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

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313293LIBER IV.
THEOREMA VI. PROPOS. VI.
SI ad baſim datæ parabolæ ordinatim applicetur recta li-
nea, tota parabola ad abſciſſam portionem per ipſam or-
dinatim applicatam erit, vt parallelepipedum ſub altitudine
dimidia baſi, ſub baſi autem quadrato totius baſis, ad paral-
lelepipedum ſub altitudine linea compoſita ex dimidia baſi,
& reliquo baſis, dempta abſciſſa ab eadem extremitate ba-
ſis, à qua portio parabolæ abſcinditur, & ſub baſi quadrato
eiuſdem abſciſſæ per dictam ordinatim applicatam: Vel erit,
vt cubus totius baſis ad parallelepipedum ſub baſi quadrato
abſciſſæ, altitudine tripla reliquæ, cum cubo dictæ abſciſſæ.
Sit parabola, HG
207[Figure 207] A, cuius baſis, HA,
& axis, vel diameter,
GO; ducatur deinde
ipſi, GO, vtcunque
parallela, ST. Dico
parabolam, AGH,
ad vtramuis portio-
num, SHT, TSG
A, vt ad, SHT, eſſe
vt parallelepip. ſub al-
titudine dimidia, H
A, quæ ſit, AX, illi
in directum conſtitu-
ta, baſi quadrato, A
H, ad parallelepipe-
dum ſub altitudine, X
T, baſi quadrato, T
H. Producatur, GO,
in, M, & circa ſemia-
xes, vel ſemidiame-
tros, HO, OM, in-
telligatur deſcriptus
ſemicirculus, vel ſe-
miellipſis, HMA,
deinde per puncta, G, M, ducantur ipſi, HA, parallelæ, B ℟,

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