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

Table of contents

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[21.] COROLL.
Page: 26 (6)
[22.] MONITVM.
Page: 26 (6)
[23.] PROBL. I. PROP. II.
Page: 30 (10)
[24.] ALITER.
Page: 30 (10)
[25.] ALITER.
Page: 31 (11)
[26.] MONITVM.
Page: 32 (12)
[27.] LEMMAI. PROP. III.
Page: 32 (12)
[28.] PROBL. II. PROP. IV.
Page: 33 (13)
[29.] MONITVM.
Page: 35 (15)
[30.] PROBL. III. PROP. V.
Page: 35 (15)
[31.] PROBL. IV. PROP. VI.
Page: 37 (17)
[32.] PROBL. V. PROP. VII.
Page: 38 (18)
[33.] MONITVM.
Page: 39 (19)
[34.] THEOR. II. PROP. VIII.
Page: 40 (20)
[35.] MONITVM.
Page: 41 (21)
[36.] LEMMA II. PROP. IX.
Page: 41 (21)
[37.] THEOR. III. PROP. X.
Page: 41 (21)
[38.] COROLL. I.
Page: 43 (23)
[39.] COROLL. II.
Page: 43 (23)
[40.] MONITVM.
Page: 43 (23)
[41.] THEOR. IV. PROP. XI.
Page: 43 (23)
[42.] COROLL.
Page: 44 (24)
[43.] MONITVM.
Page: 45 (25)
[44.] LEMMA III. PROP. XII.
Page: 45 (25)
[45.] ALITER idem breuiùs.
Page: 46 (26)
[46.] ITER VM aliter breuiùs, ſed negatiuè.
Page: 47 (27)
[47.] COROLL.
Page: 47 (27)
[48.] THEOR. V. PROP. XIII.
Page: 47 (27)
[49.] COROLL. I.
Page: 49 (29)
[50.] COROLL. II.
Page: 49 (29)
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10783
ALITER.
DVcantur ex communi centro G aſymptoti GX, GZ ſectionis ABC, quę
alterius ſimilis, & concentricæ ſectionis DEF erunt quoque 11Coroll.
40. huius. ptoti, & ipſi GX, productæ contingentes IB, ME, occurrant in X, Y, & per
G ſit G 2, regulis HI, LM parallela, recta latera ſecans in 2, & 3; cum ſit GE
æqualis GL, & GB æqualis GH, erit E 3 æqualis 3 M, & B 2 æqualis 2 I,
ſiue 3 4, quare E 4 eſt aggregatum E 3 cum B 2. Iam cum rectangulum
GE 3 ſit quarta pars rectanguli LEM, & quadratum EY eiuſdem rectangu-
li ſubquadruplum, ergo quadratum EY ęquatur rectangulo GE 3: 228. huius. que ratione eſt quadratum BX æquale rectangulo GB 2, ſed rectangulum
GE 3 excedit rectangulum GB 2 rectangulo BE 4, ſiue quadrato KE, 33Coroll.
1. huius. re quadratum EY ſuperat quadratum BX quadrato EK: ſed productis 4446. h. plicatis AN, QS vſque ad communes aſymptotos, ipſas, ac ſectiones ſecan-
tibus in 5 ADFC 6, & in 7 QR 8 9, eſt quadratum EY æquale 55ibidem. lo 5 D 6, & quadratum BX ęquale rectangulo 5 A 6; vnde quadratorum
exceſſus æquatur exceſſui rectãgulorum, ſed exceſſus quadratorum eſt qua-
dratum EK, & exceſſus rectangulorum 5 D 6, 5 A 6 eſt 66179. ſe-
pt. Pappi. ADC; vnde quadratum EK æquatur rectangulo ADC; eademque ratione
oſtendetur idem quadratum EK æquale rectangulo QR 8, quare rectangu-
la ADC, QR 8 inter ſe ſunt æqualia, ideoque R 8 ad DC, vt DA ad QR,
ſed eſt R 8 maior DC (cum ſit RS maior DN, & S 8 maior NC) ergo AD
erit maior QR, & hoc ſemper, & c. Quod iterum erat ſecundò 7732. h.dum.
Dico tandem has ſimiles concentricas Hyperbolas in infinitum produ-
ctas ad interuallum peruenire minus quolibet dato interuallo R. Nam facta
eadem penitus conſtructione, ac in vltima parte 42. huius, hoc quod expo-
nitur, non abſimili eiuſdem argumento demonſtrabitur. Quod vltimò, & c.
COROLL. I.
EX hac elicitur ſimilium, & concentricarum Hyperbolarum, per diuer-
ſos vertices ſimul adſcriptarum, Aſymptotos communes eſſe.
COROLL. II.
COnſtat etiam ex penultima parte huius, in prædictis Hyperbolis rectan-
gula ſegmentorum applicatarum vtranque Hyperbolen ſecantium,
qualia ſunt rectangula ADC, QR8, omnia inter ſe æqualia eſſe.
Quod in prima parte præcedentium 44. 45. 47. earumque primis Co-
rollarijs oſtendimus, vniuerſaliùs ſequenti Theoremate demonſtrabitur.

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