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

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9070GEOMETRIÆ 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

47[Figure 47] 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
111. Sex. El. 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.
228. Lib. 2.
ſequen.
vel 20.
Sex. El. 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-
33Defin. 10. 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.

THEOREMA XXVIII. PROPOS. XXXI.

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

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