Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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archimedes
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34
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medis eſt propoſitio prima acutiſſimi libelli de Dimenſione circuli; eſt au
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tem huiuſmodi. </
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<
s
id
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s.000677
">Quilibet circulus æqualis eſt triangulo rectangulo, cuius
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quidem ſemidiameter vni laterum, quæ circa rectum angulum ſunt, ambi
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tus verò baſi eius eſt æqualis.</
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type
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<
s
id
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s.000678
">Sit, v.g. datus circulus, cuius ſemidiameter A B; & fit triangulum rectangu
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lum A B C, cuius angulus B, ſit rectus, & latus B A,
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expan
abbr
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conſtituẽs
">conſtituens</
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angulum re
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ctum B, cum baſi B C, ſit æquale ſemidiametro A B; baſis verò B C, ſit æqua
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lis peripheriæ eiuſdem circuli dati. </
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<
s
id
="
s.000679
">demonſtrat iam ibi Archimedes acuta
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æquè, ac euidenti demonſtratione triangulum iſtud æquale eſſe circulo illi.
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</
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<
s
id
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s.000680
">quod perinde eſt, ac ſi oſtendiſſet cuinam quadrato ſit æqualis, cum per vl
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timam 2. Eucl. poſſimus triangulo huic quadratum æquale conſtruere, quod
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conſequenter dato circulo æquale erit. </
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<
s
id
="
s.000681
">Quod ſi in modum Problematis ita
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proponatur: Dato circulo æquale quadratum conſtruere, nondum inuenta
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eſt ratio, quæ demonſtratione confirmetur, qua id geometricè penitus, hoc
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eſt ad æqualitatem mathematicam, ſeu exactiſſimam effici poſſit,
<
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abbr
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totaq́
">totaque</
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>
; dif
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ficultas poſita eſſe videtur in inueſtigando, quonam modo exhibeamus li
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neam rectam B C, æqualem peripheriæ circuli dati. </
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>
<
s
id
="
s.000682
">quam nullus hactenus
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geometricè illi æqualem potuit exhibere,
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abbr
="
atq;
">atque</
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exhibita
<
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abbr
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euidẽti
">euidenti</
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demonſtra
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tione comprobare; Quamuis Archimedes acumine ſanè mirabili in lib. de
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lineis ſpiralibus, eam
<
expan
abbr
="
quoq;
">quoque</
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>
theorematicè, non tamen problematicè inue
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ſtigauit. </
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>
<
s
id
="
s.000683
">nam propoſitione 18. illius
<
expan
abbr
="
admirãdi
">admirandi</
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>
operis inuenit lineam rectam
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æqualem circumferentiæ primi circuli ſpiralis lineæ; propoſ verò 19. repe
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rit aliam rectam æqualem circumferentiæ ſecundi circuli. </
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>
<
s
id
="
s.000684
">tu ipſum conſule,
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ſi admirandarum rerum contemplatione delectaris. </
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<
s
id
="
s.000685
">Multa hac de re Pap
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pus Alexandrinus lib. 4. Math. coll. </
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<
s
id
="
s.000686
">& Ioannes Buteo vnico volumine om
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nes quadraturas tain priſcorum, quam recentiorum
<
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abbr
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cõprehenſus
">comprehenſus</
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eſt. </
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<
s
id
="
s.000687
">Qua
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re qui plura cupit, eos adeat; nos tamen infra ſuis locis explicabimus tres
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illas celebres antiquorum Antiphontis, Briſſonis, & Hippocratis quadra
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turas, quamuis falſas,
<
expan
abbr
="
quarũ
">quarum</
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>
ſæpe meminit Ariſt. & alij. </
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>
<
s
id
="
s.000688
">ſolet autem à non
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nullis diſputari, vtrum quadratura iſta problematica ſit poſſibilis, nec ne,
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cum videant eam à nemine, quamuis diu magno labore perquiſitam, hacte
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nus adinuentam eſſe. </
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>
<
s
id
="
s.000689
">ego quidem eſſe poſſibilem exiſtimo, quis enim dubi
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tare poteſt, poſſe exiſtere quadratum æquale circulo propoſito? </
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>
<
s
id
="
s.000690
">Quod ſi po
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teſt fieri, quare non etiam demonſtrari? </
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<
s
id
="
s.000691
">pręfertim cum videamus ab Archi
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mede iam inuentam eſſe, quatenus Theorema eſt. </
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>
<
s
id
="
s.000692
">& præterea conſtet, Hip
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pocratem quadraſſe lunulam, vt ſuo loco dicemus, & Archimedem in </
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chap
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</
archimedes
>