Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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beat neceſſe eſt. </
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">& ſi triangulum ſecus, ita etiam, & quadratum commutabitur,
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ex altera parte enim ei reſpondet. </
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">& ſi quadratum quatuor angulis rectis æquales,
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non habuerit angulos ne quidem triangulum duobus rectis habebit æquales)
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Hanc
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trianguli affectionem, habere ſcilicet, ſuos tres angulos æquales duobus re
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ctis angulis abundè explicaui libro 1. Priorum, ſecto 3. cap. 1. quam Eucli
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des propoſit. </
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">32. primi demonſtrauit, ex qua demonſtratione, tanquam ex
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Geometrico principio ſequitur omne
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quadrangulum habere quatuor
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angulos æquales quatuor rectis angulis; omne
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namq;
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quadrangulum eſt po
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tentia duo triangula, cum diuidatur ducta ipſius diametro in duo
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trìãgula
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.
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">quod ſi triangulus proprietatem illam non haberet,
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hæc quadrangulo
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conueniret. </
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">& ſi quadrangulum non haberet quatuor angulos æquales qua
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tuor rectis angulis, neque triangulum habere poſſet tres angulos æqua
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les duobus rectis, cum nihil ſit aliud triangulum, quàm dimidiatum qua
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drangulum.</
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320</
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<
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">Cap. 16.
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(In Geometria ſi quidem cum quis dixerit quadrangulŭm quatuor rectis
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æquales habere, & percunctatur propter quid, occurrit, quia etiam triangulŭm duo
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bus rectis æquales habet. </
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">in his igitur ex determinato ſibi principio propter quid
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aſſumpſerunt)
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Lege, quæ proximè in præcedenti loco expoſui, ea enim om
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nia huc etiam pertinent. </
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">hoc ſolum addendum ad illorum verborum (
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Ex de
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terminato ſibi principio propter quid aſſumpſerunt
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) intelligentiam, ideſt ex vna
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concluſione demonſtrata, tanquam principio alia demonſtrant; quod rectè
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fieri Ariſt. in primo Poſter. docet.</
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321</
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<
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">Cap. 31. (
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A qui proportionale in quatuor nihilominus perficitur: nam quem
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admodum A, ad B, ita C, ad D.
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) ideſt proportionalitas in quatuor terminis
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conſiſtit, quemadmodum pluribus ſupra lib. 5. cap. 3. Ethycorum explica
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tum eſt: quò nunc Lectorem ablego.</
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Ex primo Libro Moralium Eudemiorum.
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322</
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<
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">Cap. 5 (
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Vt ſi duplum multiplicium primum est, non licet multiplex com
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muniter prædicatum ſeparari, quippe, quod duplo prius eſt
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) Inter pro
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portionum genera vnum eſt, quod dicitur multiplex, quod ſub ſe
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infinitas ſpecies continet, vt Duplum, Triplum, Quadruplum, & c.
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in infinitum. </
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<
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">vbi vides, cur Ariſt. dixerit duplum eſſe primum inter multi
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plicia, cum verè naturali ordine numerorum ipſi primus debeatur locus.
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<
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">Vides etiam cur non liceat, Multiplex ipſum genus commune prædicatum
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omnibus ſpeciebus veluti Idæam ſeparari; tunc enim ait, ipſum mul
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tiplex abſtractum eſſet prius ordine ipſo primo multiplici, ſci
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licet duplo; & Duplum non eſſet primum inter mul
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tiplicia, quæ
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ſunt abſurda; non igitur
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illud tanquam Idæam licet ſepa
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ratum ponere.</
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