Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER II. per illi æquidiſtans, igitur huius plani moti, ſiue fluèntis conceptæ
in ſolido, ABC, figuræ, quæ in toto motu fieri intelliguntur, voco: Omnia plana ſolidi, ABC, ſumpta regula corum vno, quarum ali-
qua repræſentare poſſunt plana, LH, PF, BC.

170.1.

_Defin.2._
_huius._

Vlterius duæ rectæ lineæ, ON, EM, occurrant planis per, EO,
BC, tranſeuntibus iam dictis in punctis, O, N; EM, quarum, O
N, perpendiculariter, EM, verò obliquè illis incidat, puncta igi-
tur, quæ ſunt communes ſectiones omnium planorum ſ lidi, ABC,
productorum, ſiopus ſit, & rectæ, ON, vocantur ipſius omnia pun-
cta recti tranſirus, quarum aliqua ſunt puncta, H, I, N, quæ in-
teripſa, & extremum punctum, O, continentur, vt ipſæ, OH, OI,
ON, dicuntur abſciſſæ, quæ inter eadem puncta, & aliud extre-
mum, quod eſt, N, continentur, vt ipſæ, NI, NH, NO, reſiduæ
omnium abſciſſarum; tot æquales ipſi, ON, quot ſunt omnes ab-
ſciſſæ, ſiue reſiduæ omnium abſciſſarum, ON, dicuntur maximæ
abſciſſarum, ſiue omnium abſciſſarum, ON, quibus ſi adiung atur
aliqua recta linea, dicuntur abſciſſæ, reſiduæ, ſiue maximæ adiun-
cta tali linea, omnes quidem recti tranſitus in recta, ON, in, EM,
verò dicuntur eiuſdem obliqui tranſitus, eius nempè, qui in tali in-
clinatione fit.

170.1.

_Defin. 3._
_huius._
_Def. 4._
_huius._
_Def. 5._
_huius._
_Defin. 6._
_huius._
_Defin. 7._
_huius._

Dicitur autem in Coroll. Defin. 3. eadem puncta recti tranſitus,
ſiue obliqui, fieri tum ab omnibus planis propoſiti ſolidi, vt, ABC,
tum ab omnibus lineis
planiper eaſdem inciden-
tes extenſi, vt ex. gr. pla-
ni, quod tranſit per, EO,
BC, quod quidem ctiam
tranſeat per ipſas, ON,
EM, idem enim planum,
quod in ſolidum, ABC,
producit figuram, LH, in
figura plana, ABC, producit rectam, LH, & in recta, ON, pun-
ctum, H, in, EM, verò punctum, γ, quod tranſit, HL, produ-
cta, & ideò dico puncta, H, γ, poſſe dici etiam effecta àresta, γ,
H, & ſic omnia puncta recti tranſitus quę nempè ſunt in, ON, ne-
dum fieri à dictis planis parallelis ſed etiam à lineis parallelis fi-

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