Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

721. COROLLARIVM II.

SImiliter ſi compleautur parallelogramma, PC, CR, CO, ſolidum
rectangulum ſub, RC, CP, ſeu ſub, OC, CP, contentum, quod eſt
parallelepipedum, triplum erit contenti ſub triangulis prædictis ideſt
pyramidis, AEC. Contentum verò ſub parallelogrammis, TC, & , C
X, ad contentum ſub dictis trapezijs hoc eſt ad fruſtum pyramidis, GE
CI, erit vt quadratum, BC, rectangulum ſub, XI, IM, vna cum {1/3}. qua. drat. XM, retentis ſemper ijſdem reg. BC, CF. Hæc autem V [?] era ſunt
ſiue latus, AC, ſit commune præfatis triangulis, ſeu parallelogram -
mis, ſiue non, ac ſine latus, IC, ſit cõmune predictis trapezijs, ſeu paral
lelogrammis, ſiue nõvt facilè intuenti innoteſcet.

721.1.

_10.huius._

722. COROLLARIVM III.

_P_Atet vltimo ſolida rectangula ſub dictis triangulis, regulis iam
dictis, contenta, ſe babereinter ſe, vt ipſæ pyramides, nempè
æquè alta eſſe in pro portione baſium, & in eadem, vel æqualiqus ba-
ſibus exiſtentia eſſe in proportione altitudinem reſpectu baſium aſſum-
ptarum, quod eſt ſimile illi, quod animaduerſum eſt in Cor. I. & 2,
prop. ant. circa parallelogramma ſolida rectangula continentia.

723. ANNOTATIO.

ADuerte autem cum ſolidum rectangulum fuerit quadratum,
tunc vnam ſufficere exponi figuram, vt ex. g. triangulum, A
BC, quod tunc æquipollet duobus expoſitis, ABC, ACD; & con-
tentum ſolidum ſub, ABC, ACD, tunc etiam dicimus quadratum
ſolidum ipſius, ABC, regulis, BC, CF, hæc autem planarum figu-
rarum quadrata ſolida mentaliter quoque vt plurimum deſcripta
eſſe intelligemus, vt etiam ſuperius animaduerſum fuit. His au-
tem præpoſitis, nunc illa ſubiungemus, quæ aſſimilantur Prop. Sec. Elem. ac iuxta methodum indiuiſibilium lib. 2. prop. 23. oſtẽ-
ſa fuere.

724. THEOREMA XV. PROPOS. XV.

SI duæ expoſitæ fuerint ſuperficies ſolidum rectangulũ
iuxta datas regulas continentes, altera autem earum
fuerit in quotcunq; partes diuiſa per lineas ſecantes quaſ-
cunq; ſuæ regulæ intra dictam ſuperficiem parallelas, alte-

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