Viviani, Vincenzo - De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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8763

THEOR. XV. PROP. XXXIV.

Si à puncto, quod eſt in Hyperbola ducatur recta linea alteri
aſymptoton æquidiſtans, ipſa, ac ſectio, quæ inter has parallelas
intercipitur, in infinitum productę ſunt infra occurſum ſemper ma-
gis recedentes, ſed tamen nunquam perueniunt ad interuallum
æquale cuidam dato interuallo; dum earum diſtantia metiatur per
interceptas æquidiſtantes cuilibet rectæ, quæ ducta ſit ex occurſu
vtramque aſymptoton ſecans.

SIt Hyperbole ABC, cuius aſymptoti ED, EF, ſitque ex quolibet ſectio-
nis puncto B recta BGN alteri aſymptoto ED æquidiſtans, quæ intra
lectionẽ cadens, in nullo alio pũcto quam

57[Figure 57] B cum ipſa conueniet. Dico primùm (ſi 11Coroll.
11. huius. B ducatur quæcunque HBF vtranq; aſym-
ptoton ſecans) ipſam, & ſectionem IAM
infra BI eſſe sẽper magis inter ſerecedẽtes.

Applicentur quotcunque DAG, LMN
infra HB, ipſi æquidiſtantes: patet has om-
nes LN, DG, HB inter ſe æquales eſſe, ſed
eſt DA minor HI, ergo AG maior 2210. h. IB, eſtque LM minor DA, quare & MN
maior AG, & hoc ſemper ſi in infinitum
producantur; ergo linea BGN, & ſectio
IAM ſunt ſemper ſimul recedentes. Quod
primò, & c.

Et quoniam earum interuallum, per eaſ-
dem interceptas metitum, ſemper minus
eſt HB interuallo parallelarum BN, HL,
cum ſit GA minos GD, NM minos NL, &
omnes GD, NL, & c. ipſi BH equales: qua-
propter, licet huiuſmodi lineæ ſint ſemper magis recedentes, non tamen
perueniunt ad interuallum æquale interuallo BH. Quod erat tandem, & c.

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