Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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Admirabilis quædam Ap̀um industria.
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<
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id
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">Cæterum occaſione harum figurarum illud hoc loco apponere vi
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ſum eſt, quod Pappus
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abbr
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Alexãdrinus
">Alexandrinus</
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initio quinti libri collectionum
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mathematicarum ſcribit, De admirabili Apum induſtria, atque
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prudentia in conſtruendo ſuas cellulas figura hexagona regulari.
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</
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<
s
id
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s.001555
">cum enim vellent omne vacuum excludere, & præterea capaciſſimam
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abbr
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om-niũ
">om
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nium</
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figuram habere, hexagonam accepere, quæ inter prædictas tres vtrum
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que præſtat, nam & inane omne excludit, & illarum trium capaciſſima eſt,
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cum magis ad circularem figuram accedat: vt patet ex tractatu de figuris
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Iſoperimetris, qui eſt apud Clauium in ſphæra, necnon in Geometria pra
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ctica. </
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<
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id
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s.001556
">hoc ideò libentius recenſui, quia animaduerti naturales hiſtoriogra
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phos omnes latere, vel ipſum Aldobrandum noſtrum, qui quamuis indu
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ſtrioſæ Apis inſtar omnia delibauerit, iſtud tamen de Apibus artificium tan
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ta ſapientia plenum, neſcio quo modo prætermiſit.</
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121</
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<
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">Ibidem
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(In ſolidis verò duæ ſolum pyramis, & cubus)
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ideſt replent locum
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ſolidum. </
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>
<
s
id
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s.001560
">nullum reperi, qui in hoc loco explicando non errauerit; nam Græ
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ci, qui alioqui ſolent mathematica probè intelligere, hic omnes lapſi ſunt,
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<
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abbr
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ſecumq́
">ſecumque</
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; & Arabes, & Latinos in
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abbr
="
eãdem
">eandem</
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>
foueam ſupra ſe miſerè traxerunt.
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</
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<
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id
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">communis ferè error omnium fuit, pyramides plures ſimul compactas poſ
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ſe replere ſolidum locum. </
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id
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s.001562
">quod vt melius intelligamus, ſciendum eſt, reple
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re locum
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abbr
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ſolidũ
">ſolidum</
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>
nihil aliud eſſe, quam ſi plura corpora ſolida ſimul ad idem
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punctum coaptata, ita conſtipentur, vt totum ſpatium, quod eſt circa pun
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ctum illud omninò occupent, hoc eſt, nihil vacui inter ipſa relinquatur: ſi
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cut enim prædictæ tres figuræ planæ, de quibus paulò ante, replent locum
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planum, ideſt ſuperficiem; ita cubi replent ſolidum, ideſt ſoliditatem ſimul
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vniti conſtituunt, ita vt ſi octo cubi ſimul ad idem punctum
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abbr
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coaptẽtur
">coaptentur</
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>
, con
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ſtituant corpus ſolidum ex octo illius conſtatum,
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abbr
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nihilq́
">nihilque</
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; inane inter ipſos
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cubos relinquatur. </
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<
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id
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">& ſicuti planæ illæ figuræ erant conficiendis pauimentis
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aptæ, ita ſolidæ hæ muris, qui corpora ſunt ſolida,
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conſtruẽdis
">conſtruendis</
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idonea ſunt.
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<
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Notã
">Notam</
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dum præterea, quod per pyramidem debemus intelligere pyramidem
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regularem, quæ dicitur etiam Tetraedrum,
<
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abbr
="
eſtq́
">eſtque</
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>
; ſecunda inter
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abbr
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quinq;
">quinque</
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>
cor
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pora regularia rectilinea, quæ alias Platonica corpora dicuntur. </
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<
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eorumq́
">eorumque</
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;
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definitiones ſunt in 11. Elem. </
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<
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id
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s.001566
">Tetraedrum autem ſic definitur, eſt figura ſo
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lida ſub quatuor triangulis æquilateris,
<
expan
abbr
="
atq;
">atque</
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>
inuicem æqualibus contenta:
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de hac inquam eſt ſermo. </
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>
<
s
id
="
s.001567
">quia ſi liceret intelligere de irregularibus figuris,
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infinitæ reperirentur figuræ tam planæ, quam ſolidæ, quæ vtrumque locum
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complerent. </
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<
s
id
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s.001568
">Aduertendum tandem Ariſt. videri loqui de repletione loci
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ſolidi, quia tranſit à planïs figuris ad ſolidas. </
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>
<
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id
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s.001569
">& quia ſi hæ duæ pyramis, &
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cubus replent locum ſolummodo ſecundum ſuas ſuperficies, quæ ſunt trian
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gulum, & quadratum, iam de his cum proximè ante dixiſſet, quid opus fuiſ
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ſet idem poſt modum repetere. </
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<
s
id
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s.001570
">ad hæc ſi in medium ſolida hæc duo profert,
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<
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abbr
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aitq́
">aitque</
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; ipſa replere locum, intelligens, planum, profectò non loquitur forma
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liter, ideſt de ipſis, vt ſolida ſunt. </
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<
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id
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">Quare Ariſt. videretur ſibi non conſtare,
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vel perperam exiſtimaſſe plura Tetraedra complere ſoliditatem. </
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<
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">deceptus </
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