Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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adſcribatur per B Hyperbole ABC, quæ ipſi HBI erit ſimilis (cum
<
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roll. prop.
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19. huius.</
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latera ſint proportionalia) eritque ei circumſcripta (cum ſit maiorum late- rum) & </
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>
<
s
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">erit _MINIMA_ quæſita. </
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<
s
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xml:space
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">Nam quælibet alia adſcripta cum recto BE,
<
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<
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roll. prop.
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19. huius.</
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ſed cum tranſuerſo, quod ipſo BD ſit minus eſt maior ipfa ABC; </
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<
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">quælibet verò adſcripta cum eodem recto BE, ſed cum tranſuerſo BM, quod excedat
<
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<
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">ibidem.</
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BD eſt quidem minor ipſa ABC, ſed omnino ſecat Hyperbolen HBI, cum
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iuncta regula ME, & </
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<
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tem BE. </
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<
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xml:space
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">Vnde ipſa ABC erit _MINIMA_ circumſcripta cum dato recto BE,
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vti quærebatur. </
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<
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<
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">Datæ Ellipſi, cum dato latere, quodminus ſit eius recto, per ip-
<
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ſius verticem MAXIMAM Ellipſim inſcribere: </
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<
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">& </
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<
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">è contra.</
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<
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<
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">Datæ Ellipſi, cum dato recto latere, quod maius ſit eius recto,
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per ipſius verticem MINIMAM Ellipſim circumſcribere.</
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<
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</
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<
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">oportet per verticem B, cum dato recto BF _MAXIMAM_ Ellipſim inſcri-
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bere, neceſſe eſt autem, quod rectum datum BF
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minus ſit recto BE (ſi enim ei æquale eſſet, vel
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roll. prop.
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19. huius.</
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maius, etiam deſcribenda Ellipſis, vel eſſet ea- dem cum data ABC, vel hanc ipſam ſecaret, vt
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ſatis patet, cum vel ipſarum regulæ ſimul con-
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gruerent, vel ſe mutuò ſecarent.)</
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<
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<
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">Adſcribatur cum eodem trãſuerſo BD,
<
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que dato recto BF, per verticem B, Ellipſis GBL:
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</
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<
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">& </
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<
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<
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eidem ABC adſcripta cum recto BF, ſed cum
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tranſuerſo, quod minus ſit BD, eſt minor
<
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roll. prop.
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19. huius.</
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GBL, quælibet verò adſcripta cum tranſuerſo
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BM, quod excedat BD eſt quidem maior
<
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GBL, ſed omnino ſecat Ellipſim datam ABC cum & </
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<
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">iuncta regula
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roll. prop.
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19. huius.</
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omnino ſecet regulam ED. </
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<
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">Quare Ellipſis GBL erit _MAXIMA_ quæſita in-
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ſcripta cum recto dato BF. </
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</
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<
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<
s
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& </
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<
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">circumſcribenda ſit ci _MINIMA_ Ellipſis cum dato recto BE, quod debet
<
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quidem eſſe maius recto BF (nam ſi æquale, vel minus eſſet, deſcribenda
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quoque Ellipſis, vel eadem eſſet cum data GBL, vel huic eſſet
<
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">ibidem.</
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cum vel harum regulæ ſimul congruerent, vel regula deſcribendæ caderet
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tota intra regulam deſcriptæ GBL.)</
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</
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<
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<
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<
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lipſis ABC, quæ erit _MINIMA_ circumſcripta quæſita. </
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<
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que alia adſcripta datæ GBL cum recto BE, ſed cum tranſuerſo, quod maius
<
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<
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19. huius.</
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ſit BD, maior eſt ipſa GBL; </
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<
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<
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