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

Scan	Original
91	67
92	68
93	69
94	70
95	71
96	72
97	73
98	74
99	75
100	76
101	77
102	78
103	79
104	80
105	81
106	82
107	83
108	84
109	85
110	86
111	87
112	88
113	89
114	90
115	91
116	92
117	93
118	94
119	95
120	96

11894 nor ſit ſemi-tranſuerſo DB: (ſi enim datum punctum eſſet in angulis, qui
deinceps ſunt, recta linea per ipſum datum punctum, & centrum ſectionis
ducta non eſſet eius diameter, cum nunquam ſectioni occurreret, ac 11Monit.
poſt 11. h. problema, iuxta quintam ſecundarum definitionum inſolubile eſſet: & cum
fuerit in angulo ad verticem, vt in ſecunda, niſi diſtantia ED minor ſit ſemi-
tranſuerſo DB, Hyperbole ad regulam datæ adſcribi minimè poſſet, vt ſatis
patet) oportet per E _MINIMAM_ Hyperbolen circumſcribere, cuius regula
eadem ſit cum regula datæ ſectionis.

Iungatur ED, & ad partes ſectionis producatur donec ei occurrat in B,
ſumptaq; in directum DH æquali DB, erit HB tranſuerſum ſectionis 2247. pri-
mi conic. cuius vertex B: ſit ergo BI eius rectum latus, & regula HI; ſitque EK æqui-
diſtans BI, & per verticem B, cum tranſuerſo EH, & recto EK, ſiue ad ean-
dem regulam HI adſcribatur Hyperbole LEM: patet ipſam datæ ABC eſſe
inſcriptam, cum ſimul ſint nun quam coeuntes.

3345. h.

83[Figure 83]

Dico ampliùs ipſam LEM eſſe _MINIMAM_ quæſitam. Quoniam quęlibet
alia adſcripta per verticem E, cum eodem verſo HE, ſed cum recto, quod
excedat EK, maior eſt ipſa LEM; quæ verò cum recto EN, quod minus 442. Co-
roll. 19. h. EK, qualis OEQ, eſt quidem minor eadem LEM, ſed omnino ſecat 55ibidem. ABC. Nam ad productam regulam HN, ſecan@ BI in R adſcribatur per B
Hyperbole SBT; hæc tota cadet intra ABC, eruntque SBT, OEQ duæ 66ibidem. miles Hyperbolæ per diuerſos vertices adſcriptæ ad eandem regulam HR,
eſtque ABC ipſi SBT, per eundem verticem, & cum maiori recto latere BI
adſcripta, quare per præce dentem ſectiones ABC, OEQ ſe mutuò 7752. h. bunt: Vnde Hyperbole LEM eſt _MINIMA_ circumſcripta quæſita. Quod
faciendum, & demonſtrandum erat.

ALITER.

SEcetur EH bifariam in X: erit X centrum vtriuſque LEM, OEQ: ſi ergo
ex centris X, D, ducantur XY, XZ, DF ſectionum LEM, OEQ, ABC
aſymptoti, hoc eſt XY circumſcriptæ LEM; XZ inſcriptæ OEQ, quæ infra
XY cadet; & DF ſectionis ABC, quæ ipſi XY æquidiſtabit; cum XZ 88Ex vlti-
ma partre
37. huius.1111[Handwritten note 11]

Page concordance

Text layer

Text normalization

Search

Scan	Original
91	67
92	68
93	69
94	70
95	71
96	72
97	73
98	74
99	75
100	76
101	77
102	78
103	79
104	80
105	81
106	82
107	83
108	84
109	85
110	86
111	87
112	88
113	89
114	90
115	91
116	92
117	93
118	94
119	95
120	96

Scan	Original
91	67
92	68
93	69
94	70
95	71
96	72
97	73
98	74
99	75
100	76
101	77
102	78
103	79
104	80
105	81
106	82
107	83
108	84
109	85
110	86
111	87
112	88
113	89
114	90
115	91
116	92
117	93
118	94
119	95
120	96

Scan	Original
91	67
92	68
93	69
94	70
95	71
96	72
97	73
98	74
99	75
100	76
101	77
102	78
103	79
104	80
105	81
106	82
107	83
108	84
109	85
110	86
111	87
112	88
113	89
114	90
115	91
116	92
117	93
118	94
119	95
120	96