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

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[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)
[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)
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4424 ſtans. Dico ipſam cum ſectione conuenire, eamque omnino ſecare.
Iungatur CS, quæ producta ſectioni occurret, per ſecundam partem 8.
huius, eritque ſectionis diameter: quare per Coroll. 2. præcedentis, ipſa STX
ſectioni occurret, vt in X.
Præterea, cum quæcunque contingenti æquidiſtans GI ſupra RX, inter
aſymptoton, & ſectionem intercepta, maior ſit ipſa RX, ſiue ipſa GZ, pun-
ctum Z cadet extra ſectionem, & ſic de quolibet alio puncto rectæ XTS. E
contra cum quælibet intercepta LY infra RX, parallela ad DB, minor ſit ip-
ſa RX, ſiue LF, punctum F cadet intra ſectionem, idemque de quolibet alio
puncto rectæ XF: vnde recta STX ab ipſo occurſu X cum ſectione, ad partes
verticis tota cadit extra, ad oppoſitas verò partes tota cadit intra ſectionem;
ideoque in vno tantum puncto X Hyperbolen ſecat. Quod erat propoſitum.
19[Figure 19]
COROLL.
HInc eſt, lineam alteri aſymptoton æquidiſtantem per punctum, quod
ſit, vel in ipſa ſectione, vel intra, pariter in vno tantùm puncto ſe-
ctioni occurrere, eamque ſecare.
Nam recta XS ex puncto X, quod cſt in Hyperbola, vel recta FS ex pun-
cto F, quod eſt intra, æquidiſtanter ducta aſymptoto CD, ſi ad partes cen-
tri C producatur, alteri aſymptoto CE omnino occurrit, (quoniam EC, ſe-
cans DC vnam parallelarum ſecat quoque alteram CE) vnde aliqua pars,
ipſius rectæ XS, vel FS cadit in loco ab aſymptotis, & ſectione terminato,
ac ideo ex his, quæ ſuperius oſtendimus, ipſa linea in vno tantùm puncto ſe-
ctioni occurret, ac Hyperbolen ſecabit.
Qua propter, quælibet linea alteri aſymptoton æquidiſtans, dummodo ſit
ducta ex puncto, quod ſit in angulo ab aſymptotis facto, in vno tantùm pun-
cto Hyperbolæ occurrit, atque eam ſecat.

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