Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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">Si à puncto, quod eſt in Hyperbola ducatur recta linea alteri
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aſymptoton æquidiſtans, ipſa, ac ſectio, quæ inter has parallelas
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intercipitur, in infinitum productę ſunt infra occurſum ſemper ma-
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gis recedentes, ſed tamen nunquam perueniunt ad interuallum
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æquale cuidam dato interuallo; </
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<
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">dum earum diſtantia metiatur per
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interceptas æquidiſtantes cuilibet rectæ, quæ ducta ſit ex occurſu
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vtramque aſymptoton ſecans.</
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<
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">SIt Hyperbole ABC, cuius aſymptoti ED, EF, ſitque ex quolibet ſectio-
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nis puncto B recta BGN alteri aſymptoto ED æquidiſtans, quæ intra
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lectionẽ cadens, in nullo alio pũcto quam
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B cum ipſa conueniet. </
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11. huius.</
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B ducatur quæcunque HBF vtranq; </
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ptoton ſecans) ipſam, & </
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infra BI eſſe sẽper magis inter ſerecedẽtes.</
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s
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">Applicentur quotcunque DAG, LMN
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infra HB, ipſi æquidiſtantes: </
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<
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nes LN, DG, HB inter ſe æquales eſſe, ſed
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eſt DA minor HI, ergo AG maior
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IB, eſtque LM minor DA, quare & </
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maior AG, & </
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<
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producantur; </
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<
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">ergo linea BGN, & </
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IAM ſunt ſemper ſimul recedentes. </
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primò, &</
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<
s
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">Et quoniam earum interuallum, per eaſ-
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dem interceptas metitum, ſemper minus
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eſt HB interuallo parallelarum BN, HL,
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cum ſit GA minos GD, NM minos NL, & </
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omnes GD, NL, &</
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propter, licet huiuſmodi lineæ ſint ſemper magis recedentes, non tamen
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perueniunt ad interuallum æquale interuallo BH. </
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