Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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iſtud diſſerere. </
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">& quia partim rationibus phyſicis, partim geometricis vti
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tur, ideò nec omninò phyſicus nec omninò mathematicus eſt. </
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<
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quæ mathematica ſunt, ex inſtituto exponere aggrediar.</
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">Ad intelligentiam igitur huius operis neceſſarium eſt nouiſſe, quæ nam
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ſint quantitates commenſurabiles, & quæ in commenſurabiles. </
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<
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">quæ prima,
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& ſecunda definitione 10. Elem. explicantur;
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egoq́
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; eas primo Priorum oc
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caſione aſymetriæ diametri cum coſta ſatis expoſui: vtrumuis locum vide
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ris præſenti neceſſitati conſultum erit.</
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277</
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<
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">Primus locus Mathematicus eſt hic
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(Poſtremò ex ijs, quæ tradunt Mathe
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maticis imbuti diſciplinis, quiuis lineam aliquam inſecabilem eſſe concedet. </
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<
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ſi, vt aiunt, illæ commenſurabiles ſunt lineæ, quæ eadem menſura dimetiri queunt,
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& nihil impedit, quin omnes commenſurabiles re ipſa dimetiantur, extabit profe
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ctò longitudo aliqua, qua omnes commenſurabuntur; quæ neceſſario erit indiuidua,
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nam ſi dicatur eſſe diuidua, huius
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quoq;
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menſuræ partes, menſuram aliquam com
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munem habebunt, partes enim toti commenſurabiles ſunt ita, vt portio partis il
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lius, quæ dimidium totius fuerat, efficiatur dupla alterius; quoniam autem hoc
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fieri nequit, atoma debet eſſe menſura hæc communis.
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Eodem modo, & quæ ſimul ab ipſa menſura commenſuratæ, tanquam omnes ex
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ea menſura compoſitæ ſunt lineæ, veluti ex atomis conflantur.
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<
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">Affert rationem quandam ex Mathematicis, qua nonnulli probabant ex
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tare lineas atomas, ex quibus cæteræ lineæ tanquam partibus conſtarent:
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ac proinde negabant lineas eſſe in infinitum diuiduas, ſeu quamlibet lineam
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ſecari poſſe, ſed aſſerebant
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diuidẽdo
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, tandem ad indiuiduas
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eſſe.</
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">Præmiſſa igitur, vt monui commenſurabilium, & incommenſurabilium
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linearum cognitione in hunc modum, & textum Ariſtot. & rationem ipſo
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rum exponam.</
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<
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">Mathematici oſtendunt extare lineas commenſurabiles, quæ ſcilicet ea
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dem communi menſura menſurantur: at nihil impedit quin omnes
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ſurabiles</
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re ipſa menſurentur, debet ergò extare vna aliqua longitudo, qua
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omnes commenſurabiles dimetiamur. </
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<
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">hanc autem neceſſe eſt eſſe atomam,
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nam ſi diuidua ſtatuatur, poterit ſemper ſecari, & ſubſecari bifariam, qua
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re cum partes huiuſmodi ſint toti commenſurabiles, ſequetur aliam exiſtere
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menſuram, qua omnes hæ partes, & proinde tota linea commenſurentur.
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</
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<
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">Verùm hoc fieri nequit, nam hoc pacto non eſſet vna tantum longitudo om
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nium commenſurabilium linearum communis menſura, verùm plures, &
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plures in infinitum, quod eſt contra Mathematicorum placita. </
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<
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id
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">dicendum,
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itaque, communem illam omnium menſuram eſſe omnis diuiſionis exper
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tem; & propterea etiam lineas omnes commenſurabiles ex atomis lineis
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componi, quæ nimirum prædictæ communi menſuræ æquales ſint. </
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hæc
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eſt illarum prima argumentatio.</
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<
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(Idem etiam contingit in figuris planis, quæ à lineis rationa
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libus procreantur: nam omnes huiuſmodi figuræ erunt etiam inuicem commenſura
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biles, quare
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ēadem
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ratione, qua in lineis proximè vſi ſumus, ſequetur earum com
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munem menſuram eſſe pariter indiuiduam.
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<
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cõmenſurabiles
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longitudine, eſſe etiam com
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menſurabiles (vt aiunt Geometræ) potentia, ideſt ſecundum quadrata </
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