Clavius, Christoph
,
In Sphaeram Ioannis de Sacro Bosco commentarius
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Comment. in I. Cap. Sphæræ
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<
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">THEOR. 15. PROPOS. 17.</
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<
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omnibus corporibus ſibi iſoperimetris, planis ſuperficie-
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note-138-01
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note-138-01a
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xml:space
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">Sphæra ma
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ior eſt om-
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nibus cor
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poribus ſi-
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bi Iſoperi-
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metris, &
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@irca alias
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ſphæ as cir
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cũſeriptibi-
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libus, quæ
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planis ſuꝑ
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ficiebus co
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tinentur.</
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bus contineãtur; </
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">circa{q́ue} alias ſphæras circumſcriptibilia ſint, hoc eſt, quorũ
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omnes perpendiculares ad baſes productę ab aliquo puncto medio ſint equa
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les, maior eſt.</
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<
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ſphęra A, cuius centrum A, & </
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<
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circa aliquam ſphęram circum ſcriptibile ſibi iſoperimetrum C, cuius una per
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pendicularium C D. </
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<
s
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">Dico ſphęram A, maiorem eſſe ſolido C. </
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<
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">Intelligatur
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enim circa ſphæram A, corpus deſcriptum ſimile prorſus ſolido C, ita ut ſin-
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gula quoque latera contingant ſphæram A, hoc eſt, eius perpendiculares,
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quarum una ſit A B, ſint quoque æquales, nempe ſemidiametri ſphæræ A exi-
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ſtentes. </
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<
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">Itaque quoniam ambitus corporis circa ſphęram A, maior eſt ambi-
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tu ſphæræ A, (per ea, quę ab Archimede ſunt demonſtrata lib. </
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138-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/138-01
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ra, & </
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">cylindro, propoſ. </
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rit quoque eiuſdem corporis
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ambitus maior ambitu corpo-
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ris C. </
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">Quare perpendicularis
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A B, hoc eſt ſemidiametri ſphę
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ræ A, maior erit perpendicula
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ri C D. </
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<
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">Quamobrem rectangu
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lum ſolidum contentum ſub
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ſemidiametro A B, & </
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<
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parte ambitus ſphęrę A, quod
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(per præcedentẽ propoſ.) </
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ræ A, æquale eſt, maius erit,
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quàm rectangulum ſolidum
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contentum ſub perpendicula-
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ri C D, & </
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<
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corporis C, hoc eſt, (per 15. </
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poſ. </
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<
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">huius) quàm corpus C.
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</
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<
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">Sphæra igitur omnibus corpo
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ribus ſibi Iſoperimetris, quæ
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planis ſuperficiebus continean
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tur, &</
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@onſtr andum.</
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ior eſt om-
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nibus cor-
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poribus ſi
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bi iſoperi
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metris, &
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circa alias
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ſphæras cir
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cunſcripti-
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@ilibus.</
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<
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omnibus corporibus ſibiiſoperimetris, & </
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ras circumſcriptibilibus, quæ ſuperficiebus conicis contineantur, ita ut la-
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tera omnia conica ſint æqualia, maior eſt.</
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<
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<
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circulus A B C D, cui circumſcribatur figura regularis E F G H-
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I K L M, ita ut numerus laterum à quaternario menſuretur, cuiuſmodi eſt qua
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dratum, figura 8. </
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