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

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[61.] III.
Page: 57 (37)
[62.] IV.
Page: 57 (37)
[63.] V.
Page: 57 (37)
[64.] VI.
Page: 57 (37)
[65.] VII.
Page: 57 (37)
[66.] VIII.
Page: 58 (38)
[67.] IX.
Page: 58 (38)
[68.] THEOR. XI. PROP. XIX.
Page: 58 (38)
[69.] COROLL. I.
Page: 64 (40)
[70.] COROLL. II.
Page: 64 (40)
[71.] COROLL. III.
Page: 64 (40)
[72.] COROLL. IV.
Page: 65 (41)
[73.] COROLL. V.
Page: 65 (41)
[74.] COROLL. VI.
Page: 65 (41)
[75.] PROBL. VI. PROP. XX.
Page: 66 (42)
[76.] COROLL. I.
Page: 67 (43)
[77.] COROLL. II.
Page: 68 (44)
[78.] PROBL. VII. PROP. XXI.
Page: 68 (44)
[79.] MONITVM.
Page: 69 (45)
[80.] THEOR. XII. PROP. XXII.
Page: 70 (46)
[81.] PROBL. VIII. PROP. XXIII.
Page: 71 (47)
[82.] PROBL. IX. PROP. XXIV.
Page: 73 (49)
[83.] PROBL. X. PROP. XXV.
Page: 74 (50)
[84.] PROBL. XI. PROP. XXVI.
Page: 75 (51)
[85.] SCHOLIVM I.
Page: 76 (52)
[86.] SCHOLIVM II.
Page: 76 (52)
[87.] PROBL. XII. PROP. XXVII.
Page: 77 (53)
[88.] PROBL. XIII. PROP. XXVIII.
Page: 78 (54)
[89.] PROBL. XIV. PROP. XXIX.
Page: 80 (56)
[90.] PROBL. XV. PROP. XXX.
Page: 81 (57)
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6844
COROLL. II.
PAtet etiam quomodo datæ coni-ſectioni, vel circulo ABC per ipſius
verticem inſcribi poſſit Ellipſis, que ſit _MAXIMA_ circa idem tranſuer-
ſum, & ipſius rectum latus ad verſum in Parabola, vel Hyperbola datam
quamcumque teneat rationem; & in Ellipſi, vel circulo data ratio non ſit
minor ratione recti BE, ad tranſuerſum BD.
Nam ſi exempli gratia Parabolæ, vel Hyperbolæ primæ, ac ſecundæ figu-
ræ inſcribenda ſit _MAXIMA_ Ellipſis circa idem tranſuerſum latus, & cuius
rectum ad verſum datam habeat rationem, R nempe ad S: fiat vt R ad S, ita
rectum EB datæ ſectionis ad BG, nam ſi cum eodem recto EB, ac tranſuerſo
BG adſcribatur per B Ellipſis GHB, ipſa erit _MAXIMA_ circa idem tranſ-
uerſum BG, per ea, quæ ſuperius demonſtrata fuerunt. Siverò data ratio R
ad S non ſit minor ratione recti EB ad tranſuerſum BD; in tertia, quarta, &
quinta figura, fiat vt R ad S, ita EB ad BG, quod erit tranſuerſum quæſitæ
inſcriptæ Ellipſis, quæ erit _MAXIMA_, & c.
PROBL. VII. PROP. XXI.
Datæ Hyperbolæ, per eius verticem MAXIMAM Parabolen
inſcribere, & è contra.
Per verticem datæ Parabolæ, cum dato tranſuerſo latere MINI-
MAM Hyperbolen circumſcribere.
SIt data Hyperbole ABC, cuius vertex B, diameter BD, tranſuerſum la-
tus BE, rectum BF, & regula EFO oportet primùm per eius verticem B
_MAXIMAM_ Parabolen inſcribere.
Adſcribatur Hyperbolæ 115. prop.
huius.39[Figure 39] per verticem B, & cum recto BF Pa-
rabole GBH. Dico hanc eſſe _MAXI_-
_MAM_ quæſitam.
Ducta enim ex F Parabolæ regula
FI, cum hæc infra contingentem BF,
regulę EFO, nunquam occurat, (cum
ſimul conueniãt in F) ſitque regula FI
propinquior diametro BD quam pro-
ducta regula FO, erit Parabole 223. Co-
roll. prop.
19. huius. datę Hyperbolę ABC inſcripta, eritq;
_MAXIMA_: quoniam quælibet alia
Parabole ipſi ABC per verticem B
adſcripta cum recto BL, quod minus
ſit recto BF datę Hyperbolæ, 332. Co-
roll. prop.
19. huius. eſt Parabola GBH, quælibet verò ad-
ſcripta cum recto BM, quod excedat
rectum BF datę Hyperbolæ ipſa

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