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

DAta recta linea terminata, vtcumque in puncto diuiſa,
poſſibile eſt ipſam ad alteram eiuſdem partium ita
producere, vt cubus compoſitæ ex propoſita linea, & adiun-
cta, ſit æqualis cubo propoſitæ lineæ, ſimul cum cubo com-
poſitæ ex adiecta, & illi conterminante portione ſectæ lineę.

Sit data recta linea, AC, terminata, diuiſaq; vtcumque in pun-
cto, B, oftendendum eſt poſſibile eſſe ipſam ita producere ad alteram
illius partium, vt ad, C, vt cubus compoſitę ex, AC, & adiecta, ſit
æqualis cubo, AC, cum cubo compoſitæ ex eadem adiecta, & ex,
BC, portione, AC, adiectæ conterminante. Producatur ergo, C
A, ad partes, A, vt in, N, ita quod, NB, ſit tripla, BA, ſiat dein-
de, vt, NB, ad, BC, ita quadratum, BC, ad quadratum rectæ li-
neę, M, ſeorſim poſitæ: Vlterius exponatur recta, EF, æqualis com-
poſitæ ex, AC, CB, cui applicetur rectangulum æquale quadrato,

128[Figure 128] M, excedens figura quadrata,
1129. Sex.
lem, cuius latus ſit, FH, producatur
autem, AC, verſus, C, vt in,
D, ita nempè, vt, CD, ſit
æqualis, FH. Dico cubum to-
tius, AD, æquari duobus cubis,
AC, BD. Cum. n. ſit, vt, N
B, ad, BC, ita quadratum, BC,
ad quadratum, M, ideò parallelepipedum ſub altitudine, AB, (qu
eſt, {1/3}, prædictę altitudinis, NB,) & quadrato, M, æquabitur ter-
tiæ parti cubi, BC. Quoniam verò quadratum, M, æquatur rectan-
22E. Cor. 4
Gen. 34.
huius. gulo, EHF, ideſt rectangulo ſub compoſita ex, AD, BC, & ſub,
CD, ideò parallelepipedum ſub altitudine, AB, & baſi rectangulo
ſub compoſita ex, AD, BC, & ſub, DC, æquabitur tertiæ parti
cubi, BC, addatur commune parallelepipedum ſub, BC, & baſi re-
ctangulo, BDC, erit ex vna parte hoc parallelepipedum cum, {1/3}, cu-
bi, BC, ex alia verò hæcſumma; ſcilicet parallelepipedum ſub, AB,
& ſub rectangulo ſub compoſita ex, AD, BC, & ſub, DC, vna
cum parallelepipedo ſub, BC, & rectangulo, BDC, quæ quidem
ſumma efficit parallelepipedum ſub, AC, & rectangulo, ADC,

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