Clavius, Christoph
,
In Sphaeram Ioannis de Sacro Bosco commentarius
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Comment. in I. Cap. Sphæræ
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des (nempe corpus A B C D, ex illis compoſitum) æquales ſolido rectangu-
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lo L R. </
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&</
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cuiuslibet ſphærę æqualis eſt ſolido rectangulo comprehenſo
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">Sphę ra q̃li
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bet cui pa-
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rallel epipe
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do ſit ęqua
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lis.</
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ſub ſemidiametro ſphæræ, & </
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ſphæra A B C, cuius centrum D, ſemidiameter A D: </
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tem rectangulum E, contentum ſub ſemidiametro A D, & </
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tus ſpæræ A B C. </
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">Dico corpus E, ſphæræ A B C, eſſe æquale. </
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æquale; </
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<
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">ſit, ſi fieri poteſt, primum maius, ſitq́ue exceſfus corporis E, ſupra
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ſphęram A B C, quantitas F. </
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">Intelligatur circa ccntrum D, deſcripta ſphæ-
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ra GHK, maior quàm ſphæra A B C, ita tamen, ut exceſſus ſphęrę G H K,
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ſupra ſphęram A B C, non ſit maior quantitate F, ſed uel æqualis, uel mi-
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nor, hoc eſt, vt ſphæra G H K, ſit uel ęqualis ſolido E, quando nimirum
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ipſa excedit ſphæram A B C, præciſe
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quantitate F; </
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">uel minor, ſi nimirum
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ipſa excedit ſphęram A B C, mino-
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ri quantitate, quàm F. </
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enim aliqua ſphæra erit, quæ uel
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æqualis ſit magnitudini E, atque
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adeo maior, quàm ſphæra A B C;
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</
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<
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">uel maior quidem quã ſphęra A B C,
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minor vero quàm magnitudo E, quæ
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maior ponitur, quàm ſphæra A B C. </
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Inſcribatur deinde intra ſphæram
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G H K, corpus, quod non tangat
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ſphæram A B C, ita ut unaquæque
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perpendicularium ex centro D, ad
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baſes iſtius corporis eductarum ma-
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ior fit ſemidiametro A D. </
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">Si igitur
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à centro D, ad omnes angulos di-
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cti corporis ducantur lineæ rectæ,
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ut totum corpus in pyramides di-
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uidatur, quarum baſes ſunt eædem,
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quæ corporis G H K, uertex au-
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tem communis centrum D; </
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<
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">erit quæ
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libet pyramis (per 14. </
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ius) æqualis ſolido rectangulo contento ſub eius perpendiculari, & </
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parte baſis; </
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<
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">A tque idcirco ſolidum rectangulum contentum ſub ſemidiame-
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tro A D & </
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erit. </
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<
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">Et quoniam omnia ſolida rectangula contenta ſub ſingulis perpendi-
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cularibus ex centro D, ad baſes corporis dicti protractis, & </
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tijs partibus baſium, ſimul ęqualia ſunt toti corpori, efficiunt autem om-
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@es tertiæ partes baſium ſimul tertiam partem ambitus corporis, erit </
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