Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER IV. CI, & ſic eſſe quodlibet ſolidum ſimilare genitũ ex parabola, FCH,
ad ſibi ſimilare genitum ex parabola OCM, iuxta communem re-
gulam, FH, ſiue CG, ſit axis, ſiue tantum diameter, quod iuxta an-
tecedentis explicationem facilè intelligi poteſt.

492.1.

0366-02

493. COROLLARIVM III.

IN Prop. 23. aſſumpta figura Prop. 12. ſcilicet parabola, BNH,
parallelogrammis, PH, AG, & triangulo, BRH, reuoluatur pa-
rabola, BNH, vt fiat noſſrum exem-
plum, circa axem, NO, & inſimul, PH,
AG, & triangulus, BRH, circa RO,
patebit ergo cylindrum ex, PO, ad
fruſtum conoidis ex, ABOR, in reuo-
lutione genitum, eſſe vt, ON, ad com-
poſitam ex, NR, & {1/2}. RO, ipſum ve-
rò ad idem dempto cylindro ex, AO,
. ſ. AG, vt, NO, ad {1/2}. RO, ex Corollario huic Propoſitioni ſubiecto,
hoc fruſtum tandem ad conum gentium ex triangulo, RBO, vt cõ-
poſita ex, ON, dupla, MR, & {1/2}. RO, adipſam, NO; & vniuerſa-
liter quæcunque ſolida ſimilaria ex eiſdem figuris genitricibus geni-
ta, iuxta communem regulam, BH, eaſdem rationes habere, vt ſu-
pradicta ad inuicem comparata, ſiue, NO, ſit axis, ſiue tantum dia-
meter; quod ex Propol. 51. clarè patet. Intelligatur autem in ſe-
quentibus, licet ſemper aſſumatur axis, tamen pro ſolidis ſimilari-
bus etiam aſſu mptis diametris eadem ibi appoſita verificari.

493.1.

0367-01

494. COROLLARIVM IV.

IN Propoſ. 26. veluti oſtendimus in eiuſdem figura hic appoſita
omnia quadrata portionis, BSF,
ad rectangula ſub portione, BSF, & figura diſtantiarum, SEF, eſſe vt, BF,
ad FE, ſic oſtenſum fuiſſet (aſſumptis
vice quadratorum alijs figuris ſimili-
bus, & vice rectangulorum, aſſumptis
alijs ſimilibus figuris eius generis, vt
veluti eſt vnum quoduis dictorum
omnium quadratorum ad rectãgulum adiacens lateri, à quo deſcri-
bitur, ita ſit figura ab eodem latere deſcripta vice quadrati ſumpta,
ad figuram deſcriptam eodem latere vice rectanguli ſumptam, fiet

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