Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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quos ſolùm terminatos Arithmeticus accipit. </
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<
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s.005086
">eſſe autem genera hæc termi
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natæ Quantitatis Geometriæ, aut Arithmeticæ ſubiectum, ex eo patet, quod
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eas ſolas quantitates ipſi definiunt,
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deq́
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; ipſis varias paſſiones
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demonſtrãt
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,
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easq́
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; omninò ab eis diuerſas, quas Phyſicus, & Metaphyſicus in ea abſolu
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tè ſpectata conſiderant. </
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<
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id
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s.005087
">Vnde manifeſtum eſt, has affectiones, quas Ma
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thematicus contemplatur ab ipſa Quantitate, quatenus terminata eſt ema
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nare; ſunt autem æqualitas, inæqualitas, talis diuiſio, transfiguratio, pro
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portiones variæ, commenſuratio, incommenſuratio, figurarum
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abbr
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cõſtructio-nes
">conſtructio
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nes</
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, &c. </
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<
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s.005088
">Quæ ſanè affectiones ab intrinſeca Quantitatis natura minimè
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fluunt, poſita enim ea interminata, prædictæ paſſiones non conſequuntur,
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nihil enim, ea ſic poſita, eſt æquale, aut inæquale, &c. </
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<
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id
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s.005089
">ſed addita Quantita
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ti terminatione, eæ ab ea per emanationem profluunt. </
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<
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id
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s.005090
">Quapropter inrè di
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xeris formalem rationem Mathematicæ conſiderationis eſſe Terminatio
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nem; & obiectum totale adæquatum eſſe Quantitatem terminatam, qua
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tenus terminata eſt. </
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<
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id
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s.005091
">Ex hac enim terminatione variæ oriuntur figuræ, &
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numeri, quas Mathematicus definit,
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abbr
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deq́
">deque</
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; ipſis varia demonſtrat. </
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<
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id
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s.005092
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<
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abbr
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Atq;
">Atque</
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hæc
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eſt illa Quantitas, quæ dici ſolet materia intelligibilis, ad differentiam ma
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teriæ ſenſibilis, quæ ad Phyſicum ſpectat; illa enim ab hac per intellectum
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ſeparatur, ac ſolo intellectu percipitur. </
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<
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id
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s.005093
">Continuum igitur, & diſcretum,
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vtrumq;
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<
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abbr
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terminatũ
">terminatum</
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, eſt materia intelligibilis, illud Geometriæ, iſtud Arith
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meticæ. </
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<
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id
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s.005094
">Hinc etiam patet, cur dicatur Mathematicus conſiderare Quan
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titatem finitam, quia accipit terminatam, quæ finita eſt: quod enim habet
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terminus, ſeu fines, finitum eſt. </
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<
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id
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s.005095
">quod ſi dari poſſet quantitas aliqua termi
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nata, & ſimul infinita, de ea etiam Demonſtrationes Euclidis fieri poſſent;
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ſi enim daretur triangulum infinitum, eodem modo de eo oſtendi poſſet ha
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bere tres angulos æquales duobus rectis. </
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<
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id
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s.005096
">Porrò hanc terminatam Quanti
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tatem eſſe Geometriæ, & Arithmeticæ ſubiectum minimè cognouerunt ij,
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qui Geometricas demonſtrationes impugnarunt, vt in eorum ſcriptis vide
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re eſt, quæ prima eis fuit errandi occaſio.</
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<
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id
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">Porrò ex hac mathematica abſtractione à materia ſenſibili, fit vt materia
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hæc abſtracta perfectionem quandam acquirat, quam perfectionem mathe
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maticam appellant. </
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<
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id
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">v. g. triangulum abſtractum eſt omninò planum ex tri
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bus lineis omninò rectis,
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tribusq́
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; angulis punctis omninò indiuiduis con
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ſtitutum, quale in rerum natura (exceptis fortè cœleſtibus) vix puto repe
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riri poſſe. </
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<
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id
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s.005099
">vnde nonnulli ſolent Mathematicis illud obijcere; entia ſcilicet
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mathematica non extare, niſi per ſolum intellectum. </
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<
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id
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s.005100
">Verumenimuerò ſcien
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dum eſt entia hæc mathematica, quamuis in ea perfectione non extent, id
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tamen eſſe per accidens, conſtat enim naturam, & artem figuras mathema
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ticas præcipuè intendere, quamuis propter materiæ ſenſibilis ruditatem, &
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imperfectionem, quæ perfectas omninò figuras ſuſcipere nequit, ſuo ſine
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fruſtrentur; natura enim in truncis arborum cylindri figuram affectat, in
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pomis, & vuarum acinis aut ſphæricam, aut ſphæroidem, in cornea oculi
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circulum; imò oculus ipſæ maximè ſphæricus eſt. </
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<
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">Sol,
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reliquaq́
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; aſtra com
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muni omnium conſenſu omninò ſphærica ſunt. </
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<
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">ipſa aquæ ſuperficies globo
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ſa eſt. </
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s.005103
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<
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abbr
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terraq́
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; ipſa niſi obſtaret materiæ craſſities, & diuerſitas, rotunda pla
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nè euaderet. </
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<
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