Casati, Paolo
,
Terra machinis mota : dissertationes geometricae, mechanicae physicae hydrostaticae
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bus feruntur. </
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<
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>Ponatur enim CT ſemidia
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metri pars milleſima, hoc eſt mill. 4. & eo
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amplius; ſegmentorum MON & MVN Ra
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tio inuenietur, ex ijs quæ Archimedes docet
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l. 2. de ſph. </
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<
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>prop. 2. ſunt enim ſeg
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menta illa æqualia conis eandem baſim MN
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habentibus, hi autem ex Eucl. l. 12. prop. </
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14 inter ſe ſunt vt altitudines: Quapropter
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inuentis conorum altitudinibus, quas Ar
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chimedes docet, innoteſcit Ratio ſegmen
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torum ſphæricorum conis illis æqualium̨. </
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Cum itaque CT ſit Radij (1/1000), ſegmenti
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MVN altitudo eſt 999, ſegmenti verò
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MON altitudo eſt 1001. Fiat igitur vt alti
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tudo ſegmenti maioris 1001 ad ſummam
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ex eadem altitudine & Radio 2001, ita al
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titudo ſegmenti ſphærici minoris 999, ad
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coni æqualis altitudinem 1997. Similiter vt
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altitudo minoris ſegmenti 999 ad ſummam
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ex eadem & Radio 1999, ita altitudo ſeg
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menti ſphærici maioris 1001 ad coni æqua
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lis altitudinem 2003. Eſt igitur MON ad
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MVN vt 2003 ad 1997: atque adeò ſeg
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mentum maius addit vltra hemiſphærium
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ſolùm totius globi (6/4000). Quare vt tellus ve
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niret in T, ſolum ſegmentum ſphæricum̨
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MSORN vt ſummum deorſum versùs C
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vrgeret; cui tamen, ne poſtea deſcendet, </
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