Clavius, Christoph
,
In Sphaeram Ioannis de Sacro Bosco commentarius
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Ioan. de Sacro Boſco.
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cuiuslibet corporis planis ſuper ficiebus contenti, & </
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quodlibet,
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in qua ſphę
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ra deſcribi
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poteſt, cui
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parallelepi-
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pedo æqua-
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le ſit.</
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ram aliquam circumſcriptibilis, hoc eſt, à cuius puncto aliquo medio omnes
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perpendiculares ad baſes eius productæ ſunt æquales, æqualis eſt ſolido re-
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ctangulo contento ſub una perpendicularium, & </
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<
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poris.</
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corpus planis ſupeificiebus contentum A B C D, circa ſphæram
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E F G H, cuius centrum I, deſcriptum, in quo ducantur ex I, ad puncta con-
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tactuum lineę rectæ I E, I F, I G, I H, quæ ad baſes ſolidi erunt perpendicula-
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res. </
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<
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<
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">per rectam I E, ducatur planum faciens in ſphæra, per propoſ.
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<
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">in baſi rectam A B, tanget circulus
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E F G H, rectam A B, in puncto E, propterea quòd ſphæra baſim non ſecat,
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ſed tangit. </
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per I E, ducatur aliud planum à priori dif-
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135-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/135-01
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ferens, fiet alius circulus in ſphęra, & </
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nea recta in eadem baſi ſecans rectam A B,
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in E, ad quã etiam I E, perpẽdicularis erit
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Ac propterea I E, ad baſim ſolidi per illas
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rectas ductam perpendicularis erit. </
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<
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ter oſtendemus, rectas I F, I G, I H, ad
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alias baſes eſſe perpendiculares. </
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que ſolidum rectangulum L R, cuius baſis
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K L M N, ſit æqualis tertiæ parti ambitus
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corporis A B C D; </
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">altitudo uero, ſiue per
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pendicularis L P, æqualis uni perpendicu-
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lariũ ex centro I, ad baſes corporis ABCD,
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cadentiũ; </
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">quæ omnes inter ſe ęquales ſunt
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ex defi. </
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A B C D, æquale eſſe. </
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centro I, ad oẽs angulos corporis ABCD,
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rectę lineę, vt totum corpus in pyramides,
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ex quibus componitur, diuidatur: </
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<
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quidem pyramidum baſes e
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ędem ſunt, quę
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corporis, vertex autem communis centrum I. </
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tem propoſ.) </
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<
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">quælibet harum pyramidum æqualis eſt ſolido rectangulo ſub
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perpendiculari L P, quæ ſingulis perpendicularibus corporis A B C D, æqua-
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lis ponitur, & </
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quot ſunt pyramides, erunt omnia hęc ſimul æqualia ſolido rectangulo L R.
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<
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">(Si enim rectangulum K L M N, diuidatur in tot rectangula, quot baſes ſunt
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in ſolido propoſito, ita ut primum æquale ſit tertię parti unius baſis, & </
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cundum tertiæ parti alterius, & </
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">ita deinceps, quandoquidem totum rectangu-
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lum K L M N, æquale ponitur tertię parti totius ambitus ſolidi, intelligan-
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tur autem ſuper illa rectangula conſtitui parallelepipeda; </
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<
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æqualia parallelepipedo L R.) </
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<
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ramidibus ſint ęqualia, per propoſ. </
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<
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