Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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cem diuertere argumentationem, præſertim tam inualidam. </
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<
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id
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">nam multis modis im
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becillis eſt eiuſmodi ratio, & quouis modo licet euitare, ne aut inuſitata dicere, aut
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argui videamur.
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<
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">Refellit hoc loco ſuperiores rationes in tribus locis præmiſſis allatas,
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quibus nonnulli probabant quantitatem ex indiuiduis conſtare, & proinde
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concedenda eſſe quædam Quanta, omninò atoma; ſic igitur inquit. </
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<
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id
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">Quod
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verò de commenſurabilibus lineis dicunt, omnes videlicet vnica quadam,
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abbr
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eademq́
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; determinata menſura menſurari oportere, falſum omninò eſt, &
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contra mathematicorum dogmata, non enim Geometræ hoc aſſerunt, cùm
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ipſorum demonſtrationibus aduerſetur; ſed
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abbr
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tantũ
">tantum</
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dicunt omnes lineas, quæ
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ad inuicem ſunt commenſurabiles, commenſurari, vna
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abbr
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eademq́
">eademque</
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; menſura,
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ſed non tamen vnica, ideſt non vnica, ac determi
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nata. </
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<
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id
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">poſſunt enim eſſe plures
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abbr
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eædemq́
">eædemque</
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; menſuræ
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communes plurium quantitatum commenſura
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bilium, vt præſentium trium linearum 4. 6. 8.
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communis
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abbr
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mẽſura
">menſura</
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eſt linea 2. binarius enim tres
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numeros 4.6. & 8. menſurat. </
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<
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">& ſi linea 2. bifariam
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ſecetur, erit dimidium eius linea 1. quæ pariter
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erit communis menſura trium prædictarum li
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nearum, cûm vnitas ſit omnium numerorum communis menſura. benè ve
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rum eſt, quod Geometræ, quando ſimpliciter loquuntur de huiuſmodi com
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muni menſura, intelligunt de ea, quæ inter omnes eſt maxima: vt in prædi
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ctis tribus lineis maxima earum communis menſura eſt linea 2.
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Atq;
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hoc ſi
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bi volunt Geometræ, ex quibus totus hic textus intelligi poteſt.</
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281</
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<
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">Quintus locus
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(Ob rectæ verò lineæ motum in ſemicirculum, quam neceſſe eſt
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in rectum ita diuidere, vt infinitæ circunferentiæ, & interualla totidem inuenian
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tur)
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Interpres latinus ſic vertit
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(Ob rectæ verò lineæ motum in ſemicirculum
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diuiduas non credere, &c.)
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vbi verba illa
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(Diuiduas non credere)
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pro arbitrio,
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ac ſine ratione, imò contra rationem addidit: tum quia in Græco textu non
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extant, tum quia ſenſus totius ſententiæ is eſt, vt potius debuiſſet affirmati
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uè dicere
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type
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(Diuiduas credere)
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nam Ariſtoteles videtur ſic
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argumẽtari
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, quan
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do recta linea A B, vt in appoſita figura mo
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uetur intrando in ſemicirculum C A D B, ita
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vt primò ſit in ſitu A B, ſecundò in E F, tertiò
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in G H, & ſimiliter in alijs omnibus ſemicir
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culi locis, neceſſariò accidit, vt infinitæ peri
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phęriæ, quales
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abbr
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sũt
">sunt</
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A B, E A B F, G E A B F H,
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cadant inter infinitas partes lineæ ingredien
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tis, vt ſunt A B, E F, G H,
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tam tota recta
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ingrediens, quàm totus ſemicirculus, diuidatur in partes infinitas, ita vt
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nulla pars lineæ rectæ,
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neq;
">neque</
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vlla ſemicirculi ſuperſit, quæ ſe ſe mutuò non
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diuidantur, ergò nihil tam in linea, quàm in ſemicirculo remanet, quod non
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ſecetur: tota igitur linea recta, & periphæria illa diuidua eſt, quam ob rem
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nullo modo conſtare poteſt ex indiuiduis, ex quibus manifeſtum eſt perpe
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ram additamentum illud factum eſſe, & ſimul ratio, & textus Ariſt. eadem
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opera patefacta ſunt.</
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