Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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rum laterum. </
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<
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xml:space
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">Dico hanc eſſe _MINIMAM_ quæſitam: </
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<
s
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xml:space
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">Nam quælibet alia, quę
<
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adſcribitur cum recto maiore ipſo BL, maior eſt ipſa ABC, quælibet
<
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rol. 19. h.</
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quæ adſcribitur cum recto minore ipſo BL, eſt quidem minor ABC,
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">ibidem.</
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vel ſecat Hyperbolen ABC, quod accidet, cum rectum latus terminet inter
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E, & </
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<
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">L, vt in O, nam iuncta regula GO, ſi producatur, infra
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rol. 19. h.</
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BO cum regula DE conueniret, ideoque, & </
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<
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<
s
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xml:space
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">veltota cadit intra
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HBI quod fit quando rectum latus, vel ſit idem cum recto BE, vel
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">3. 1. Co-
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rol. 19. h.</
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ipſo BE, quale eſt BF, quoniam ſi iungatur regula GF, ipſa, atque regula
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DE ſe mutuò ſecarent ſupra contingentem BE, ideoque infra diſiunctim ſi-
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mul procederent. </
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<
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">Quare huiuſmodi Hyperbole ABC, quæ ſimilis eſt datæ
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HBI erit _MINIMA_ circumſcripta quæſita. </
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<
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">Datæ Hyperbolæ, cum dato recto latere, quod recto datæ ſit
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minus, per eius 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 recto latere, quod maius ſit recto
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datę, per eius verticem MAXIMAM Hyperbolen circumſcribere.</
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<
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<
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xml:space
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DE; </
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">oportet per eius verticem B, cum dato recto BF, quod minus ſit re-
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cto BE, _MAXIMAM_ Hyperbolen inſcribere.</
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<
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tranſuerſo BG, rectoque BF adſcriba-
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tur per B ipſi ABC, Hyperbole
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quæ datæ ABC erit ſimilis (cum ipſa-
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rum latera ſint proportionalia) eritque
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inſcripta (cum ſit minorum
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">5. Co-
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rol. 19. h.</
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quàm dico eſſe _MAXIMAM_ quæſitam:
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</
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<
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recto BF, ſed cum tranſuerſo, quod ex-
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cedat BG minor eſt ipſa HBI,
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rol. 19. h.</
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que verò adſcripta cum eodem recto
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BE, ſed cum tranſuerſo, quod ſit minus
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tranſuerſo BG, quale eſt BL, eſt quidẽ
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maior ipſa HBI, ſed omnino ſecat
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perbolen ABC cum iũcta regula
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rol. 19. h.</
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& </
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<
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gentem BE omnino ſecet: </
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<
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HBI erit _MAXIMA_ inſcripta cum dato
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recto BF, Quod primò, &</
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<
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<
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<
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regula GF, & </
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<
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">datum rectum latus ſit BE ipſo BF maius, cum quo oporteat
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_MINIMAM_ Hyperbolen circumſcribere.</
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