & in his quandoque error
<
lb
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contingit, ſi quis non diligenter omninò
<
lb
/>
aduertat. </
s
>
<
s
id
="
s.011067
">Cuius rei exemplum eſt: ſit cir
<
lb
/>
culus A B C, in eo diameter B C, cui
<
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/>
<
figure
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"/>
<
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/>
ſupereſt ad perpendiculum D A: ex A in
<
lb
/>
quam videtur deduci poſſe linea aliqua ſe
<
lb
/>
cans BC, vt A E F, ita vt ſit CE ad EA,
<
lb
/>
vt AE ad EF, quia CB poteſt quantumuis
<
lb
/>
augeri, quod tamen fieri non poteſt: etſi
<
lb
/>
fieri poſſet, Aliza regula non indiguiſſe
<
lb
/>
mus: quia poſita BC, 10. AE puta 6. fieret
<
lb
/>
<
expan
abbr
="
cõfeſtim
">confeſtim</
expan
>
ED cognita, ideoque & EC & EB,
<
lb
/>
& quia proportio C E ad E A, eſt velut
<
lb
/>
EF ad EB, ex demonſtratis ab Euclide in
<
lb
/>
3. Elementorum, fieret, vt aggregato pri
<
lb
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mæ, & quartæ quantitatis, tum tertia co
<
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gnitis, vt quantitates cognoſcerentur. </
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>
<
s
id
="
s.011068
">Igi
<
lb
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tur cubi, & alicuius numeri æqualis, de
<
lb
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cem rebus notum eſt capitulum. </
s
>
<
s
id
="
s.011069
">Diſſolu
<
lb
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tio paralogiſmi eſt, quia iam AD eſt me
<
lb
/>
dia inter partes C D & BD, vt notum eſt
<
lb
/>
per ſe, & ſemper creſcit proportio A E ad
<
lb
/>
EF, magis quam CE ad E A, igitur pro
<
lb
/>
portio CE ad E A minor eſt proportione
<
lb
/>
AE ad EF. </
s
>
<
s
id
="
s.011070
">Vbicunque tamen punctus aſ
<
lb
/>
ſumatur in circunferentia A B ſemper de
<
lb
/>
duci poterit, quia proportio partis CB ter
<
lb
/>
minatæ ad deductam ex puncto illo ad per
<
lb
/>
pendiculum eſt maior, quam deductæ ad
<
lb
/>
ad perpendiculum AD reſiduum, cui ſem
<
lb
/>
per eſt æquale, & prior proportio minùs
<
lb
/>
augetur quam poſterior, igitur quandoque
<
lb
/>
peruenient ad æqualitatem. </
s
>
<
s
id
="
s.011071
">In vniuerſum
<
lb
/>
igitur paralogiſmi fiunt, vel cum aſſumitur
<
lb
/>
aliquid in
<
expan
abbr
="
cõſtructione
">conſtructione</
expan
>
problematis, quo
<
expan
abbr
="
nõ
">non</
expan
>
<
lb
/>
vtimur in demonſtratione, vel cum vtimur
<
lb
/>
principio non vero, ſed veriſimili, vel cum
<
lb
/>
aſſumimus non demonſtrata pro demonſtra
<
lb
/>
tis, vel pro medio, quod medium non eſt.
<
lb
/>
</
s
>
<
s
id
="
s.011072
">Omnia autem hæc magis contingunt in
<
lb
/>
<
figure
id
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id.016.01.246.3.jpg
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xlink:href
="
016/01/246/3.jpg
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number
="
106
"/>
<
lb
/>
remotis à ſenſu, vt corporibus, & diuerſi </
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>
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archimedes
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