Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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occurret, ſi ergo ipſa DL producatur, omnino ſecabit Hyperbolen
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">35. h.</
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ſed DL tota cadit extra ſectionem ABC, cum ſit eius aſymptotos, quare
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occurſus rectæ DL, cum ſectione EN, cadet extra ABC, ac ideò EN ſecabit
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priùs circumſcriptam ABC: </
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<
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xml:space
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">vnde ſectio HEK eſt _MAXIMA_ inſcripta quæſi-
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ta, cum dato recto EF. </
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<
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<
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<
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<
s
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">IAM oporteat datæ Hyperbolę HEK, cuius aſymptoti IM, IQ, per datum
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extra ipſam punctum B, quod (per ea, quæ in 53. </
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<
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">huius) ſit vel in angulo
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ad verticem aſymptotalis, vt in prima figura, vel in ipſo aſymptotali MIQ,
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vt in ſecunda, cum dato recto latere _MINIM AM_ Hyperbolen circumſcri-
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bere.</
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<
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<
s
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">Iungatur BI, & </
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0124-01
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producatur vſque oc-
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currat datæ ſectioni
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HEK in E; </
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<
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">erit I E,
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ipſius ſemi-tranſuer-
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ſum, cuius rectum la-
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tus ſit EF, & </
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<
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">ex B cõ-
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cipiatur adſcribi Hy-
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perbole TBV ſimilis,
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& </
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<
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">concentrica datæ
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HEK, cuius rectum
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ſit BS; </
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">& </
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<
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">datũ rectum
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BR, in caſu primæ fi-
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guræ (in quo datum punctum B cadit in angulo ad verticem aſymptotalis
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MIQ) ſit cuiuslibet longitudinis; </
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<
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">in ſecundo verò non ſit minus BS, & </
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">per B
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cum recto BR adſcribatur Hyperbole ABC ſimilis datæ HEK, quæ item ſi-
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milis erit TBV, & </
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<
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">erit ergo in ſecunda figura, ob Hyper-
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bolarum ABC, TBV ſimilitudinem, rectum BR ad BS vt ſemi- tranſuerſum
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BD ad ſemi-tranſuerſum BI, eſtq; </
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BD; </
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<
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">ex quo centrum D ſectionis ABC, vel cadet in I, vel ſupra I centrum
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ſimilis ſectionis HEK: </
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<
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">vnde ipſa ABC erit omnino datæ HEK
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pta.</
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<
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">Dicotandem ipſam ABC eſſe _MINIM AM_ quæſitam: </
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<
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">Quoniam alia Hy-
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perbole, quæ per B adſcribitur, cum eodem recto BR, ſed cum ſemi-tranſ-
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uerſo, quod minus ſit BD, eſt maior ipſa ABC; </
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<
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19. huius.</
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cto BR, & </
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">cum ſemi-tranſuerſo BX, quod excedat BD, qualis dicatur eſſe
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ſectio TBV, eſt quidem minor eadem ABC, ſed omnino ſecat datã KEH.</
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<
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<
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">ibidem.</
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Ductis enim ſimilium Hyperbolarum ABC, HEK aſymptotis DL, IM; </
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erunt inter ſe parallelæ; </
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<
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<
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Hyperbole ABC, TBV per eundem verticem B adſcriptæ, cum eodem re-
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cto BR earum aſymptoti DL, XY infra contingentem ex vertice B ſe mutuò
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ſecabunt, & </
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<
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">cum XY ſecet DL, & </
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<
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36. huius.</
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ſed eſt IM aſymptotos HEK, vnde XY producta ſecabit quidem HEK,
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XY tota cadit extra TBV, cũ ſit eius aſymptotos; </
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<
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ſectione HEK, extra Hyperbolen TBV, vnde ipſa TBV ſecabit priùs inſcri-
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ptam ſectionem HEK. </
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<
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quæſita: </
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">Quod ſecundò faciendum, ac demonſtrandum
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erat.</
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