Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER II. ac voluntas, pulchras demonſtrationes etſi difficiles, ac longas infracto
quodam animi vigore ſuperandi, potius quam ab ipſis ſuperari velint. Poterat quidem in plures Propoſitiones commodius diſtribui, ſed cum-
illæ omnes in hanc ſimpliciſſimam eſſent conſpiraturæ, eas omnes ſub
hac vna Propoſit. colligaui, quamtamen in Sectiones ceu in tot mem-
bra distinguere placuit, ne Lectoris mens nimium defatigaretur. Porrò
quanti hæc Propoſitio ſit momenti, ſicut & præcedens Propoſ. 15. atten-
ta præcipuè earum vniuerſalitate, neminem, qui eaſdem intellex erit,
fore puto, qui itidem non agnoſcat; quid enim fuit, quo ad figuras pla-
nas, Euclidem lib. 6. Elementorum in Propoſ 19. demonſtraſſe ſimilia-
triangula, & in Propoſ. 20. ſimilia Polygona eſſe in dupla ratione la-
te um homologorum, necnon lib. 12. Propoſ. 2. Circulos eſſe, vt diame-
trorum quadrata, hoc eſt in dupla ratione diametrorum? Similiter in eo,
quod ſpectat ad ſolida, quid fuit ipſum nobis in lib. 12. Propoſ. 8. oſten-
diſſe ſimiles Pyramides eſſe in tripla ratione laterum homologorum, & in Prop. 12. ſimiles conos, & cylindros eſſe in triplaratione diametro-
rum quæ ſunt in baſibus, & in Propoſ. 18. Sphæras itidem eſſe in tri-
pla proportione diametrorum? Quid tandem fuit alios quoq; demonſtraſ-
ſe, quædam alia ſimilia ſolida, vt portiones Sphærarum, necnon Sphæ-
roidearum, & Conoide arum figurarum, eſſe in tripla ratione linearum,
vel laterum homologorum? Præ huius comparatione, quod in his duabus
tantum Propoſitionibus edocemur; omnes . n. ſimiles figuras planas in
Prop. 15. & omnes ſolidas in ſubſequenti Propoſ. 17. comprebendimus,
quod mebercle conſideratione dignum videtur.

208. THEOREMA XVII. PROPOS. XVII.

OMnia ſimilia ſolida ſunt in tripla ratione linearum, vel
laterum homologorum, quę ſunt in eorundem homo-
logis figuris.

209. A. DEMONSTRATIONIS SECTIO I.

SInt duo vtcunq; ſimilia ſolida, V & , AP. Dico hæc eſſe in tri-
pla ratione linearum, ſiue laterum homologorum, quæ ſunt in
eorundem homologis figuris. Quia ergo dicta ſolida ſunt ſimilia, po-
terunt duci duo plana oppoſita tangentia in vnoquoque propoſito-
rum ſolidorum (quæ in ſolido, AP, repræſententur peripſas, AH,
P {00/ }, & in ſolido, V & , peripſas, V Σ, & 2,) homologis eorundem
figuris æquidiſtantia, inter quæ etiam ducibilia erunt alia duo plana
æqualiter ad ipſa, & ad eandem partem inclinata, in quibus iacebunt

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