Cavalieri, Buonaventura - Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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172152GEOMETRIÆ& rectangulis bis ſub, GN, NP, fient omnia quadrata, GQ, hęc
ſi iunxeris omnibus quadratis, FK, cum rectangulis bis ſub, FK, K
Q, fient omnia quadrata, FR, quę tandem ſi iunxeris omnibus qua-
dratis, DM, cum rectangulis bis ſub, DM, MR, fient omnia qua-
drata, DS, quę cum ſint minora omnibus quadratis figurę, Ω, hinc
figuræ circumſcriptæ omnia quadrata excedunt omnia quadrata in-
ſcriptę minori quantitate, quam ſint omnia quadrata, Ω, & ideò ex-
cedunt omnia quadrata trianguli, OES, multò minon quantitate:
Quia ergo omnia quadrata, AS, ad omnia quadrata trianguli, OE
S, cum omnibus quadratis, Ω, erant vt omnia quadrata, Τ β, ad om-
nia quadrata trianguli, & Ζ β, hinc omnia quadrata, AS, ad om-
nia quadrata figurę circumſcriptę triangulo, OES, habebunt maio-
rem rationem, quam omnia quadrata, Τ β, ad omnia quadrata tri-
anguli, & Ζ β.

Nunc diuidatur ſimiliter, & β in punctis, ℟, Δ Σ, ac, OS, in
punctis, P, Q, R, & per puncta, ℟ Δ Σ, parallelæ ipſi, Ζ β, du-
cantur, ℟ V, Δ Χ, Σ Υ, ſecantes, & Ζ, in punctis, r, 3, 6, per quę
vſque ad proximas parallelas ipſis, & β, ΤΖ, æquidiſtantes ducan-
tur, Φ Γ, Λ 3, 46, vt triangulo, & Ζ β, ſit circumſcripta figura ex

100[Figure 100] parallelogrãmis,
Φ ℟, Δ Δ, 4 Σ, Υ
β, cõpoſita, quia
ergo, vt, OS, ad,
SR, ita eſt, & β,
ad, β Σ, vt au-
tem, OS, ad, S
R, ita ſunt om-
1110. huius. nia quadrata, A
S, ad omnia qua-
drata, DS, &
vt, & β, ad, β
Σ, rta ſunt omnia
quadrata, Τ β, ad
omnia quadrata,
Υ β, ergo omnia
quadrata, AS, ad omnia quadrata, DS, ſunt vt omnia quadrata,
Τ β, ad omnia quadrata, Υ β, quia verò omnia quadrata, Υ β, ad
omnia quadrata, 6 β, . @. ad omnia quadrata, 4 Σ, ſunt vt quadra-
229. huius. tum, Ζ β, ad quadratum, 7 β, . @. ad quadratum, 6 Σ, . @. vt quadra-
tum, β & , ad quadratum, & Σ, . @. vt quadrarum, SO, ad quadra-
tum, OR, ideſt vt quadratum, ES, ad quadratum, HR, ideſt, vt
omnia quadrata, DS, ad omnia quadrata, FR, ergo ex æquali

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