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

Table of contents

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[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)
[91.] PROBL. XVI. PROP. XXXI.
Page: 83 (59)
[92.] THEOR. XIII. PROP. XXXII.
Page: 84 (60)
[93.] THEOR. IV. PROP. XXXIII.
Page: 85 (61)
[94.] MONITVM.
Page: 85 (61)
[95.] THEOR. XV. PROP. XXXIV.
Page: 87 (63)
[96.] THEOR. XVI. PROP. XXXV.
Page: 88 (64)
[97.] THEOR. XVII. PROP. XXXVI.
Page: 88 (64)
[98.] COROLL.
Page: 89 (65)
[99.] THEOR. XIII. PROP. XXXVII.
Page: 90 (66)
[100.] THEOR. XIX. PROP. XXXVIII.
Page: 91 (67)
[101.] LEMMA IV. PROP. XXXIX.
Page: 92 (68)
[102.] THEOR. XX. PROP. XXXX.
Page: 92 (68)
[103.] COROLL.
Page: 93 (69)
[104.] THEOR. XXI. PROP. XXXXI.
Page: 94 (70)
[105.] COROLL.
Page: 95 (71)
[106.] THEOR. XXII. PROP. XXXXII.
Page: 95 (71)
[107.] ALITER.
Page: 97 (73)
[108.] COROLL. I.
Page: 98 (74)
[109.] COROLL. II.
Page: 98 (74)
[110.] LEMMA V. PROP. XXXXIII.
Page: 99 (75)
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page |< < (149) of 347 > >|
173149 punctis G, H, in Ellipſis peripheria vbi-
139[Figure 139] cunque inter ſemi-axes aſſumptis, ſint
contingentibus perpẽdiculares GI, HL.
Conſtat, ſi cum centris E, L, I, F, inter-
uallis verò EA, LH, IG, FB, circuli de-
ſcribantur, ipſos Ellipſi ABCD inſcri-
ptos eſſe, ac _MAXIMOS_ ad 1126. 92. h.
1. Coroll.
20. h. A, H, G, B inſcriptibilium. Dico iam
inter hos _MAXIMOS, MAXIMV M_
eſſe qui ad A, _MINIMVM_ verò, qui
ad B inſcribitur. Aliorum autem inſcri-
ptum ad punctum H, quod à vertice
B maioris axis magis remouetur, maio-
rem eſſe inſcripto ad punctum G, quod
ipſi vertici propius eſt.
Etenim quelibet perpendicularis LH,
IG inter ſemi-axes, minor eſt ſemi- axe maiori EA, ſed maior ſemper 2291. h. mi- recto F B: vnde circulus ex E A erit _MAXIMVS_, & ex F B _MINI-_
_MVS_ inſcriptibilium: ſed L H maior eſt I G: quapropter circulus 3394. h. L A, erit maior circulo ex I G, Quod probandum erat.
THEOR. LI. PROP. C.
MINIMORVM circulorum ad puncta Ellipticæ periphe-
riæ circumſcriptorum, MINIMVS eſt, qui ad verticem maio-
ris axis circumſcribitur. MAXIMVS verò qui ad verticem
minoris. Aliorum autem is, cuius contactus à vertice minoris
axis magis diſtat, minor eſt.
ESto Ellipſis ABCD, cuius axis maior A C, minor B D, centrum E,
& ſumpta ſit BF æqualis dimidio recti, cuius tranſuerſum latus eſt
BD, & ex punctis G, H, vbi-
cunque in Ellipſis peripheria
140[Figure 140] inter ſemi- axes aſſumptis, ſint
contingentibus perpendicula-
res GI, H L. Conſtat iam, ſi
ex centris E, L, I, F, cum in-
teruallis EA, LH, I G, F B de-
ſcribantur circuli, ipſos Ellipſi
ABCD circumſcriptos eſſe, &
_MINIMOS_ ad puncta A, 4426. 92. h.
1. Coroll.
20. h. G, B, circumſcriptibilium. Di-
co tamen inter hos _MINI-_
_MOS, MINIMVM_ eſſe, qui
ad A; _MAXIMVM_, quiad

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