Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIE ptam ab, HM, prædictæ homologa, habet duplicatam rationem
eius, quam, EF, habet ad, HM, ergo vt quadratum, EF, ad qua-
dratum, HM, ita eſt figura, EF, ad ſibi ſimilem figuram deſcriptã
ab, HM, & permutando vt quadratum, EF, ad figuram quamcuq; aliam deſcriptam ab, EF, ita erit quadratum,
HM, ad figuram prędictæ ſimilem deſcriptam
ab, HM, prædictæ homologa, ergo quadratũ
ſolidum figuræ, DEF, & ſolidum ſimilare quo-
dcumq; genitum ex figura, DEF, luxta comu
nem regulam, EF, ſunt ſolida proportionaliter
analoga ſecundum communem regulã, EF, ergo erunt inter ſe vt fi-
guræ planæ ab eodem latere, vt ab, EF, deſcriptę. Eodẽ modo oſtẽ-
demus quadratum ſolidũ, ABC, & ſolidũ aliud quodcumq; ſimilare
genitum ex figura, ABC, iuxta cõmunẽ regulam, BC, eſſe inter ſe, vt
figuræ à, BC, deſcriptæ, ſunt autem duo quadrata, BC, EF, & duæ
aliæ quæcumq; ſimiles figuræ planæ deſcriptæ ab homologis, BC,
EF, proportionales, ergo & dicta ſolida proportionalia erunt, nẽpè
vt quadratũ, BC, ad figuram, BC, ſic erat quadratum ſolidũ, ABC,
ad ſolidum ſimilare genitũ ex, ABC, ſed vt quadratũ, BC, ad figurã,
BC, ita eſt qua dratum, EF, ad figuram, EF, prædictæ ſimilem, & ita
etiam quadratum ſolidum, DEF, ad ſolidum prædicto ſimilare ge-
nitum ex, DEF, ergo quadratum ſolidum, ABC, ad ſolidum ſimi-
lare, ABC, eſt vt quadratum ſolidum, DEF, ad ſolidum præ dicto
ſimilare genitũ ex, DEF, & permutando quad. ſolidũ, ABC, ad qua-
dratũ ſolidũ, DEF, erit vt ſolidũ quodcũq; ſimilare genitũ ex, ABC,
ad ſibi ſimilare gen tũ ex, DEF, luxta dictas regulas, quod oſtendere
opus erat.

747.1.

15. 1. 2.
15. l. 2.
0556-01
3. huius.

748. ANNOTATIO.

HVius demonſtratio ſimilis eſt demonſtrationi Prop. 33. 1. 2. cui
per hanc ſuppletur, Coro laria autem iuxta methodum ibi
adhibitam facilè quoq; deducentur, illam vero huc reſeruaui, vt
promptiorem pro colligendis ſequentibus Corollarijs lib. 3. ex hac
pendentibus eam haberemus. Adhibuit quidem nomen ſolidi ſi-
milaris, quod per indefinitum numerum parallelorum planorum
fuit pariter explicatum lib. 2. ad B. Defin. 8. attamen ſi vice om-
nium planorum, ſeu deſcriptarum figurarum, ſubſtituamus quot-
cumq; plana, ſeu deſcriptas figuras, ita vt perimetri deſcriptarum
figurarum iacere intelligantur in ſuperficie ipſum ſolidum ambiẽ-
te, intelligemus nihilominus, licet nonnihil diuerſo modo, eſſe idẽ
ſolidum, quod dicitur ſimilare, ac à propria genitrice deſcriptum,

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