Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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tioribus nobis, & natura procedere, tales ſunt Geometricæ vt paulo ſupra
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patuit, ergò ipſæ potiſſimæ erunt demonſtrationes.</
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<
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id
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">2. Ex Themiſtio cap, 2. ſuæ paraphr. </
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<
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id
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">2. Poſter. Demonſtratio potiſſima
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debet oſtendere, & quod, & Propter quid. </
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<
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id
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s.005235
">quod profectò cæteris demon
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ſtrationibus melius præſtant Geometricæ, & Arithmeticæ. </
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<
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id
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s.005236
">v. g. demonſtra
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tio 32. 3. oſtendit angulum in ſemicirculo eſſe rectum, quod omninò igno
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tum erat; & affert cauſam, quæ pariter ignorabatur. </
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<
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id
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">Idem ferè faciunt aliæ
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omnes. </
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<
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id
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">in Mathematicis verò medijs, in Phyſica, & Metaphyſica effectus
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plerumq;
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noti ſunt, ſed cauſæ latent; dicendum igitur Geometricas demon
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ſtrationes ex Auerroe, & Themiſtio præſtantiſſimas eſſe.</
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<
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id
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">Tertia, quæ eſt euidentiſſima, ſumatur ex reſolutione aliquot demonſtra
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tionum. </
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<
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">Quid enim opus eſt diſputationem hanc per extraneas ambages
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agitare? </
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id
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">cum licear quaſi in rem præſentem ire, & veluti demonſtrationum
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anatome facta oculis ipſis earum media contueri. </
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<
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id
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">ſed prius in memoriam
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redigendum eſt, illam eſſe perfectiſſimam demonſtrationem, quæ non ſolùm
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rei demonſtrandæ cauſam propriam, & adæquatam affert, verùm etiam
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euidentiſſimè oſtendit talem paſſionem ab illa cauſa procedere, ita vt non
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poſsit, vt ait Ariſt. aliter res ſe habere, in quo profectò Mathematicæ ex
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cellunt. </
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<
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id
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">Cauſa verò hæc in Geometria, & Arithmetica aliquando eſt mate
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rialis, quando ſcilicet vtuntur pro Medio partibus, reſpectu totius; vel eſt
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formalis, quando nimirum Medium eſt definitio ſubiecti, aut paſsionis. </
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<
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id
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">non
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me tamen latet omnem perfectam demonſtrationem alio ſenſu dici à qui
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buſdam procedere per cauſam formalem, quia in ea continetur cauſalis de
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finitio paſsionis, quæ definitio cauſam ipſius exhibet, & proinde tanquam
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forma ipſius eſt, quæ rem in eſſe conſtituat.</
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<
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id
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">Secundò notandum eſt: Omnem demonſtrationis diſcurſum reſolui tan
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dem in aliquid, aut per ſe notum, aut à poſteriori comprobatum. </
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<
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">Satis. </
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">n.
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</
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id
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">eſt, vt cauſa euidentur appareat,
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abbr
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quocunq;
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id modo fiat. </
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<
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s.005249
">hoc dixi propter
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nonnullos, qui cùm in Geometricę demonſtrationibus lineam, aut diuiſionem
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aliquam, rei, quæ oſtenditur, non intrinſecam animaduertunt, ſtatim exi
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ſtimant eas per extrinſeca
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abbr
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demõſtrare
">demonſtrare</
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: ſed decipiuntur; quia non animad
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uertunt lineas illas, aut partitiones, non eſſe medium demonſtrationis, ſed
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adhiberi ad medij inuentionem, & connexionem cum paſſione. </
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<
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id
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">Quod au
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tem eorum dubitatio omninò vana ſit ex eo patet, quod plurimæ ſunt de
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monſtrationes, quæ ſine vlla linearum conſtructione, aut diuiſione compro
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bentur, vti ſunt 15.33 34.42. 36. in ſolo primo elementorum. </
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<
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">atque hæc
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erroris eorum præcipua cauſa eſt.</
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<
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id
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">His præmiſſis, primò oſtendemus cauſam formalem in Geometricæ de
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monſtrationibus reperiri deinde materialem. </
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<
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abbr
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idq́
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; primò per reſolutionem
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primę Euclidis, quæ à cauſa formali procedit. </
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">& quia hæc demonſtratio
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non theorema, ſed problema eſt, ideò ſciendum, quòd minimè aduerſarij
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animaduerterunt, in omni problemate per
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quandã
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<
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linearũ
">linearum</
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conſtructionem
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doceri aliquid effici. </
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<
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id
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">v. g. in præſenti docet Euclides, qua ratione deſcrip
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tis
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quibuſdã
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circulis circa datam lineam,
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ductisq́
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; aliquot lineis modo prę
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ſcripto, gignatur
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triangulũ
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æquilaterum, vt rem conſideranti manifeſtum
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eſt. </
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<
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">quare nullo modo lineamenta illa, vt illę circulorum ſemidiametri ſunt </
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