Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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ſum ſit, AV, centrum, O, aſymptoti indefinitè producti, NP, HY,
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per puncta autem, AV, ſint ductæ ordinatim, NH, YP, productæ
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vſq; </
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<
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">ad aſymptotos, in punctis, N, H, Y, P, ipſis incidentes, quæ
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fectiones tangent, deinde iunctis, NY, HP, producantur ipſæ tun-
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0416-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0416-01
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gentes vſq; </
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<
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">ad ſectiones illis in punctis, F, E, C, D,
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occurrentes, iunganturque, FD, EC, & </
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">37. Secun.
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Con.</
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ipfam, AV, ordinatim applicetur, XL, incidens, F
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E, in, X, &</
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">, DC, in, L, quæ erit ſecunda diameter,
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& </
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<
s
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">producatur, AV, indeſinitè incidens ipſis, FD,
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EC, in punctis, R, Z, erit ergo, FC, parailelogrã-
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">3. 1. Secun.
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Con.</
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mum, nam rectangulum, YFN, .</
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<
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<
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">rectangulum, E
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NF, eſt æquale quadrato, AO, ideſt rectangulo, C
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HD, item quadratum; </
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<
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">NX, eſt æquale quadrato,
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HL, & </
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<
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tum, XF, erit æquale rectangulo, CHD, cum quadrato, LH, .</
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</
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<
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">ideò, XF, erit æqualis ipſi, LD, & </
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<
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E, æqualis duplæ, CD, & </
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<
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">eidem parallela, vnde, FD, erit, EC,
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parallela, & </
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">ambæ ordinatim ad axim, vel diametrum, RZ, or-
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dinatim applicatæ, & </
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<
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">, FC, erit
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parallelogrammum, ſitregula latus tranſuerſum, AV, Dico nũc
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omnia quadrata parallelogrammi, FC, eſſe ſexquialtera omnium
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">31, huius.</
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quadratorum figuræ, FADCVE; </
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">& </
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<
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">hęc eſſe quadrupla omnium
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quadratorum triangulorum, NOY, HOP; </
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<
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">nam omnia quadrata,
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FC, ad omnia quadrata figuræ, FADCVE, oſtenſa ſunt eſſe, vt
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quadratum, DC, ad quadratum, AV, cum {1/3}. </
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<
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autem quadratum, HP, æquale quadrato, AV, & </
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<
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quadratum, DC, ad quadratum, HP, cum {1/3}. </
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<
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">quadrati, HP, vel vt
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quadratum, RZ, ad quadratum, AV, cum, {1/3}. </
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<
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ducantur nunc aſymptoti, NP, HY, verſus, EC, cui productæ in-
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cidant in S, I, eſt ergo rectangulum, SEI, æquale quadrato, YV,
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Con.</
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.</
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">ideò rectangulum, SEI, cum quadrato, EZ,
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duplum eſt quadrati, EZ, vel quadrati, YV, eſt autem rectangulũ,
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SEI, cum quadrato, EZ, ęquale quadrato, SZ, & </
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<
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SZ, duplum eſt quadrati, YV, eſt autem, vt quadratum, SZ, ad
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quadratum, YV, ita quadratum, ZO, ad quadratum, OV, ergo
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quadratum, ZO, erit duplum quadrati, OV, vel eorum quadru pla
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.</
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<
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<
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<
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omnia quadrata, FC, ad omnia quadrata figuræ, FADCVE, eſſe
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vt quadratum, RZ, ad quadratum, AV, cum {1/3}. </
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<
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<
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</
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<
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<
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<
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duplum quadrati, AV, ideò quadratum, RZ, erit {6/3}. </
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