Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
s
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xml:space
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">Quoniam, quæcunque ſectio ſimilis ſectioni DBE adſcripta per B ſectioni
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ABC, cumrecto BM, quod minus ſit recto BF, minor eſt ſectione
<
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roll. prop.
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19. huius.</
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quælibet verò adſcripta cum recto BO; </
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<
s
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xml:space
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">quod maius ſit recto BF eſt quidem maior ipſa DBE, ſed datam ABC omnino ſecat; </
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<
s
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xml:space
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"> quoniam ipſius
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xml:space
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">ibidem.</
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ON, quæ æquidiſtat regulæ FH, ſecat infra contingentem BF
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roll. prop.
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19. huius.</
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FIG, nam altera parallelarum FH ab eadem FIG ſecatur in F: </
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<
s
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xml:space
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">vnde ipſa
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DBE eſt _MINIMA_ ſibi ſimilium, &</
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<
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<
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<
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</
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19. huius.</
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<
s
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xml:space
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">Nunc verò ſit coni-ſectio DBE, cuius rectum BF, & </
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<
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">regula FH, ipſique
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circumſcripta ſit cum eodem recto BF, per verticem B coni-ſectio ABC, quæ
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erit _MINIMA_ circumſcripta, per iam demonſtrata, eiuſque regula ſit GFI.
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</
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<
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xml:space
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">Dico hanc _MINIMAM_ ſectionem ABC eſſe quoque _MINIMAM_ ſibi ſimi-
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lium, eidem ſectioni DBE per verticem circumſcriptarum.</
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<
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<
s
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xml:space
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">Nam quælibet coni-ſectio ſimilis ABC, adſcripta per B datæ ſectioni DB
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E, cum recto BO, quod maius ſit recto BF maior eſt ſectione ABC,
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roll. prop.
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19. huius.</
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libet verò adſcripta cum recto BM, quod minus ſit recto BF eſt quidem
<
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minor ipſa ABC, ſed datam ſecat DBE, quoniam ipſius regula QM, quę re-
<
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gulæ GFI æquidiſtat, ſecat regulam FH, nam altera parallelarum GFI ſecat
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infra BF ipſam FH in F. </
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<
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xml:space
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">Quare ipſa ABC eſt _MINIMA_ ſibi ſimilium, &</
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xml:space
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">Datæ Hyperbolæ, cum dato quocunque tranſuerſo latere, per
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ipſius verticem MAXIMAM Hyperbolen inſcribere: </
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<
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">& </
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<
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<
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">Datæ Hyperbolæ cum dato quolibet tranſuerſo latere per eius
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verticem MINIMAM Hyperbolen circumſcribere.</
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<
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</
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<
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xml:space
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">SIt data Hyperbole ABC, cuius
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vertex B, tranſuerſum latus BD,
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rectum BE, & </
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<
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mò cum dato quocunque alio tranſ-
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uerſo latere, per verticem B, _MAXI_-
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_MAM_ Hyperbolen inſcribere.</
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<
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<
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">Iam, vel datum tranſuerſum latus
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exceditranſuerſum BD, datę Hyper-
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bolæ, vel eodem minus eſt. </
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<
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mùm quale eſt BG; </
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<
s
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"> adſcribatur Hy- perbolę ABC per verticem B, cum
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<
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dato tranſuerſo BG, & </
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<
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recto BE Hyperbole HBI. </
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<
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ſam HBI datæ ABC eſſe inſcriptam;</
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<
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roll. prop.
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19. huius.</
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quàm dico eſſe _MAXIMAM_: </
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<
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quælibet alia ipſi HBI adſcripta cum
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eodem tranſuerſo BG, ſed cumrecto,
<
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quod ſit minus BE, ſemper minor
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roll. prop.
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19. huius.</
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ipſa HBI, quelibet vero adſcripta </
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