Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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angulo recto C, ergo quadratum eius ex corol
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lario 47. primi, duplum erit quadrati B C, quare
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etiam circulus B C D F, duplus erit circuli A B
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G C, per 2. duodecimi, & ſemicirculus B C D,
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duplus erit ſemicirculi B A C: & quadrans B E
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C G, æqualis erit ſemicirculo B A C: ablato igi
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tur communi ſegmento B E C H, remanet lunu
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la B A C E, æqualis triangulo B C G, quod trian
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gulum ſi per vltimam ſecundi quadretur, erit lu
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nula B A C, conſequenter quadrata. </
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s.000853
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<
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abbr
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hucuſq;
">hucuſque</
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be
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nè procedit Hippocrates. </
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<
s
id
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s.000854
">ſed vt reliquum circu
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li quadret, ſic pergit, ponatur recta L M, dupla
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ipſius B C, ſupra quam ſemicirculus deſcribatur
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L O M, cui inſcribatur hexagoni
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æquilateri dimidium L Q S M, & ſu
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per tribus hexagoni lateribus, ſint
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tres ſemicirculi, vt in figura. </
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<
s
id
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s.000855
">&
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abbr
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quo-niã
">quo
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niam</
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diameter L M, dupla eſt
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abbr
="
vniuſ-cuiuſq;
">vniuſ
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cuiuſque</
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>
<
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abbr
="
diametrorũ
">diametrorum</
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>
B C, L Q, Q S,
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S M, erit ſemicirculus L O M, ęqua
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lis quatuor ſemicirculis prædictis
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per 2. duodecimi, & per 4. ſecundi
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lb
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ablatis igitur tribus
<
expan
abbr
="
ſegmẽtis
">ſegmentis</
expan
>
com
<
lb
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munibus L N Q, Q O S, S P M, relinquetur trapezium L Q S M, æquale ſe
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micirculo B A C, & tribus lunulis L H Q N, Q R S O, S X M P, abſcindan
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tur
<
expan
abbr
="
itaq;
">itaque</
expan
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de trapezio tria triangula æqualia tribus lunulis, eo modo, quo ſu
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pra in prima figura factum eſt, & quod relinquetur æquale erit ſemicirculo
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B A C. quod deinde quadretur per vlt. </
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>
<
s
id
="
s.000856
">ſecundi, ſed aduerte, quod quando
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ait, abſcindantur de trapezio tria triangula æqualia lunulis, eo modo, quo
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ſupra, committit deceptionem, quia eodem modo, quo ſupra minimè id fa
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cere poſſumus, quia in ſuperiori figura triangula erant conſtituta ſuper la
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tus B C, quadrati B C D F, intra circulum deſcripti, qui circulus facit cum
<
lb
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B C, maius
<
expan
abbr
="
ſegmentũ
">ſegmentum</
expan
>
, quam faciat ſemicirculus L O M, cum lateribus L Q,
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Q S, S M. & propterea ſemicirculus iſte non habet eandem proportionem
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ad vnamquamque lunularum ſuarum, quam habet ſemicirculus ſuperior
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B C D, ad lunulam B A C E.
<
expan
abbr
="
atq;
">atque</
expan
>
hæc eſt fallacia, quam authorem ſuum mi
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nimè latuiſſe putandum, cuius Ariſt. ſæpius mentionem in ſequentibus fa
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ciet : quì enim fieri poteſt, vt tam acutus inuentor, adeo manifeſtum erro
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rem non vidiſſet, verum propter adinuenti excellentiam, authori ſuo pla
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cuit paralogyſmus. </
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>
<
s
id
="
s.000857
">mirabilis tamen ſemper habita eſt illa ſuperior lunulæ
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quadratio. </
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>
<
s
id
="
s.000858
">Ex quibus ſatis clara eſſe poſſunt ea, quæ ad
<
expan
abbr
="
Mathematicũ
">Mathematicum</
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>
per
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tinent, ad locum hunc de Abductione declarandum. </
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>
<
s
id
="
s.000859
">facta eſt igitur abdu
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ctio ab Hippocrate in quadratione trium poſteriorum lunularum, in qua
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rum quadratione diu immoratus, nunquam niſi cum paralogyſmo quadra
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re valuit. </
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>
<
s
id
="
s.000860
">Hæc pluribus, vt ſequentibus etiam textibus, in quibus huius te
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tragoniſmi fit mentio ſatisfacere poſſimus. </
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<
s
id
="
s.000861
">Hippocrates iſte Chius eſt alter </
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