Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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Parabolen inſcribere, & </
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<
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<
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<
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">Datæ Parabolæ per punctum extra ipſam datum MINIMAM
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Parabolen circumſcribere.</
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<
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</
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<
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<
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<
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tum _MAXIMAM_ Parabolen inſcribere.</
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<
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<
s
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BDE, cuius rectum
<
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latus ſit BF, (quod
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in poſterùm intelli-
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gatur ſemper ex ver-
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tice cõtingenter ap-
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plicatum ſectioni,
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prout in prę;</
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<
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bus factum eſt, & </
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<
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quinta primarũ defi-
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nitionũ monuimus)
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& </
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<
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">per verticem D,
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circa diametrũ D E
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adſcribatur datæ Parabolæ ABC Parabole GDH, cuius rectum DI
<
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le ſit recto BF; </
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<
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">nam ipſa erit congruens datæ Dico hanc eſſe _MAXIMAM_
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in ſcriptam quæſitam.</
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<
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">Nam cum ipſæ ſint congruentes Parabolæ per diuerſos vertices ſimul ad-
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ſcriptæ erunt inter ſe nunquam coeuntes: </
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<
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">quare GDH datæ ABC erit
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datum punctum D inſcripta.</
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<
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<
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quod minus ſit ipſo DI minor eſt Parabola GDH, quæ verò cum recto
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roll. 19. h.</
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quod excedat ipſum DI, qualis eſt MDN, eſt quidem maior GDH,
<
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">ibidem.</
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omnino ſecat circumſcriptam ABC. </
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<
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& </
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vt Li ad ID, erit componendo BE ad ED, vt LD ad DI; </
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<
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ſub extremis BE, & </
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<
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<
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1. huius.</
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rabola ABC, æquale erit rectangulo ſub medijs ED, DL ſiue quadrato
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plicatę; </
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<
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<
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Parabole DN occurrit ſibi adſcriptæ BA, per diuerſos vertices in puncto M,
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& </
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Itaque congruens Parabole GDH erit _MAXIMA_ inſcripta quæſita. </
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<
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primò, &</
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<
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<
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_MINIMAM_ Parabolen circumſcribere.</
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<
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<
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<
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per B, cum recto BF, quod æquet ipſum DI, congruens Parabole ABC:</
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