Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ hos circulos eſſe ſimiles iuxta meam definitionem ſimilium plana-
rum figurarum, & eorum, & ductarum oppoſitarum tangentium in-
cidentes eſſe ipſas diametros, AC, OQ, quæ etiam de ſemicirculis
verificantur. Diametri ergo, AC, OQ, diuidantur fimiliter ad ean-
dem partem in punctis, E, M, à quibus vſque ad circumferentiam
ducantur ipſæ, EB, MN, parallelæ dictis tangentibus, quæ cum
ad angulos rectos diametros diuidant, etiam ipſę, BE, NM, erunt
illis perpendiculares, igitur quadratum,
BE, erit ęquale rectangulo, AEC, ſi-
cuti quadratum, NM, æquale rectan-
gulo, OMQ, rectangulum autem, A
EC, ad quadratum, EC, eſt vt, AE,
ad, EC, ideſt vt, OM, ad, MQ, ideſt
vt rectangulum, OMQ, ad quadratum,
MQ, ideſt vt quadratum, NM, ad qua-
dratum, MQ, ergo quadratum, BE,
ad quadratum, EC, eſt vt quadratum,
NM, ad quadratum, MQ, (quæ au-
tem hic ſupponuntur, vel petantur ex
Eucl. lib. Elem. vel ex ſequenti meo lib. in quo, quæ hic aſſumuntur indepen-
denter ab hoc Lemmate demonſtratur)
ergo, BE, ad, EC, erit vt, NM, ad,
MQ, permutando, BE, ad, NM, e-
rit vt, EC, ad, MQ, vel vt, AC, ad, OQ, igitur, quæ æquidi-
ſtant ipſis tangentibus, FA, HO, & ſimiliter ad eandem partem
vtcumque diuidunt ipſas, AC, OQ, & iacent inter ipſas, & circui-
tus ſemicirculorum, ABC, ONQ, ad eandem partem, eodem or-
dine ſumptæ, ſunt vt ipſæ, AC, OQ, quæ dictis tangentibus inci-
dunt ad eundem angulum ex eadem parte, quęideò ſunt earum inci-
dentes, ergo ſemicirculi, ABC, ONQ, ſunt figuræ planæ fimiles
ſuxta meam definitionem, quarum & oppoſitarum tangentium, quę
ab extremitate diametrorum ducuntur, incidentes ſunt ipſi diame-
tri; ſic etiam patebit ſemicirculos, ADC, OZQ, necnon circu-
los, AC, OQ, eſſe ſimiles, iuxta eandem definitionem; quod oſten-
dendum erat.

116.1.

0090-01
1. Sex. El.
8. Lib. 2.
ſequen.
vel 20.
Sex. El.
Defin. 10.

117. THEOREMA XXVIII. PROPOS. XXXI.

POſitis infraſcriptis definitionibus ſimilium cylindro-
rum, & conorum, ſequitur definitio generalis, quam
de ſimilibus ſolidis ipſe attuli.

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