Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER VI.
"/>
eumſcriptæ ſuper inſcriptam ſunttrapezia, HL, LK, KI, cum tri-
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angulo, IFQ, quę, quia ęquantur trapezijs, ΓV, VN, NQ, & </
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triangulo, IFQ, (nam dicta trapezia ſunt reſidua triangulorum in
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ęqualibus baſibus, & </
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<
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">altitudinibus conſtitutorum) ideſt triangulo,
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FΓG, ſubinde ſunt minora ſpatio, Ω, & </
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<
s
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xml:space
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">ideo circumſcriptã ſuperat
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inſcriptaminori ſpatio, quam ſit Ω, ergo trilineum, FLHG, excedit
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inſcriptã multò minori ſpatio, excedit autem ſpatium reſiduum cir-
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culi, ECDB, iam dictum ſpatio Ω, ergo ſigura inſcriptaerit maior
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dicto ſpatio reſiduo; </
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<
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">quod ſerua.</
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<
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<
s
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">Diuidatut nunc, AB, ſim liter, ac diuiditut, FG, in punctis, 3,
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4, 7, centro autem communi, A, ad diſtantiam punctorum, 3, 4,
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7, deſcribantur circumferentiæ, 35Δ, 4ΣRβ, 789M, ſecantes ſpi-
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ralem in punctis, S, R, M, per quæ tranſeant eductæ à centro, A,
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productæque vſque ad circumferentiam, ECDB, rectæ, AD, AC,
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AE, vt igitur in præhabita demonſtratione oſtendemus circumfer.
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<
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">rectam, IQ, inter ſe æquales eſſe, & </
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<
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tiam, RΣ4, æquari rectæ, KT, &</
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<
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">, M987, ipſi, LV, & </
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<
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">Corol. 1.
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3.huius.</
note
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circumferentia ad circumfer. </
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">Σ4, eſt, vt, 3 A, ad, A4, ideſt vt, QF,
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ad, FT, ideſt vt, IQ, ad, NT, eſt autem ęqualis, 53, ipſi, IQ, ergo,
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Σ4, erit ęqualis ipſi, NT, & </
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<
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">eſt, 34, ęqualis ipſi, QT, ergo faſcia, 53
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4Σ, erit ęqualis trapezio, IQTN; </
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<
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xml:space
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">eodem modo oſtendemus faſciã,
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R9874, æquari trapezio, KV, & </
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">faſciam, MECDB7, ęquari tra-
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pexio, PLVG, & </
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<
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">ideo figura compoſita ex dictis faſcijs ęqualis
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erit figurę compoſitę ex his trapezijs inſcriptę trilineo, FLHG, eſt
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autem hæc figura inſcripta maior ſpatio reſiduo circuli, ECDB, ab
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eo dempto ſpatio ſub ſpirali, & </
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<
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xml:space
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">voluta, AB, ergo figura compo-
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ſita ex dictis ſpatijs erit maior ſpatio dicto reſiduo, cui tamen eſt
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inſcripta, quod eſt abſurdum, non ergo trilineum, FLHG, maius
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eſt dicto reſiduo.</
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">Sit, ſi fieri poteſt, minus ſpatio eodem,
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Ω, ſit autem vt ſupra trilineo, FLHG, circumſcripta figura, ex
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trapezijs, KQ, LT, HV, & </
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<
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">alia ei-
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dem in cripta ex trapezijs, PO, OT, NQ, ita vt earum differentia
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ſit minor ſpatio, Ω, igitur circumſcripta excedet trilineum, FLH
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G, multò minori ſpatio, ergo circumſcripta figura minor erit ſpa-
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tio reſiduo jam dicto circuli, ECDB, quod excedit trilineum, FLH
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G, ſpatio, Ω, quod tamem eſt abſurdum, nam ſectorem, AS3, pa-
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ret ęqualem eſſe triangulo, FIQ, faſciamque, ΑRΣ43, æquari oſtẽ
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dem us trapezio, kQ, modo ſupra adhibito, & </
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ſi trapezio, LT, & </
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<
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">totam faſciam, 679C, trapezio, HV, vnde fi-
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gura compoſita ex dictis faſcijs, & </
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