Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
s
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xml:space
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">Quod tandem HI, aſymptotos inſcriptæ DEF, ſecet circumſcriptam Hy-
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perbolen ABC, iam ſatis patet ex dictis. </
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<
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<
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xml:space
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">_E_N tibi Lector Geometra admiranda quædam Naturæ ſympto-
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mata circa Aſymptoticas lineas iam olim à nobis detecta, ac ſi-
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mul directa demonſtratione firmata, dum in Conicis hucuſque
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animaduertimus non tantùm binas dari lineas in eodem plano
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exiſtentes, quæ licet ſemper inter ſe magis accedant, nunquam tamen (quòd
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ſanè mirum eſt) etiam ſi in infinitum productæ, ſimul conueniunt; </
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<
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">quales
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ſunt, conuexa linea hyperbolica, & </
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<
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">celebris illa recta Aſymptotos Apoll. </
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<
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xml:space
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">ab
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ipſo tunc negatiuè, à nobis verò in 8. </
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<
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xml:space
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<
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<
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">huius affirmatiuè demonſtrata:
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</
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<
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">verùm alias quoque, eiuſdem penitus naturæ reperiri, alteram nempe con-
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uexam, concauam alteram, quales ſunt binæ congruentes parabolæ, vel hy-
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perbolæ; </
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<
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">item binæ ſimiles hyperbolæ, quarum centrum interioris, aut in ipſā
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cadat, aut infra centrum exterioris, atque omnes ſint per diuerſos vertices
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ſimul adſcriptæ; </
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<
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<
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">elicitur ex ipſa 48. </
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huius. </
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">Præterea, non ſolùm rectam Aſymptoton, & </
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<
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">Hyperbolen dari, quæ
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dum ad ſe propius ſemper accedunt, ad interuallum aliquando perueniunt mi-
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nus quolibet dato interuallo, vti ex ipſo Apollonio, & </
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<
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ſed congruentes item parabolas, & </
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<
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tices ſimul adſcriptas hac ipſa admirabili affectione eſſe præditas, veluti in
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42. </
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admiratione dignum videtur, binas pariter lineas inueniri, quæ licet nun-
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quam coeuntes, & </
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<
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">in infinitum productæ ad ſe propius accedentes, non ta-
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men vnquam perueniunt ad interuallum cuiuſdam determinatæ magnitudi-
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nis: </
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<
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">huiuſmodi enim ſunt congruentes Hyperbolæ, pariterque hyperbolæ ſimi-
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les per diuerſos vertices ſimul adſcriptæ, prout didicimus in 44. </
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Alias amplius deteximus lineas, quarum diſtãtia perpetuò augetur, ſed nun-
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quam tamen peruenit ad interuallum æquale cuidam terminato interuallo: </
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les enim ſunt recta linea alteri aſymptoton æquidiſtans, & </
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vna cum eadem curua hyperbolica: </
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dem verticem ſimul adſcriptæ, prout in 34. </
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binas dari lineas ad eaſdem partes in infinitum productas, nunquam coeun-
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tes, quæ ſimul, ac ſemel ſunt, & </
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diſtantes: </
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ſimul adſcriptæ, vti ex noſtra 42. </
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<
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