Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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ſita cum dato recto CL. </
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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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">Iam ſit data Hyperbolæ portio AMCNE, cuius tranſuerſum CH, rectum
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CL, regula HLG, baſis AE, diameter CI, & </
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<
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">oporteat, per verticem C, _MI_-
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_NIMAM_ Parabolæ portionem circumſcribere.</
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<
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<
s
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">Producatur applicata AI, conueniens cum re-
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gula HL in G, & </
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<
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IC contingentem ſecans in F, cumque recto CF
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adſcribatur per C Parabole ABCDE, quæ
<
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cabit Hyperbolen in ijſdem punctis A, & </
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<
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rationem ſuperius allatam, & </
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<
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CD erit circumſcripta; </
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<
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">_MINIMA_ portio.</
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<
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roll. prop.
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19. huius.</
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<
s
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">Quoniam, quæ cum recto maiore ipſo CF eſt
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maior ipſa ABCDE, quæ verò cum recto
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roll. prop.
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19. huius.</
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re ipſo CF eſt quidem minor ABCDE, ſed
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">ibidem.</
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tota cadit intra Hyperbolen AMCN ſi
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rectum æquale fuerit ipſo CL, & </
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nus eſſet BL; </
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<
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ſupra applicatam AE tum cum rectum ſit medium inter CF, & </
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<
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roll. prop.
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19. huius.</
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eſt CP: </
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<
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">nam regula, quæ ex P, ducitur æquidiſtans CI, omninò ſecat regu-
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lam LG infra contingentem CF, & </
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bolæ portio ABCDE, eſt _MINIMA_ circumſcripta quæſita. </
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<
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faciendum erat.</
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minus ſit tranſuerſo, vel recto datæ Hyperbolæ, per eius verticem
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MAXIMAM Hyperbolæ portionem inſcribere: </
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<
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<
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">Datæ portioni Hyperbolæ, cum dato tranſuerſo vel recto, quod
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excedat tranſuerſum, aut rectum datæ Hyperbolæ, per eius verti-
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cem MINIMAM Hyperbolæ portionem circumſcribere.</
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<
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tranſuerſum CF, rectum CG, regula FGL,
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baſis AE, diameter CH. </
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dato tranſuerſo CI, quod minus ſit ipſo CF
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_MAXIMAM_ Hyporbolæ portionem inſcribere.</
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<
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<
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regula FG in L, & </
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<
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">iuncta IL contingentem CG
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ſecant in M, cum regula IM, per verticem C ad-
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ſcribatur portioni ABCDE Hyperbole
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OE, quę datam ABCD ſecabit in A, & </
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roll prop.
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19. huius.</
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ipſi erit inſcripta. </
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<
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_MAXIMAM_ quæſitam.</
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<
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<
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">Quoniam, quę adſcribitur cum eodem tranſ-
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uerſo CI, ſed cum recto, quod ſit minus CM, eſt minor ipſa ANCO,
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prop. 19.
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huius.</
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