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

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515495LIBER VII.
PRopoſit. antacedens, aliter, quoad priorem partem,
oſtenſa.
345[Figure 345]
Sint quęcũq; figurę planę ęqualiter analogę iuxta regulã, GM,
ipſę, BHIC, DQK, quarum oppoſitę tangentes, AF, GM, regula pa-
riter, GM, parallelarũ, autẽ ipſi, GM, quotcumque portiones in vna-
que dictarum figurarum integrę ſint, ſiue non.
Dico eaſdem ęqua-
les eſſe.
Incidat ergo parallelis, AF, GM, quomodocumque recta
linea, EL, in eiſdem terminata, moueatur autem, GM, verſus, A
F, ſemper eidem, AF, ęquidiſtanter donec illi congruerit, interim
autem vnum punctum moueatur in eadem, GM, ſic mota, deſcri-
bens ambitum, I βΕ, figurę ęqualiter analogę ipſi, DQK, &
aliud
punctum in eadem motum ad aliam partem, EL, deſcribat ambi-
turn figurę, EYL, ęqualiter a@ alogę ipſi, BHIC, in quibus quidem
ſic deſcriptis figuris conceptę ipſi, GM, parallelarum portiones
quęcumque integrę ſint.
Erit ergo figura, @ βL, ęqualis figurę, E
YL, eſto autem quod in figura, DQK, conceptę portiones paral-
lelarum ipſi, GM, non omnes ſint integrę, ſed aliquę fractę per in-
teriorem ambitum, nempè, quę intercipiuntur parallelis, Q6, ΦΩ,
11Ex antec.
Lem.
in quibus habeantur duo figurę fruſta, 67RΩ, CΦR, in quorum
tamen vnoquoque dictę parallelarum port ones integrę habean-
tur, ſit autem in motu, GM, a quodam runcto deſcripta linea,
&
γ5, nempè ambitus figurę, 5 & ΣΤ, eodem modo, quo delcripti
fuerunt ambitus, @β@, EYL, g@ręinquam, 5&
Σ @, ęqualiter ana-
logę fruſto, 7R Ω@;
er tergorel@qu@ figura, 5Δ& , qualiter analo-
ga ſrulto, QΦ@, cumtota, Τ ΔΣ ſit toti compoſito ex fruſti, QΦ
R, 7R Ω6, ęqualiter analoga, &
ſunt portiones ipſi, GM,

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