Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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retur. </
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<
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id
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">mirum eſt, quam breui ex apertiſſimis ad obſcuriſſima trahat, & ex
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humillimis in altiſſima ſtatim aſſurgat.</
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</
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<
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<
s
id
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s.005528
">Sed iam Arithmeticæ etiam fructus inſpiciamus: in qua pręter ea, quæ
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Euclides, Iordanus, & Maurolicus egregia ſanè adinuenerunt, quàm mira
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bile eſt illud veluti ſcientiarum monſtrum, ac portentum, quod Algebram
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vocant? </
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<
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id
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">nihil fortaſſe in tota peritiæ Encyclopedia ſubtilius, profundius ni
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hil, non humano ingenio par eſt, ſed quid cœlitus reuelatum dixeris: nume
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ros illos, quos ſurdos vocant, & qui nullo modo exprimi poſſunt, addit, ſub
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trahit, multiplicat, diuidit, perinde ac ſi numeri communes eſſent: illis ve
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rò, quos minores, quàm nihil
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abbr
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cõfingit
">confingit</
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, quid abſtruſius? </
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<
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">quibus tamen
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abbr
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vtriſq́
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;
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admirandas adeò diſſoluit quæſtiones, & enigmata, vt ij, qui hanc callent
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eruditionem, nihil in numerorum infinita ditione
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abbr
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obſcurũ
">obſcurum</
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, nihil arduum ti
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meant; vt propterea eos non homines, ſed vel intelligentias quaſdam ſepa
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ratas, aut præſtigiatores quoſdam eſſe exiſtimes.</
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<
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id
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">Hanc tandem Geometriæ, & Arithmeticæ tractationem abſoluentes, ex
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prędictis breuiter earum prærogatiuas ſic perſtringamus: quarum.</
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<
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id
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">Prima ſit, quòd omnes ſcientiæ partes ab inuicem diſtinctas obtinent, vi
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delicet primo loco definitiones,
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abbr
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easq́
">easque</
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; eſſentiales. </
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<
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">Secundò, poſtulata. </
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<
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id
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">Ter
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tiò, axiomata, quę ſunt tria principiorum genera; ex quibus ſcientia dedu
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citur. </
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<
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id
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">quapropter quarto loco ſuccedunt propoſitiones cum ſuis demon
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ſtrationibus: quæ partim problemata, partim Theoremata ſunt. </
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<
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id
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">hunc por
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rò doctrinæ ordinem pulcherrimum ab Ariſt. etiam traditum, præterquam
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in Mathematicis, & maximè hiſce puris nuſquam eſt reperire.</
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<
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id
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">Secunda, ex principiorum autem præmiſſorum certitudine fit, vt proce
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dant à notioribus nobis, & natura.</
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<
s
id
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">Tertia, quod omnes earum comprobationes ſunt
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demõſtrationes
">demonſtrationes</
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, partim
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à priori, partim à poſteriori, vbi nihil probabile, nulla opinionum diſcordia,
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ſed totum euidens, concors, & verum cernitur.</
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<
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id
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">Quarta, demonſtrationes à priori ſunt tantum à cauſis intrinſecis mate
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ria, & forma.</
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<
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">Quinta, demonſtrationes earum, vt plurimum, & quod, & propter quid
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ſimul manifeſtant.</
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<
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">Sexta, eſt mirabilis, & perpetua demonſtrationum connexio, & dependen
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tia ab inuicem.</
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De Mathematicis medijs, Aſtronomia, Perſpectiua,
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Mathematica, Muſica. </
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<
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">Cap. 5.
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<
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id
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">De materia harum, cùm apud Philoſophos conueniat, nihil eſt,
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cur de ea dicamus. </
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<
s
id
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">Eas verò habere perfectiſſimas demonſtra
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tiones, quibus etiam mirabiles veritates,
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easq́
">easque</
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; ſcitu iucundiſſi
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mas nobis patefaciunt, vna,
<
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abbr
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eademq́
">eademque</
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, opera breuiter demonſtra
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bimus. </
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<
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id
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">non deeſt tamen Ariſt. authoritas 1. Poſter. tex. 30. aſſerentis eas
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habere cauſas demonſtrationum, ſic. </
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<
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id
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">Hic enim ipſum quidem quòd ſenſi
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tiuorum eſt ſcire, ipſum verò propter quid Mathematicorum, hi
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namq́
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; </
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