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

Table of contents

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[111.] THEOR. XXIII. PROP. XXXXIV.
[112.] COROLL.
[113.] Quod ſuperiùs promiſimus oſtendetur ſic.
[114.] THEOR. XXIV. PROP. XXXXV.
[115.] COROLL.
[116.] LEMMA VI. PROP. XXXXVI.
[117.] THEOR. XXV. PROP. XXXXVII.
[118.] ALITER.
[119.] COROLL. I.
[120.] COROLL. II.
[121.] THEOR. XXVI. PROP. XXXXVIII.
[122.] MONITVM.
[123.] THEOR. XXVII. PROP. XXXXIX.
[124.] THEOR. XXVIII. PROP. L.
[125.] COROLL.
[126.] PROBL. XVII. PROP. LI.
[127.] PROBL. XVIII. PROP. LII.
[128.] ALITER.
[129.] ALITER breuiùs.
[130.] PROBL. XIX. PROP. LIII.
[131.] ALITER.
[132.] ALITER breuiùs.
[133.] PROBL. XX. PROP. LIV.
[134.] ALITER breuiùs.
[135.] PROBL. XXI. PROP. LV.
[136.] PROBL. XXII. PROP. LVI.
[137.] COROLL. I.
[138.] COROLL. II.
[139.] PROBL. XXIII. PROP. LVII.
[140.] COROLL.
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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-
ABC, PEQ occurrunt ſimul in pun-
cto
Q, in quo etiam ſe mutuò ſecabunt.
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.
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.

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