Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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recto FDG, minor eſt ipſa FDG, quæ verò cum recto maiori, eſt
<
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roll. 19. h.</
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maior FDG, qualis eſt HDI, ſed omnino ſecat latera dati anguli ABC:</
s
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<
s
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<
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symbol
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xlink:label
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">ibidem.</
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quoniam ducta BL aſymptoto ſectionis HDI, ipſa cadet extra BA, ſed
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eſt aſymptotos inſcriptæ FDG, quare ipſa BH producta ſecabit Hyperbolen
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circumſcriptam DH, eadem ratione BC ſecabit DI: </
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<
s
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">quapropter Hyperbole
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FDG eſt dato angulo _MAXIMA_ inſcripta quæſita. </
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<
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<
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</
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<
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<
s
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xml:space
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">Siverò data magni-
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0136-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0136-01
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tudo E, vel ei æqualis
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DO, minor fuerit di-
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ſtantia DB inter datum
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punctum, & </
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<
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">dati angu-
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li ABC verticem, vt in
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ſecunda figura; </
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<
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tur ex O, rectæ OP, OH,
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aſymptotis BA, BC æ-
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quidiſtantes, & </
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<
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aſymptotos OP, OH
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<
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">4. ſec.
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conic.</
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deſcribatur per D Hy perbole FDG: </
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<
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">& </
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<
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erit _MAXIMA_ inſcripta quæſita.</
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<
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">Quoniam, quæ cum eodem tranſuerſo, ſed cum recto minori adſcribitur
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per D, minor eſt FDG, quæ verò cum recto maiori, qualis eſt IDL, eſt
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roll. 19. h.</
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dem maior, ſed omnino ſecat latera dati anguli BA, BC: </
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<
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">ibidem.</
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OM aſymptoto circumſcriptæ IDL, cadet extra OP aſymptoton
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">ex 37. h.</
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FDG, & </
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<
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">producta ſecabit BA, cum ſecet in O alteram parallelam OP; </
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<
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re BA producta ſecabit quidem Hyperbolen DIL: </
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<
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">vnde FDG eſt
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_MA_ quæſita. </
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<
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">Sitandem DO, quæ ipſi E æqualis eſt, excedat DB. </
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">Fiat vt OB ad OD,
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ita OD ad OF, & </
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66. h.</
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mi-tranſuerſo OD, per puncta A,D,C, deſcribatur Hyperbole ADC,
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ca diametri ſegmentum DF, & </
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quęſitam.</
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<
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">Quoniam, cum ſit FO ad OD, vt DO ad OB, erit rectangulum FOB æqua-
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le quadrato OD, quare BA, BC Hyperbolen contingent; </
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<
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37. primi
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conic. à
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Comand.</
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le ADC dato angulo ABC erit inſcripta; </
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<
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">eritque _MAXIMA_; </
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<
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">quoniam, quæ
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cumrecto minori cadit intra, quæ verò cum maiori cadit quidem
<
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">2. Co-
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roll. 19. h.</
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ADC, ſed neceſſariò ſecat dati anguli latera BA, BC, cum ſectio Hyper-
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bole in infinitum produci poſſit, & </
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</
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">ibidem.</
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quare ipſa ADC eſt _MAXIMA_ inſcripta quæſita, per datum punctum D.
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</
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<
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<
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ED, EF, per datum extra ipſam punctum G, _MINIMV M_ angulum circũ-
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ſcribere.</
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<
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">Itaque, vel datum punctum G congruit cum centro E, vel cadit in angu-
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lo aſymptotali, vel in eo, qui huic eſt ad verticem; </
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<
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G, & </
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<
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ter, non autem ſi datum punctum alibi cadat. </
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