Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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verò cum recto, quod excedat CM, eſt quidem maior ipſa ANCO,
<
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roll. 19. h.</
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veltota cadit extra ABCDE, cum Hyperbole, cuius regula IG ſit ei
<
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cumſcripta, & </
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<
s
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">eò ampliùs ea, quæ cum recto quod excedat CG; </
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<
s
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ſecat Hyperbolen ABCD ſupra portionis baſim AE ſi rectum cadat
<
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M, & </
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<
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">G. </
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<
s
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">Vnde hæc Hyperbolæ portio ANCOE eſt _MAXIMA_ inſcripta
<
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quæſita, cum dato tranſuerſo CI. </
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<
s
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">Quod erat primò, &</
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<
s
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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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">Siautem inſcribẽda ſit _MAXIMA_ Hyperbolæ portio cum dato recto CM,
<
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quod ſit minus recto CG (cum æ quali enim, vel maiori ſemper eſſet circum-
<
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ſcripta) iuncta LM, & </
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<
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<
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tranſuerſo latere CI, ac recto CM adſcribatur per C Hyperbole
<
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quæ ſecabit Hyperbolæ portionem ABCD in A & </
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<
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<
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<
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roll. 19. h.</
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Dico hanc eſſe _MAXIMAM_ quæſitam. </
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<
s
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">Quoniam quæ adſcribitur per C cum
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eodem recto CM, ſed cum tranſuerſo, quod excedat CI, minor eſt
<
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19. huius.</
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bola ANCO, quæ verò cum tranſuerſo, quod minus ſit ipſo CI, & </
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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maior eadem ANCO, ſed omninò ſecat Hyperbolen ABCDE ſupra
<
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roll. 19. h.</
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catam AE. </
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>
<
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">Eſt igitur huiuſmodi Hyperbolæ portio ANCO _MAXIMA_ in-
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ſcripta quæſita cum dato recto CM. </
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<
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">Quod erat ſecundò, &</
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<
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">c.</
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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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">Ampliùs, ſit data Hyperbolæ portio ANCOE, cuius verſum CI, rectum
<
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CM, regula IML, baſis AE, ac diameter CI, cui oporteat per verticem C,
<
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cum dato tranſuerſo CF, quod maius ſit CI _MINIMAM_ Hyperbolæ portio-
<
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nem circumſcribere.</
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>
<
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</
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<
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<
s
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">Producatur ſemi-baſis AH conueniens cum regula IM, in L, & </
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<
s
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">iungatur
<
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FL contingentem CM ſecans in G, & </
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<
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">cum tranſuerſo CF, ac recto CG ad-
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ſcribatur per verticem C Hyperbole ABCDE, quæ occurret datæ
<
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">6. huius.</
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bolæ ANCO in punctis A, E, eique erit circumſcripta ſupra baſim AE,& </
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<
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">erit
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_MINIMA_ Hyperbolæ portio quæſita.</
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<
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</
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<
s
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">Quoniam, quæ adſcribitur cum eodem verſo CF, ſed cum recto maiore
<
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ipſo CG, eſt quoque maior Hyperbola ABCD, quę verò cum recto
<
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">1. Corol.
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19. huius.</
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re ipſo CG, eſt quidem minor eadem ABCD, ſed veltota cadit intra
<
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roll. 19. h.</
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tam ANCO ſi nempe rectum æquale fuerit ipſo CM, & </
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<
s
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">eò magis ſi
<
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">ibidem.</
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eſſet CM; </
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<
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">vel ſaltem ſecat Hyperbolen ANCO ſupra baſim AE,
<
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19. huius.</
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rectum cadat inter CM, & </
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<
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">CG; </
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<
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">tunc enim harum regulæ ſe mutuò ſecarent,
<
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ſupra eandem baſim AE. </
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>
<
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="
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xml:space
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">Vnde Hyperbolæ portio ABCDE, eſt _MINIMA_
<
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circumſcripta quæſita cum dato tranſuerſo CF. </
s
>
<
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">Quod tertiò, &</
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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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">Demùm eidem datæ Hyperbolæ ANCO, ſit circumſcribenda _MINIMA_
<
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Hyperbole cum dato recto CG, quod excedat datæ rectum CM. </
s
>
<
s
xml:id
="
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">Facta ea-
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dem conſtructione, iungatur LG diametro occurrens in F, & </
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<
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">cum tranſuerſo
<
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CF, ac dato recto CG adſcribatur per C Hyperbole ABCDE, quæ
<
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roll. 19. h.</
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ſecabit in A, & </
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<
s
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">E eique erit circumſcripta, & </
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<
s
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">erit _MINIMA_ quæſita. </
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<
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<
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">6. huius.</
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quæ cum eodem recto CG, ſed cum tranſuerſo, quod minus ſit CF, maior
<
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eſt ipſa ABCD, quę verò cum tranſuerſo, quod maius ſit ipſo CF, quale
<
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">1. Co-
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roll. 19. h.</
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CP, eſt quidem minor, ſed omnino ſecat, portionem ANCO ſupra
<
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xlink:label
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">3. Corol.
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19. huius.</
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AE, cum iuncta regula PG, & </
s
>
<
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">producta, ſecet regulam IL ſupra ipſam baſim
<
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AE. </
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>
<
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">Quare Hyperbolæ portio ABCD eſt _MINIMA_ circumſcripta quæſita
<
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cum dato recto CG. </
s
>
<
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="
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">Quod tandem faciendum erat.</
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