Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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nem rectanguli, DC, CE, vel ſub, RZ, EC, ad quadratum, AV,
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cum {1/3}. </
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<
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">quadrati, kI, ergo omnia quadrata, FC, demptis omnibus
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quadratis oppoſitarum hyperbola-
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rum, FAD, EVC, regula, EC, ad
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omnia quadrata figuræ, FADCVE,
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regula, DC, vel, AV, habebunt ra-
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tionem compoſitam ex ractione re-
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ctanguli, AOZ, bis cum {2/3}. </
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<
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ti, KI, ad rectangulum, AZO, & </
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<
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ratione rectanguli ſub, RZ, EC, ad
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quadratum, AV, cum {1/3}. </
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<
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xml:space
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">quadrati,
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KI, .</
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<
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">i. </
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<
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">cum {4/12}. </
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<
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xml:space
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">quadrati, KI, quæ
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ſunt {4/3}. </
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<
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xml:space
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">quadrati, LI, .</
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<
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xml:space
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<
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xml:space
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">rectanguli,
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<
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">Corol, 21.
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huius.</
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AZV, vnde rectangulum ſub, AZ,
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& </
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<
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">ſexquitertia, ZV, erit æquale ter-
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tiæ parti quadrati, kI, erit igitur di-
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cta ratio compoſita ex ratione pri-
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mò dicta, & </
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<
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xml:space
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">ex ratione fectanguli
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ſub, RZ, EC, ad quadratum, AV,
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cum {1/3}. </
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<
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xml:id
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xml:space
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">quadrati, kI, ſiue cum rectangulo ſub, AZ, & </
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<
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ZV, quod oſtendere propoſitum erat.</
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">THEOREMA XXVI. PROPOS. XXVII.</
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<
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">figura intelligantur de-
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ſcriptæ ſectiones, quæ ab Apollonio coniugatæ vo-
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cantur, quæ ſint, Y & </
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">B, HTN, coniugatæ prædictis, FAD,
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EVC, habentes ſcilicet quadratum tranſuerſi lateris, & </
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">T,
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æquale rectingulo ſub alio tr anſuerſo latere, AV, & </
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iuxta qua n poſſunt, ſiue latere recto oppoſitarum ſectionũ,
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FAD, EVC, & </
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<
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">regula ſit DC, latus parallelogrammi, FC,
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expoſitis primò ſectionibus oppoſiti, FAD, EVC, circum-
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ſcriptum, æquidiſtans earu nlateri tranſuerſo, AV: </
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nia quadrata, FC, ad omnia quadrata figuræ, FADCVE,
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demptis omnibus quadratis oppoſitarum hyperbolarum,
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Y & </
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<
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">B HTN, quæ portionibus laterum, FE, DC, inter op-
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poſitas ſectiones, Y & </
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">B HTN, exiſtentium conſtituuntur,
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erunt vt parallelepipedum ſub dimidia baſis primò expoſi-
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tarum alterutrius, hyperbolarum, vt ſub, ZC, & </
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