Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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<
s
id
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s.002620
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<
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pagenum
="
151
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xlink:href
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009/01/151.jpg
"/>
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figure
id
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id.009.01.151.1.jpg
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place
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text
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xlink:href
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009/01/151/1.jpg
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number
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79
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lb
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ipſi æquidiſtanter, dum punctum A, mouetur
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ad B. his duabus lationibus A, latum. </
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>
<
s
id
="
s.002621
">neceſſa
<
lb
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riò motu mixto progredietur per diametrum
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lb
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A M, quod ſic probari poteſt; ſit iam A, mo
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lb
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tum primo motu
<
expan
abbr
="
vſq;
">vſque</
expan
>
ad D, linea verò ex ſe
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lb
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cundo motu ſit in G F E, quo motu punctum
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A, quod erat in D,
<
expan
abbr
="
tractũ
">tractum</
expan
>
erit in F. quod pun
<
lb
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ctum eſt in diametro A M, quoniam enim mo
<
lb
/>
uetur duobus motibus, cum lineis A B, A C, proportionalibus, motus au
<
lb
/>
tem
<
expan
abbr
="
hucuſq;
">hucuſque</
expan
>
ſunt A D, A E, quæ debent eſſe proportionales, cum A B, A C
<
lb
/>
compleatur rectangulum A D F E, erunt ſimiliter proportionalia F E, D E,
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cum ſint æqualia duobus D A, A E, quare per 26. 6. cum quadrilaterum
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paruum A D F E, ſit ſimile toti A B M C, erit A M,
<
expan
abbr
="
vtriuſq;
">vtriuſque</
expan
>
diameter, ergò
<
lb
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punctum F, in quo eſt A, eſt in diametro A M. eodem modo, de quouis pun
<
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cto in linea A B, ad quod A, perueniat, probabitur ab altero motu deſcen
<
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diſſe vſque ad diametrum. </
s
>
<
s
id
="
s.002622
">ſemper ergò latum A, per rectam A M, diame
<
lb
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trum quadrilateri, cum illis motibus proportionalibus progreditur, quod
<
lb
/>
probandum erat. </
s
>
<
s
id
="
s.002623
">è conuersò manifeſtum etiam eſt, quod ſi quid ſecundum
<
lb
/>
diametrum duabus fertur lationibus, eas lationes eſſe proportionales late
<
lb
/>
ribus quadrilateri, cuius eſt illa diameter, ſi enim illæ lationes non ſunt la
<
lb
/>
teribus proportionales, latum illud non feretur ſecundum diametrum il
<
lb
/>
lam, ſed ſecundum aliam alterius quadrilateri.</
s
>
</
p
>
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p
type
="
main
">
<
s
id
="
s.002624
">Quod ſi quid duabus lationibus nullam habentibus proportionem per
<
lb
/>
petuò ferratur, impoſſibile eſt ipſum motu mixto lineam rectam deſcribere.
<
lb
/>
</
s
>
<
s
id
="
s.002625
">ſi enim dixeris illud poſſe deſcribere rectam lineam, tunc circa rectam il
<
lb
/>
lam tanquam diametrum deſcribam quadrilaterum, & poſtea oſtendam, vt
<
lb
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proximè oſtenſum eſt, illud latum eſſe ſecundum laterum illius proportio
<
lb
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nem, quare impoſſibile eſt id, quod mouetur duabus lationibus nullam in
<
lb
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uicem rationem habentibus, ferri per lineam rectam: quapropter
<
expan
abbr
="
dicẽdum
">dicendum</
expan
>
<
lb
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eſt hoc modo
<
expan
abbr
="
latũ
">latum</
expan
>
, neceſſariò ferri circulariter, ſiue per lineam circularem.
<
lb
/>
</
s
>
<
s
id
="
s.002626
">Quod autem ea, quæ deſcribit circulum linea, dum altero eius manente
<
lb
/>
extremo circumagitur, duabus ſimul feratur lationibus, ex quibus motus
<
lb
/>
orbicularis oriatur, manifeſtum eſt ex ſuperioribus, quia & antrorſum, &
<
lb
/>
retrorſum impellitur; tùm etiam, quia ſi rectà tenderet recta
<
expan
abbr
="
deſcribẽs
">deſcribens</
expan
>
cir
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<
figure
id
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id.009.01.151.2.jpg
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place
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number
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80
"/>
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culum, nunquam ad diametri perpendiculum
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perueniret, ſed tamen peruenit, ita vt ſit ipſa
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à centro perpendicularis diametro. </
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>
<
s
id
="
s.002627
">ſit circuli
<
lb
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figura A B C D, in qua extremum diametri
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lb
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B, feratur ad alterum extremum vbi D, per
<
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ipſius diametri B D, circumuolutionem circa
<
lb
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centrum F, neceſſe eſt aliquando B, perueniat
<
lb
/>
ad C. ſi igitur B, feretur duabus lationibus
<
lb
/>
aliquo modo proportionatis, v. g. vt eſt pro
<
lb
/>
portio lateris B E, ad E C, latus, ſequeretur
<
lb
/>
ex demonſtratis ipſum B, ferri per
<
expan
abbr
="
rectã
">rectam</
expan
>
B C,
<
lb
/>
quæ diameter eſſet quadrilateri B E C G. ſed </
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>
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</
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</
archimedes
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