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

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[151.] LEMMA VII. PROP. LXVI.
Page: 133 (109)
[152.] SCHOLIVM.
Page: 133 (109)
[153.] PROBL. XXV. PROP. LXVII.
Page: 134 (110)
[154.] MONITVM.
Page: 134 (110)
[155.] PROBL. XXVI. PROP. LXVIII.
Page: 135 (111)
[156.] PROBL. XXVII. PROP. LXIX.
Page: 137 (113)
[157.] PROBL. XXVIII. PROP. LXX.
Page: 138 (114)
[158.] LEMMA VIII. PROP. LXXI.
Page: 139 (115)
[159.] LEMMA IX. PROP. LXXII.
Page: 140 (116)
[160.] PROBL. XXIX. PROP. LXXIII.
Page: 141 (117)
[161.] LEMMA X. PROP. LXXIV.
Page: 141 (117)
[162.] PROBL. XXX. PROP. LXXV.
Page: 142 (118)
[163.] COROLL. I.
Page: 143 (119)
[164.] COROLL. II.
Page: 143 (119)
[165.] MONITVM.
Page: 143 (119)
[166.] THEOR. XXXVI. PROP. LXXVI.
Page: 144 (120)
[167.] SCHOLIVM.
Page: 145 (121)
[168.] THEOR. XXXVII. PROP. LXXVII.
Page: 146 (122)
[169.] PROBL. XXXI. PROP. LXXVIII.
Page: 147 (123)
[170.] MONITVM.
Page: 148 (124)
[171.] LEMMA XI. PROP. LXXIX.
Page: 148 (124)
[172.] LEMMA XII. PROP. LXXX.
Page: 149 (125)
[173.] THEOR. XXXVIII. PROP. LXXXI.
Page: 149 (125)
[174.] PROBL. XXXII. PROP. LXXXII.
Page: 150 (126)
[175.] COROLL.
Page: 152 (128)
[176.] THEOR. XXXIX. PROP. LXXXIII.
Page: 153 (129)
[177.] ALITER affirmatiuè.
Page: 153 (129)
[178.] PROBL. XXXIII. PROP. LXXXIV.
Page: 154 (130)
[179.] SCHOLIVM.
Page: 155 (131)
[180.] THEOR. XL. PROP. LXXXV.
Page: 155 (131)
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6642
PROBL. VI. PROP. XX.
Datæ coni ſectioni, vel circulo, per eius verticem, cum dato
tranſuerſo latere, quod in Ellipſi, vel circulo non excedat eius
tranſuerſum, MAXIMAM Ellipſim inſcribere, & è contra.
DAtæ Ellipſi, vel circulo, per eius verticem _MINIMAM_ coni-ſectionem
circumſcribere cum dato, pro circumſcribenda Hyperbola, quocunq;
tranſuerſo latere, pro Ellipſi verò, cum tranſuerſo dato, quod maius ſit tranſ-
uerſo datæ Ellipſis, vel circuli.
38[Figure 38]
Sit quælibet coni-ſectio, vel circulus ABC, cuius diameter BD, latus
rectum BE, regula EF; oportet circa diametri ſegmentum BG per verticem
B _MAXIMAM_ Ellipſin inſcribere.
Adſcribatur ſectioni ABC per eius verticem, & circa diametrum 117. huius. cum recto BE Ellipſis GHB. Dico hanc eſſe _MAXIMAM_ quæſitam.
Nam iuncta ipſius regula GE, cum hæc diſiunctim procedat à regula EF,
ſitque propior diametro, Ellipſis quoq; GHB inſcripta erit ſectioni 221. Co-
roll. prop.
19. huius.& erit _MAXIMA_ inſcriptibilium: quoniam quæcunque Ellipſis cum eadem
tranſuerſa diametro BG adſcripta, & cum recto BI, quod minus ſit recto BE
minor eſt Ellipſi GBH, quælibet verò Ellipſis eidem diametro BG 332. Co-
roll. prop.
19. huius. pta cum recto BL, quod maius ſit dato recto BE maior eſt quidem 442. Co-
roll. prop.
19. huius. GHB, ſed omnino _e_ ſecat ſectionem ABC, cum eius regula GL ſecet ſectio-
nis regulam EL, infra contingentem BE. Vnde Ellipſis GHB eſt _MAXIMA_.
Quod primò, & c.

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