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 |< < (104) of 347 > >|
128104 cum quadrato intermediæ partis DC; rectangulum ergo ACB ſuperat re-
ctangulum ADB; & hoc ſemper; ergo rectangulum ACB, ſub æqualibus
partibus compræhenſum, eſt _MAXIMV M._ Quod primo, & c.
Item, quadrato dimidiæ A C æquatur
93[Figure 93] rectangulum A D B, vna cum quadrato
DC, & eidem quadrato AC æquatur re-
ctangulum AED vna cum quadrato EC,
ergo rectangulum A D C cum quadrato
DC, æquale erit rectangulo AEB, cum
quadrato EC, eſt autem quadratum DC
minus quadrato EC, cum ſit linea DC mi-
nor EC, ex hypoteſi; ergo rectangulum
ADC maius erit rectangulo AEB. Quod ſecundò, & c.
THEOR. XXXII. PROP. LXI.
Si fuerint duæ quæcunque coni-ſectiones, non excepto circulo,
eiuſdem, vel diuerſi nominis per diuerſos vertices ſimul adſcriptæ,
quæ in eiuſdem communis ordinatim ductæ extremis punctis ſimul
conueniant, è quorum altero eadem recta linea vtranque ſectionem
contingat, ea coni-ſectio cuius vertex cadit infra verticem alterius
erit alteri inſcripta, & in ijſdem tantùm applicatæ extremis ſe con-
tingent.
SInt duæ quælibet coni-ſectiones ABC, ADC non excepto circulo, eiuſ-
dem, vel diuerſi nominis per diuerſos vertices B, D ſimul adſcriptæ,
94[Figure 94] quarum communis diameter ſit BH, communiſq; applicata ſit AC, in cuius
extremis A, C, ſectiones ſimul occurrant, & ex eorum altero veluti ex

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