Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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ſphæram in plana vlla reſoluere,
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neq;
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in alias plures ſuperficies, quia ſphæ
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ra ambitur vnica tantum ſuperficie ſphærica. </
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<
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ra generant, vt facit Plato in Timæo, accipíunt primò triangulum æquila
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terum, & ex quatuor triangulis æquilateris ſimul compactis conficiunt py
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ramidem; & hoc modo alia ſolida à pluribus ſuperficiebus ambita conſti
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tuunt: verum hac ratione nullo modo poſſunt ſphæram componere, quia
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vnica tantum,
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eaq́
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; ſphærica ſuperficie compræhenditur:
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hoc pacto iſti
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diuidentes, & componentes corpora fidem faciunt, ſphæram, cum ex nullis
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componatur, ſolidorum eſſe primam.</
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106</
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<
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">Tex. 25.
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(Est autem, & ſecundum numerorum ordinem aſſignantibus, ſic po
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nentibus rationabiliſſimam, circulum quidem ſecundum vnum; triangulum autem
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ſecundum dualitatem, quoniam duo recti. </
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<
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">circulus non erit figura)
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In ordine figurarum conueniens eſt, inquit, primam
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facere circulum propter ſimpliciſsimam ipſius naturam, cum vnica, ac per
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fecta circulari linea comprehendatur:
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Triangulũ
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verò ſecundam, quoniam
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duo anguli recti, ideſt, quia triangulum habet tres angulos æquales duobus
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rectis angulis; quod fusè explicatum eſt lib. 1. Priorum, ſecto 3. cap. 1. De
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mum ſi primum locum dederimus triangulo, nullus alius remanet pro cir
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culo, quod eſt inconueniens, ergo circulus prima figura erit.</
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107</
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<
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">Tex. 31.
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(At verò, quod aquæ ſuperficies talis ſit, manifeſtum eſt hac ſuppoſi
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tione ſumpta, quod apta natura eſt ſemper confluere aqua ad magis concauum: ma
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gis autem concauum eſt, quod centro propinquius est. </
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<
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id
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">ducantur ergo ex centro A,
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linea A B, & linea A C, & producatur, in qua B C,
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ducta igitur ad baſim linea, in qua A D, minor eſt eis,
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quæ ex centro. </
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">magis igitur concauus locus eſt, quare
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influet aqua, donec
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æquetur. </
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<
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">æqualis eſt autem eis,
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quæ ex centro linea A E, quare neceſſe eſt apud eas, quæ
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ex centro, eſſe aquam, tunc enim quieſcet. </
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">linea autem,
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quæ eas, quæ ex centro tangit, circularis eſt, ſphærica
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igitur aquæ ſuperficies eſt, in qua B E C.)
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toto hoc
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textu lineari demonſtratione probat aquæ manen
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tis ſuperficiem eſſe ſphæricam: quæ demonſtratio
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perſpicua euadit, ſi figura, quæ in codicibus tam
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græcis, quam latinis,
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etiam in commentarijs deſideratur, quemadmo
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dum fecimus, reſtituatur. </
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<
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id
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">ſit igitur in præcedenti figura A, centrum mundi,
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ex quo educantur duæ rectæ lineæ æquales A B, A C, quæ deinde alia recta
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B C, coniungantur. </
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<
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recta alia ex centro A, quæ pertingat
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ad B C, quæ baſis eſt trianguli B A C, & producatur vlterius quantumlibet
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in E. intelligatur demum circumferentia tranſire per puncta B, & C, quia
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illæ duæ lineæ A B, A C, ſunt æquales, quæ circumferentia alteram A D, quæ
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fuit protracta, ſecet in E. </
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<
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defluit ad locum magis concauum, ideſt, ad loca centro A, terræ propin
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quiora, quale eſſet in figura locus D, reſpectu locorum B, & C, quia A D,
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linea minor eſt ijs, quæ ex centro eductæ ſunt A B, A C. quapropter aqua
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debet defluere ex B, ad D, vel ex C, ad idem D, donec pertingat ad E. qui
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locus non eſt decliuior punctis B, & C. quare cum loca B, E, C, quæ ſunt </
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