Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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quadratum ad inſcriptum circulum, & </
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">in, ℟8, ſumpta, 37, æqua
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lis exceſſui, quo, 3℟, ſuperat {2/3}. </
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<
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">tertiæ proportionalis duarum, 8℟,
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℟4, patet ergo, quod cylindrus, Sφ, ad tympanum, SYφ, eſt vt, ℟
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8, ad, 87. </
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">Quoniam vero, vt, LO, ad, OQ, ſic eſt, QO, ad, OR,
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34. l. 3.</
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ideò vt, LO, ad, OR, vel, T8, ipſi æqualem, ita quadratum, LO,
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ad quadratum, OQ, vel ita quadratum, RO, ſeu quadratum, ℟8,
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ad quadratum, NO, vel ita circulus, ℟φ, ad circulum, NP, ergo
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duo cylindri, Sφ, KP, quorum axes reciprocè baſibus reſpondent,
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erunt æquales, quod ſerua. </
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<
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">Vlterius, quia vt, IE, ad, EG, ſic eſt,
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gener. 34.
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l. 2.</
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8℟, ad, ℟4, & </
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">vt, EG, ad, EF, ſic quadratum ad inſcriptum circu-
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lum, & </
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">ita etiam, ℟4, ad, ℟3, ergo ex æquali, IE, ad, EF, erit vt,
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8℟, ad, ℟3. </
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<
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G, ad {2/3}. </
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<
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</
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<
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">tertiæ proportionalis duarum, 8℟, ℟4, ideò ex æquali, vt, IE, ad,
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{2/3}. </
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<
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">tertiæ proportionalis duarum, IE, EG, ita, 8℟, erit ad {2/3}. </
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<
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proportionalis duarum, 8℟, ℟4, eædem autem, IE, 8℟, ad, FE, 3
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℟, erant in eadem ratione, ergo ad exceſſus duarum, EF, ℟3, ſu-
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per {2/3}. </
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℟4, ex alia, erunt in eadem ratione .</
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">i. </
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">vt, IE, ad, FH, ita erit, 8℟,
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ad, 37, ſed etiam, vt, IE, ad, EF, ſic eſſe oſtenſum eſt, 8℟, ad, ℟3,
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ergo, coll@gendo, vt, IE, ad, EH, ita, 8℟, ad, ℟7, & </
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ſionem rationis, & </
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">conuertendo, vt, Hl, ad, IE, ideſt vt, AD, ad,
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LO, ideſt vt cylindrus, BAC, ad cylindrum, NLP, vel illi æqualẽ,
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Sφ, (vt oſtenſum eſt) ita, 78, ad, 8℟, ſed vt, 78, ad, 8℟, ita tym-
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panum, SYφ, ad cylindrum, Sφ, ergo, vt cylindrus, BAC, ad cy-
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34. l. 3.</
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lindrum, Sφ, ita tympanum, SYφ, ad cylindrum, Sφ, ergo cylin-
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drus, BAC, æquaturtympano, SYφ, cuius axis, T8, ſemidiametro
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baſis, ℟8, eſt æqualis, quod, &</
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ſe in uenire tympana ſphæralia, quorum axes ſemidiametris
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baſium ſint æquales, quæ ad datum quodcunq; </
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inuenire.</
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