Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
List of thumbnails
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 347
>
61
62
63
(39)
64
(40)
65
(41)
66
(42)
67
(43)
68
(44)
69
(45)
70
(46)
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 347
>
page
|<
<
(44)
of 347
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div129
"
type
="
section
"
level
="
1
"
n
="
76
">
<
pb
o
="
44
"
file
="
0068
"
n
="
68
"
rhead
="
"/>
</
div
>
<
div
xml:id
="
echoid-div131
"
type
="
section
"
level
="
1
"
n
="
77
">
<
head
xml:id
="
echoid-head82
"
xml:space
="
preserve
">COROLL. II.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1548
"
xml:space
="
preserve
">PAtet etiam quomodo datæ coni-ſectioni, vel circulo ABC per ipſius
<
lb
/>
verticem inſcribi poſſit Ellipſis, que ſit _MAXIMA_ circa idem tranſuer-
<
lb
/>
ſum, & </
s
>
<
s
xml:id
="
echoid-s1549
"
xml:space
="
preserve
">ipſius rectum latus ad verſum in Parabola, vel Hyperbola datam
<
lb
/>
quamcumque teneat rationem; </
s
>
<
s
xml:id
="
echoid-s1550
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1551
"
xml:space
="
preserve
">in Ellipſi, vel circulo data ratio non ſit
<
lb
/>
minor ratione recti BE, ad tranſuerſum BD.</
s
>
<
s
xml:id
="
echoid-s1552
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1553
"
xml:space
="
preserve
">Nam ſi exempli gratia Parabolæ, vel Hyperbolæ primæ, ac ſecundæ figu-
<
lb
/>
ræ inſcribenda ſit _MAXIMA_ Ellipſis circa idem tranſuerſum latus, & </
s
>
<
s
xml:id
="
echoid-s1554
"
xml:space
="
preserve
">cuius
<
lb
/>
rectum ad verſum datam habeat rationem, R nempe ad S: </
s
>
<
s
xml:id
="
echoid-s1555
"
xml:space
="
preserve
">fiat vt R ad S, ita
<
lb
/>
rectum EB datæ ſectionis ad BG, nam ſi cum eodem recto EB, ac tranſuerſo
<
lb
/>
BG adſcribatur per B Ellipſis GHB, ipſa erit _MAXIMA_ circa idem tranſ-
<
lb
/>
uerſum BG, per ea, quæ ſuperius demonſtrata fuerunt. </
s
>
<
s
xml:id
="
echoid-s1556
"
xml:space
="
preserve
">Siverò data ratio R
<
lb
/>
ad S non ſit minor ratione recti EB ad tranſuerſum BD; </
s
>
<
s
xml:id
="
echoid-s1557
"
xml:space
="
preserve
">in tertia, quarta, & </
s
>
<
s
xml:id
="
echoid-s1558
"
xml:space
="
preserve
">
<
lb
/>
quinta figura, fiat vt R ad S, ita EB ad BG, quod erit tranſuerſum quæſitæ
<
lb
/>
inſcriptæ Ellipſis, quæ erit _MAXIMA_, &</
s
>
<
s
xml:id
="
echoid-s1559
"
xml:space
="
preserve
">c.</
s
>
<
s
xml:id
="
echoid-s1560
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div132
"
type
="
section
"
level
="
1
"
n
="
78
">
<
head
xml:id
="
echoid-head83
"
xml:space
="
preserve
">PROBL. VII. PROP. XXI.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1561
"
xml:space
="
preserve
">Datæ Hyperbolæ, per eius verticem MAXIMAM Parabolen
<
lb
/>
inſcribere, & </
s
>
<
s
xml:id
="
echoid-s1562
"
xml:space
="
preserve
">è contra.</
s
>
<
s
xml:id
="
echoid-s1563
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1564
"
xml:space
="
preserve
">Per verticem datæ Parabolæ, cum dato tranſuerſo latere MINI-
<
lb
/>
MAM Hyperbolen circumſcribere.</
s
>
<
s
xml:id
="
echoid-s1565
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1566
"
xml:space
="
preserve
">SIt data Hyperbole ABC, cuius vertex B, diameter BD, tranſuerſum la-
<
lb
/>
tus BE, rectum BF, & </
s
>
<
s
xml:id
="
echoid-s1567
"
xml:space
="
preserve
">regula EFO oportet primùm per eius verticem B
<
lb
/>
_MAXIMAM_ Parabolen inſcribere.</
s
>
<
s
xml:id
="
echoid-s1568
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1569
"
xml:space
="
preserve
">Adſcribatur Hyperbolæ
<
note
symbol
="
a
"
position
="
left
"
xlink:label
="
note-0068-01
"
xlink:href
="
note-0068-01a
"
xml:space
="
preserve
">5. prop.
<
lb
/>
huius.</
note
>
<
figure
xlink:label
="
fig-0068-01
"
xlink:href
="
fig-0068-01a
"
number
="
39
">
<
image
file
="
0068-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0068-01
"/>
</
figure
>
per verticem B, & </
s
>
<
s
xml:id
="
echoid-s1570
"
xml:space
="
preserve
">cum recto BF Pa-
<
lb
/>
rabole GBH. </
s
>
<
s
xml:id
="
echoid-s1571
"
xml:space
="
preserve
">Dico hanc eſſe _MAXI_-
<
lb
/>
_MAM_ quæſitam.</
s
>
<
s
xml:id
="
echoid-s1572
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1573
"
xml:space
="
preserve
">Ducta enim ex F Parabolæ regula
<
lb
/>
FI, cum hæc infra contingentem BF,
<
lb
/>
regulę EFO, nunquam occurat, (cum
<
lb
/>
ſimul conueniãt in F) ſitque regula FI
<
lb
/>
propinquior diametro BD quam pro-
<
lb
/>
ducta regula FO, erit Parabole
<
note
symbol
="
b
"
position
="
left
"
xlink:label
="
note-0068-02
"
xlink:href
="
note-0068-02a
"
xml:space
="
preserve
">3. Co-
<
lb
/>
roll. prop.
<
lb
/>
19. huius.</
note
>
datę Hyperbolę ABC inſcripta, eritq;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1574
"
xml:space
="
preserve
">_MAXIMA_: </
s
>
<
s
xml:id
="
echoid-s1575
"
xml:space
="
preserve
">quoniam quælibet alia
<
lb
/>
Parabole ipſi ABC per verticem B
<
lb
/>
adſcripta cum recto BL, quod minus
<
lb
/>
ſit recto BF datę Hyperbolæ,
<
note
symbol
="
c
"
position
="
left
"
xlink:label
="
note-0068-03
"
xlink:href
="
note-0068-03a
"
xml:space
="
preserve
">2. Co-
<
lb
/>
roll. prop.
<
lb
/>
19. huius.</
note
>
eſt Parabola GBH, quælibet verò ad-
<
lb
/>
ſcripta cum recto BM, quod excedat
<
lb
/>
rectum BF datę Hyperbolæ ipſa </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>