Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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121 - 130
131 - 140
141 - 150
151 - 160
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recto BI, quod excedat BL, eſt
<
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">ibidem.</
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0072-01
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dem maior ipſa HBI, ſed vel ſecat Hy-
<
lb
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<
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b
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xml:space
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">1. Co-
<
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roll. prop.
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19. huius.</
note
>
perbolen ABC, quod accidit ſi iun- cta regula GL, ac infra contingentem
<
lb
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BL producta, ſecet productam regu-
<
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lam DE; </
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>
<
s
xml:id
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xml:space
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">vel cadit extra eandẽ ABC,
<
lb
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quando iuncta regula GL, cum
<
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xlink:label
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xml:space
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">ibidem.</
note
>
gula DE infra eandem contingentem
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nunquam conueniat. </
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<
s
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xml:space
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di Hyperbole HBI erit _MAXIMA_
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quæſita.</
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<
s
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">Si deniq; </
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<
s
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">datũ trã ſuerſum latus BM
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ſit minus tranfuerſo BD, ducatur MF
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ipſi BE parallela, & </
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<
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">cũ tranſuerſo BM,
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ac recto BF, per vcrticem B, Hyper-
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bolæ ABC adſcribatur
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">6. huius.</
note
>
HBI, quæ ipſi ABC ſimilis erit, cum
<
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ſit tranſuerſum DB ad rectum BE, vt
<
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tranſuerſum MB ad rectum BF, eritq;
<
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</
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>
<
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xml:space
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">inſcripta Hyperbolæ ABC, cum ſit minorum laterum. </
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<
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xml:space
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">Dico hanc
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e
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<
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19. huius.</
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_MAXIMAM_ quæſitam.</
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<
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<
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">Quoniã quælibet alia, quæ cum recto minore ipſo BF adſcribitur, ſemper
<
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<
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f
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">2. Co-
<
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roll. prop.
<
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19. huius.</
note
>
eſt minor HBI, quæ verò cum recto, quod excedat BF, eſt quidem maior ipſa HBI, ſed vel ſecat Hyperbolen ABC, quod ſit cum rectum cadit inter
<
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F, & </
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<
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">producta, ſecat regulam
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">ibidem.</
note
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infra contingentem BE; </
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<
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">vel cadit tota extra ABC, quod euenit cũ
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">1. Co-
<
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rol. prop.
<
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19. huius.</
note
>
velidem fuerit cum recto BE, vel maius ipſo BE, quale eſt BL; </
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>
<
s
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xml:space
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<
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iuncta regula ML infra contingentem BE, diſiunctim procederet à regula
<
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<
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xml:space
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">3. 1. Co-
<
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roll. prop.
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19. huius.</
note
>
DE, cum eam ſecaret priſu4;</
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>
<
s
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">s ſupra BE. </
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<
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_XIMA_ quæſita. </
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<
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">Amplius, ſit data Hyperbole HBI, cuius tranſuerſum latus ſit BD, rectum
<
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BE, & </
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<
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">regula DE, & </
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>
<
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">ipſi oporteat per verticem B _MINIMAM_ Hyperbolen
<
lb
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circumſcribere, cum dato quolibet tranſuerſo latere.</
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<
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<
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<
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xml:space
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">Si datum tranſuerſum circumſcribendæ Hyperbolæ fuerit minus ipſo BD,
<
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quale eſt BM: </
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>
<
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">adſcribatur datæ HBI, per verticem B Hyperbole
<
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l
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huius.</
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cuius tranſuerſum ſit BM, rectum verò ſit idem BE: </
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<
s
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">3. Co-
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rol prop.
<
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19. huius.</
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ſcripta, eritque _MINIMA_ quæſita; </
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>
<
s
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xml:space
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">quoniam quælibet alia adſcripta cum
<
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tranſuerſo BM, ſed cum recto quod excedat BE, quale eſſet BL, eſt maior ipſa ABC; </
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>
<
s
xml:id
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xml:space
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">quælibet verò adſcripta, cum eodem tranſuerſo BM, & </
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<
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<
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<
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prop. 19.
<
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huius.</
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cto quod minus ſit BE, eſt quidem minor ipſa ABC, ſed vel ſecat Hyper- bolen HBI, tum cum earum regulæ infra contingentem BE ſe mutuò ſecant,
<
lb
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<
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xlink:label
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xml:space
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">ibidem.</
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vel cadit intra HBI, quando earundem regulæ infra prædictam
<
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roll prop.
<
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19. huius.</
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tem nunquam ſimul conueniant. </
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<
s
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">Quare ipſa ABC erit _MINIMA_ quæſita.</
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<
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</
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<
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<
s
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">Si autem datum tranſuerſum latus fuerit maius ipſo BD quale eſt BG; </
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>
<
s
xml:id
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">du-
<
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<
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xlink:label
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">ibidem.</
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catur GL parallela ad DE, & </
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>
<
s
xml:id
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">datæ Hyperbolæ HBI cum tranſuerſo BG, re-
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ctoque BL adſcribatur per B Hyperbole ABC, quæ datæ HBI erit
<
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symbol
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xlink:label
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">6. huius.</
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cum ipſarum latera ſint proportionalia, eritque circumſcripta, cum ſit </
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