Full text: Viviani, Vincenzio: De maximis et minimis, geometrica divinatio

330. THEOR. XLV. PROP. LXXII.

Si Cylindricus plano ſecetur baſi æquidiſtante, erit Cylin-
dricus ad Cylindricum, vt altitudo ad altitudinem.

HOc eadem penitus conſtructione, ijſdemque argumentis demonſtrabi-
tur, ac 13. duodecimi Elem. opetamen præcedentis Corollarij; ani-
maduertendo ſimul, quod dum Cylindricus plano ſecatur baſi æquidiſtante,
in ipſa ſectione oritur figura ſimilis, & æqualis, ſiue in totum congruens baſi
Cylindrici: nam ipſæ Cylindricus, ex motu parallelo ſuæ baſis procreari
concipitur, ex definitione, & c.

331. SCHOLIVM.

EX hac pendet huius concluſionis demonſtratio, quod eſt conuerſum
prop. 71. huius; nempe.

Cylindrici æqualium baſium ſunt inter ſe, vt altitudines; quod oſtenditur
vt in 14. duodecimi Elementorum.

332. THEOR. XLVI. PROP. LXXIII.

Cylindrici, quorum baſes altitudinibus reciprocantur, inter ſe
ſunt æquales: & è conuerſo.

HVius Theorematis demonſtratio elicitur ex præcèdenti, eſtque omni-
nò ſimilis 15. duodec. Element. itaque breuitatis gratia, hanc ipſam
o mittimus, ſimulque nonnullas alias Cylindricorum affectiones, cum hìc
de ijs diſſerere non ſit opus.

333. THEOR. XLVII. PROP. LXXIV.

Solida Acuminata proportionalia, quorum baſes altitudinibus
ſint reciprocè proportionales inter ſe ſunt æqualia.

SInt duo Acuminata ſolida proportionalia, quorum Canones A B C, D
E F ſint ſuper baſes A C, D F, & circa diametros B G, E H; baſes
verò horum ſolidorum ſint Acuminata plana A L C, N F O circa diametros
A C, D F, ſitque vnius ſolidi altitudo B I, ad alterius altitudinem E Q re-
ciprocè, vt baſis N F O ad baſim A L C. Dico huiuſmodi ſolida inter ſe
æqualia eſſe.

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