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

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134114GEOMETRIÆ nes lineas figurę, D, tunc enim comparare continuum ad continuum
non eſſet niſi ipſa indiuiſibilia comparare; ſed eſto, quod hoc ſit fal-
ſum, vel quod, etiamſi verum ſit, tamen legitima ratione ad hoc pro-
bandum nondum peruenerimus; nihilominus adhuc dico ipſa indi-
uiſibilia. ſ. omnes lineas figurę, A, ad omnes lineas figuræ, D, eſſe
vt figuram, A, ad figuram, D. Quoniam ergo aſſumpſimus figu-
ras, B, C, ſingulas æquales figuræ, A, & , E, æqualem figuræ, D,
omnes lineæ ſingularum figurarum, A, B, C, erunt æquales omni-
11Perante-
ctd. bus lineis figuræ, A, ſumptis iuxta dictam regulam (quacunque re-
gula dictæ omnes lineæ ſint aſſumptæ) & ideò quotuplex erit com-
poſitum ex figuris, ABC, figuræ, A, totuplex erit compoſitum ex
omnibus lineis figurarum, ABC, omnium linearum figuræ, A, &
ideò habebimus æquè multiplicia primæ, & tertiæ vtcunq; ſumpta;
ſimiliter oſtendemus compoſitum ex figuris, E, D, æquè multiplex

74[Figure 74] eſſe figuræ, D, ac compoſitum ex omnibus li-
neis figurarum, E, D, multiplex eſt omnium
linearum figuræ, D, quæ ſunt æquè multipli-
cia ſecundæ, & quartę vtcunque ſumpta, quia
ergo ſi multiplex primę. ſ. compoſitum ex figu
ris, ABC, ſuperauerit multiplex ſecundę, ſci-
licet compoſitum ex figuris, DE, etiam mul-
tiplex tertiæ. ſ. compoſitum ex omnibus lineis
figurarum, ABC, ſuperabit multiplex quartæ
. ſ. compoſitum ex omnibus lineis figurarum, DE, & ſi multiplex pri-
22Elicitur
ex antec. mæ fuerit æquale multiplici ſecundæ, etiam multiplex tertię erit æ-
quale multiplici quarte, ſcilicet ſi compoſitum ex figuris, ABC,
fuerit æquale compoſito ex figuris, DE, etiam eorundem compo-
ſitorum omnes lineæ erunt æquales, & ſi minus, minus, ideò prima
33Defin. 5.
Qui. El. ad ſecundam erit, vt tertia ad quartam, ſcilicet figura, A, ad figu-
ram, D, erit vt omnes lineæ figuræ, A, ad omnes lineas figuræ, D,
ſumptas iuxta datas regulas. ſ. iuxta quaſcunq; regulas, quod in fig.
44Coroll. I.
huius. planis erat oſtendendum.

Verum ſi intellexerimus, A, D, eſſe figuras ſolidas, aſſumentes,
C, B, ſingulas æquales ipſi, A, & , E, ipſi, D, oſtendemus com-
poſitum ex figuris, ABC, tam multiplex eſſe figurę, A, ac compo-
ſitum ex omnibus planis figurarum, A, B, C, multiplex eſt omnium
planorum figurę, A, & ſic compoſitum ex figuris, D, E, tam mul-
tiplex eſſe figuræ, D, ac compoſitum ex omnibus planis figurarum,
DE, multiplex eſt omnium planorum figuræ, D, & tandem per
antecedentem Propoſitionem oſtendemus, ſi multiplex primæ ſupe-
rauerit multiplex ſecundę, etiam multiplex tertiæ ſuperaturum mul-
tiplex quartæ, & ſi minus, minus, vel ſi æquale, & ęquale fore,

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