Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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re, vel cum dato recto, quod ſit minus recto datæ Parabolæ, per
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eius verticem MAXIMAM Hyperbolæ portionem inſcribere; </
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è contra.</
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">Datæ portioni Hyperbolæ, per eius verticem MINIMAM Pa-
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rabolæ portionem circumſcribere.</
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<
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">SIt data Parabolę portio ABCDE, cuius rectum CF, regula FG, baſis AE,
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diameter CI, & </
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">oporteat primùm cum dato quocunque tranſuerſo CH
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_MAXIMAM_ Hyperbolæ portionem inſcribere.</
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<
s
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">Producatur applicata AI vſque ad occurſum
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cum regula in G, & </
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">iungatur HG, ſecans CF in
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L, & </
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<
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">cum tranſuerſo CH, rectoque CL adſcriba-
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tur portioni ABCDE per verticem C
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bole AMCNE, quæ Parabolen ABCDE ſecabit
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in A, & </
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<
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xml:space
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">ipſarum regulæ ſe mutuò
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roll. prop.
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19. huius.</
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in occurſu eiuſdem communis applicatæ AE) & </
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ſupra baſim AE erit datæ Parabolę inſcripta. </
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dico hanc portionem AMCNE eſſe _MAXIMAM_
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quæſitam.</
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<
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">Quoniam quælibet alia Hyperbole adſcripta
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cum eodem tranſuerſo CH, ſed cum recto, quod
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minus ſit recto CL, minor eſt ipſa
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roll. prop.
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19. huius.</
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quælibet verò adſcripta cum recto, quod excedat CL, eſt quidem
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">ibidem.</
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ipſa AMCNE, ſed veltota cadit extra ABCDE, cum Hyperbole, cuius re-
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gula ſit quæ ducitur per H & </
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<
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">eò
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gis, quæ cum recto CO maiore ipſo CF; </
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<
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">vel ſaltem ſecat Parabolen
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19. huius.</
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ſupra portionis baſim AE, cum quælibet regula ducta ex H inter L, & </
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per P, & </
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<
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">infra contingentem CF producta, ſecet regulam FG inter ipſam
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contingentem, & </
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NE eſt _MAXIMA_ inſcripta quæſita cũ dato tranſuerſo CH. </
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<
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">Si verò inſcribenda ſit _MAXIMA_ Hyperbolæ portio cum dato recto CL,
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quod minus ſit recto Parabolæ CF, (nam cum æquali, vel maiori ſemper eſ-
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ſet circumſcripta) iungatur GL, & </
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IC ſecabit in H, cum eadem ſecet FG alteram Parallelarum ipſi diametro;
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</
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<
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<
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">cum tranſuerſo HC, rectoque CL adſcribatur per C Hyperbole
<
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NE, quæ ſecabit, vt ſupra, Parabolen ABCDE in A, & </
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<
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roll. prop.
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19. huius.</
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ſcripta, eritque _MAXIMA_. </
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<
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">Nam quæ cum eodem recto CL, ſed cum tranſ-
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uerſo, quod excedat CH, minor eſt ipſa AMCNE; </
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<
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19. huius.</
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uerſo CQ minore ipſo CH, eſt quidem maior Hyperbola AMCNE,
<
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omnino ſecat Parabolen ABCDE ſupra baſim AE, cum & </
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<
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rol. 19. h.</
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infra contingentem producta, ſecet regulam FG ſupra eandem applicatam.
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<
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