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
Table of Notes
<
1 - 14
[out of range]
>
[Note]
Page: 55
[Note]
Page: 55
[Note]
Page: 55
[Note]
Page: 56
[Note]
Page: 58
[Note]
Page: 58
[Note]
Page: 58
[Note]
Page: 58
[Note]
Page: 63
[Note]
Page: 63
[Note]
Page: 63
[Note]
Page: 66
[Note]
Page: 66
[Note]
Page: 66
[Note]
Page: 66
[Note]
Page: 67
[Note]
Page: 67
[Note]
Page: 67
[Note]
Page: 67
[Note]
Page: 67
[Note]
Page: 67
[Note]
Page: 68
[Note]
Page: 68
[Note]
Page: 68
[Note]
Page: 69
[Note]
Page: 69
[Note]
Page: 69
[Note]
Page: 69
[Note]
Page: 69
[Note]
Page: 69
<
1 - 14
[out of range]
>
page
|<
<
(63)
of 347
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div201
"
type
="
section
"
level
="
1
"
n
="
94
">
<
pb
o
="
63
"
file
="
0087
"
n
="
87
"
rhead
="
"/>
</
div
>
<
div
xml:id
="
echoid-div202
"
type
="
section
"
level
="
1
"
n
="
95
">
<
head
xml:id
="
echoid-head100
"
xml:space
="
preserve
">THEOR. XV. PROP. XXXIV.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2210
"
xml:space
="
preserve
">Si à puncto, quod eſt in Hyperbola ducatur recta linea alteri
<
lb
/>
aſymptoton æquidiſtans, ipſa, ac ſectio, quæ inter has parallelas
<
lb
/>
intercipitur, in infinitum productę ſunt infra occurſum ſemper ma-
<
lb
/>
gis recedentes, ſed tamen nunquam perueniunt ad interuallum
<
lb
/>
æquale cuidam dato interuallo; </
s
>
<
s
xml:id
="
echoid-s2211
"
xml:space
="
preserve
">dum earum diſtantia metiatur per
<
lb
/>
interceptas æquidiſtantes cuilibet rectæ, quæ ducta ſit ex occurſu
<
lb
/>
vtramque aſymptoton ſecans.</
s
>
<
s
xml:id
="
echoid-s2212
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2213
"
xml:space
="
preserve
">SIt Hyperbole ABC, cuius aſymptoti ED, EF, ſitque ex quolibet ſectio-
<
lb
/>
nis puncto B recta BGN alteri aſymptoto ED æquidiſtans, quæ intra
<
lb
/>
lectionẽ cadens, in nullo alio pũcto quam
<
lb
/>
<
figure
xlink:label
="
fig-0087-01
"
xlink:href
="
fig-0087-01a
"
number
="
57
">
<
image
file
="
0087-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0087-01
"/>
</
figure
>
B cum ipſa conueniet. </
s
>
<
s
xml:id
="
echoid-s2214
"
xml:space
="
preserve
">Dico primùm (ſi
<
note
symbol
="
a
"
position
="
right
"
xlink:label
="
note-0087-01
"
xlink:href
="
note-0087-01a
"
xml:space
="
preserve
">Coroll.
<
lb
/>
11. huius.</
note
>
B ducatur quæcunque HBF vtranq; </
s
>
<
s
xml:id
="
echoid-s2215
"
xml:space
="
preserve
">aſym-
<
lb
/>
ptoton ſecans) ipſam, & </
s
>
<
s
xml:id
="
echoid-s2216
"
xml:space
="
preserve
">ſectionem IAM
<
lb
/>
infra BI eſſe sẽper magis inter ſerecedẽtes.</
s
>
<
s
xml:id
="
echoid-s2217
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2218
"
xml:space
="
preserve
">Applicentur quotcunque DAG, LMN
<
lb
/>
infra HB, ipſi æquidiſtantes: </
s
>
<
s
xml:id
="
echoid-s2219
"
xml:space
="
preserve
">patet has om-
<
lb
/>
nes LN, DG, HB inter ſe æquales eſſe, ſed
<
lb
/>
eſt DA minor HI, ergo AG maior
<
note
symbol
="
b
"
position
="
right
"
xlink:label
="
note-0087-02
"
xlink:href
="
note-0087-02a
"
xml:space
="
preserve
">10. h.</
note
>
IB, eſtque LM minor DA, quare & </
s
>
<
s
xml:id
="
echoid-s2220
"
xml:space
="
preserve
">MN
<
lb
/>
maior AG, & </
s
>
<
s
xml:id
="
echoid-s2221
"
xml:space
="
preserve
">hoc ſemper ſi in infinitum
<
lb
/>
producantur; </
s
>
<
s
xml:id
="
echoid-s2222
"
xml:space
="
preserve
">ergo linea BGN, & </
s
>
<
s
xml:id
="
echoid-s2223
"
xml:space
="
preserve
">ſectio
<
lb
/>
IAM ſunt ſemper ſimul recedentes. </
s
>
<
s
xml:id
="
echoid-s2224
"
xml:space
="
preserve
">Quod
<
lb
/>
primò, &</
s
>
<
s
xml:id
="
echoid-s2225
"
xml:space
="
preserve
">c.</
s
>
<
s
xml:id
="
echoid-s2226
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2227
"
xml:space
="
preserve
">Et quoniam earum interuallum, per eaſ-
<
lb
/>
dem interceptas metitum, ſemper minus
<
lb
/>
eſt HB interuallo parallelarum BN, HL,
<
lb
/>
cum ſit GA minos GD, NM minos NL, & </
s
>
<
s
xml:id
="
echoid-s2228
"
xml:space
="
preserve
">
<
lb
/>
omnes GD, NL, &</
s
>
<
s
xml:id
="
echoid-s2229
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s2230
"
xml:space
="
preserve
">ipſi BH equales: </
s
>
<
s
xml:id
="
echoid-s2231
"
xml:space
="
preserve
">qua-
<
lb
/>
propter, licet huiuſmodi lineæ ſint ſemper magis recedentes, non tamen
<
lb
/>
perueniunt ad interuallum æquale interuallo BH. </
s
>
<
s
xml:id
="
echoid-s2232
"
xml:space
="
preserve
">Quod erat tandem, &</
s
>
<
s
xml:id
="
echoid-s2233
"
xml:space
="
preserve
">c.</
s
>
<
s
xml:id
="
echoid-s2234
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>