Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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definitio illius rei, de qua diſſeritur. </
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">Porrò exemplum mathematicum hic
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allatum ſic videtur explicandum: Conetur aliquis demonſtrare hanc pro
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poſitionem; ſi linea ducta fuerit æquidiſtans lateri vnius plani trianguli, ſe
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cabit & latera, & locum, ideſt ſuperficiem illam triangularem ſimiliter, ideſt
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in eadem proportione, vt in triangulo A B C,
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linea D E, parallela baſi B C, ſecat latera A B,
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& A C, in punctis D, & E, in eadem ratione,
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in qua etiam fecat totum triangulum, ita vt
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eadem ſit proportio lineæ A D, ad D B, & lineæ
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A E, ad E C, quæ eſt partium totalis trianguli
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A B C, ſcilicet quæ eſt partis A D E, ad partem
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E D C, fiue ad partem D E B. quod conſtat ex
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ſecunda 6. Elem. </
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<
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">Inquit ergo Ariſt. </
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">Si quis
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vellet hoc demonſtrare nondum præmiſſa defi
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nitione eorum, quæ habent eandem rationem, ſiue nondum definitione al
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lata quantitatum proportionalium, hic difficile id valeret oſtendere: at ve
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rò allata prius definitione quantitatum proportionalium facile demonſtra
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bit. </
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<
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">Subdit verò Ariſt. dictam definitionem, dicens, tunc quantitates eſſe
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proportionales, quando habent eandem ablationem, ideſt, eandem diuiſio
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nem, ideſt, eadem diuiſio ne tantum proportionaliter de vna, quantum de
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altera magnitudine reſecatur: Quemadmodum etiam Euclides loco cita
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to probat, latera illius trianguli, & ſuperficiem eſſe ſimiliter diuiſa, ex quo
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ſequitur eſſe proportionalia. </
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">Porrò Euclides definit. </
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">ſeptima 5. paulo ali
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ter definit quantitates proportionales eſſe illas, quæ eandem habent ratio
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nem, v. g. ſi ſit, vt prima ad ſecundam, ita tertia ad quartam. </
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<
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quoad Mathematicas ſpectat, huic loco ſatisfactum ſit.</
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82</
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<
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">Cap. 4. loco 86.
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(Tentandum autem, & ea, in quæ ſæpiſſimè incidunt diſputa
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tiones, tenere, nam quemadmodum in Geometria ante opus eſt circa elementa exer
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citatum eſſe, & in numeris circa capitales promptè ſe habere, & multum refert ad
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hoc, & alium numerum cognoſcere multiplicatum)
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Elementa vocabant antiqui
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demonſtrationes faciliores, & ſimpliciores, quales propriè ſunt omnes, quæ
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ſex prioribus libris Euclidianis continentur: ex illis enim tanquam ex ele
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mentis abſtruſiores, & difficiliores demonſtrationes deducebant. </
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atq;
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hæc
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eſt ratio, cur Euclides ſuos libros elementa nuncupauerit. </
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<
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">ait igitur curan
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dum eſſe horum elementorum cognitionem in promptu habere, quia fre
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quens de ipſis incidit diſputatio. </
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<
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">Per capitales numeros intelligo ſimplices
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ab vnitate,
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ad nouem incluſiuè. </
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">& quando ait, alium numerum cogno
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ſcere multiplicatum, ſignificat vtile valdè eſſe ad quotidianum vſum
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cognoſcere, quemnam numerum producant numeri capitales,
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ſi ad inuicem multiplicentur, quamuis huiuſmodi co
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gnitio facilis, ac leuis ſit: qua de cauſa vide
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mus vſque in hanc diem pueros diu in
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Abaco memoriter perdiſcen
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do detineri.</
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