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

315. DEFINITIONES.
I.

PLANA ACVMINATA SIMILIA vocentur illa, quæ inter ſe ſint
proportionalia, & quorum diametri ſuper baſes ſint æqualiter inclinatæ, ac
ijſdem baſibus proportionales.

Hoc eſt ſi ſint duo quælibet plana Acuminata proportionalia A B C, D
E F, quorum diametri B G, E H cum baſibus A C, D F æquales angulos
alterum alteri conſtituant, nempe A G B
ipſi D H E, & qui ei eſt deinceps C G B
reliquo F H E ſit æqualis, ſitque diame-
ter B G ad baſim A C, vt diameter E H
ad baſim D F; huiuſmodi plana inter ſe
vocentur SIMILIA ACVMINATA. Vnde, & duæ ſimiles Ellipſes vocari pote-
runt ſimilia Acuminata, cum vtraque ex
duobus proportionalibus Acuminatis con-
ſtet, ſiue ex dua [?] bus ſemi-Ellipſibus, per diametros æqualiter inclinatas diſ-
ſectis, quarum diametri ſunt baſibus proportionales, & c. Idemque de duo-
bus circulis, & c.

315.1.

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316. II.

SOLIDVM ACVMINATVM REGVLARE, vel tantùm SOLIDVM
ACVMINATVM, voco omnem figuram ſolidam ad alteram partem defi-
cientem, circa planum Acuminatum deſcriptam, cuius omnia plana baſi ſo-
lidi æquidiſtantia per Acuminati applicatas ducta, ſint quoque plana Acu-
minata, eidem baſi, ac inter ſe ſimilia, & ſimiliter poſita, & quorum homo-
logæ diametri ſint ipſæ applicatæ prædicti Acuminati, & c.

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Eſto planum quodcunque Acuminatum A B C, cuius baſis A C, dia-
meter B D, vertex B, & ipſa A C, ſit vel diameter circuli, aut Ellipſis,
vel cuiuſcun que ipſarum figurarum portionis, aut diameter Parabolæ,
vel Hyperbolæ, vel cuiuslibet alij plani Acuminati A E C F, quod tan-
quam baſis, ad quemlibet inclinationis angulum cum plano A B C ſit

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