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

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11692

Cum ſit BE ad EM, vt OH ad HE, erit

81[Figure 81] componendo BM ad ME, vt OE ad EH,
vel vt RM ad MN; quapropter rectan-
gulum BMN ſiue quadratum 11Coroll.
1. huius. AM in Hyperbola ABC, æquale erit re-
ctangulo EMR, ſiue quadrato 22ibidem. MP in Hyperbola PEQ; ac ideò lineæ
MA, MP ſunt æquales, quare Hyperbo-
læ ABC, PEQ occurrunt ſimul in pun-
cto Q, in quo etiam ſe mutuò ſecabunt.
Nã ſumpto in ſectione QEP infra P quo-
libet puncto S, per quod applicata STV,
ſectionem ABC, diametrum, ac regulas
ſecans in T, V, X, Y: cum ſit EM minor
EV, habebit BE ad EM, vel OH ad HE,
vel YX ad XV, maiorem rationem quam
BE ad EV, & componendo YV ad VX
maiorem rationem, quàm BV ad VE, vnde rectangulum YVE, ſiue 33Coroll.
1. huius. dratum VS in Hyperbola EAS, maius erit rectangulo XVB, ſiue 4416. ſept.
Pappi.55Coroll.
1. huius. to VT in Hyperbola ABC: vnde punctum S cadit extra Hyperbolen ABC,
ac ideò ipſæ Hyperbolæ ſe mutuò ſecant, ſicuti in altero extremo Q, eiuſ-
dem applicatæ. Erit ergo Hyperbole IEL, quæ datæ ABC ſimilis eſt, & ad
eandem regulam, _MAXIMA_ inſcripta quæſita. Quod erat, & c.

Verùm cum ad inueſtigationem MAXIMAE, & MINIMAE in-
ſcriptæ, ac circumſcriptæ ſectionis, mlreferat ignorare quo nam in puncto,
maior, vel minor quæſitarum ſectionum, datæ ſectioni occurrat, ſufficit
enim oſtendere ipſas, vbicunq; ſit earum occurſus, aliquando ſe mutuò ſeca-
re) ideò in proximè ſequentibus problematibus, hac omiſſa methodo per appli-
catarum potentias, tanquam prolixiori, & minus concinna, hoc ipſum aliter
elegantiori induſtria demonſtr abimus, & licet id pluribus, ac varĳs aggreſ-
ſionibus conſequi poſsit, vt in hac, & proxima propoſitione videre licet, ta-
men eas eligemus, quæ apportunæ magis nobis videbuntur.

ALITER.

SEcetur igitur E F bifariam in 2, erit 2 centrum Hyperbolarum IEL,
PEQ, ex quo ductis harum aſumptotis, videlicet 2 3 inſcriptæ IEL,
& 2 4 circumſcriptæ PEQ, quæ cadet extra aſymptoton 2 3, ex D 66Exvlti-
ma parte
37. huius. que agatur D 5 aſymptotos Hyperbolæ ABC.

Iam cum Hyperbolæ ABC, IEL ſimiles ſint, per diuerſos vertices, & ad
eandem regulam FGH ſimul adſcriptæ, erunt earum aſymptoti D 5, 2 3
inter ſe parallelæ ſed 2 4 inter ipſas cadit, & alteram 2 3 ſecat in 2, 77Coroll.
45. huius. re ipſa 2 4 producta ad partes 4, ſecabit & reliquam D 5; ſed eſt 2 4
aſymptotos ſectionis SPEQ, & quædam recta D 5 occurrit ei, ac

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