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
page
|<
<
(97)
of 347
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div307
"
type
="
section
"
level
="
1
"
n
="
134
">
<
pb
o
="
97
"
file
="
0121
"
n
="
121
"
rhead
="
"/>
</
div
>
<
div
xml:id
="
echoid-div311
"
type
="
section
"
level
="
1
"
n
="
135
">
<
head
xml:id
="
echoid-head140
"
xml:space
="
preserve
">PROBL. XXI. PROP. LV.</
head
>
<
p
>
<
s
xml:id
="
echoid-s3268
"
xml:space
="
preserve
">Datæ Hyperbolæ, per punctum intra ipſam datum, cum dato
<
lb
/>
ſemi-tranſuerſo latere, quodtamen non excedat diſtantiam inter
<
lb
/>
datum punctum, & </
s
>
<
s
xml:id
="
echoid-s3269
"
xml:space
="
preserve
">datæ ſectionis centrum, MAXIMAM Hyper-
<
lb
/>
bolen inſcribere: </
s
>
<
s
xml:id
="
echoid-s3270
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3271
"
xml:space
="
preserve
">è contra.</
s
>
<
s
xml:id
="
echoid-s3272
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3273
"
xml:space
="
preserve
">Datæ Hyperbolæ, per punctum extra ipſam datum, cum dato
<
lb
/>
ſemi-tranſuerſo latere MINIMAM Hyperbolen circumſcribere.</
s
>
<
s
xml:id
="
echoid-s3274
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3275
"
xml:space
="
preserve
">Oportet autem datum punctum, vel eſſe in angulo aſymptotali,
<
lb
/>
vel in eo, qui eſt ad verticem; </
s
>
<
s
xml:id
="
echoid-s3276
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3277
"
xml:space
="
preserve
">ſi in primò caſu, neceſſe eſt, vt ſe-
<
lb
/>
mi-tranſuerſum excedat interuallum inter datum punctum, & </
s
>
<
s
xml:id
="
echoid-s3278
"
xml:space
="
preserve
">cen-
<
lb
/>
trum datæ ſectionis: </
s
>
<
s
xml:id
="
echoid-s3279
"
xml:space
="
preserve
">in ſecundò verò ſit cuiuslibet longitudinis.</
s
>
<
s
xml:id
="
echoid-s3280
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3281
"
xml:space
="
preserve
">ESto Hyperbole ABC, cuius centrum D, & </
s
>
<
s
xml:id
="
echoid-s3282
"
xml:space
="
preserve
">datum intra ipſam punctum
<
lb
/>
ſit E: </
s
>
<
s
xml:id
="
echoid-s3283
"
xml:space
="
preserve
">oporret primò per E, cum dato ſemi-tranſuerſo EF (quod ſit mi-
<
lb
/>
nus interuallo ED) _MAXIMAM_ Hyperbolen inſcribere.</
s
>
<
s
xml:id
="
echoid-s3284
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3285
"
xml:space
="
preserve
">Iungatur E D
<
lb
/>
<
figure
xlink:label
="
fig-0121-01
"
xlink:href
="
fig-0121-01a
"
number
="
86
">
<
image
file
="
0121-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0121-01
"/>
</
figure
>
ſecans ABC in B,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s3286
"
xml:space
="
preserve
">ex ipſa ED de-
<
lb
/>
matur EF æ qualis
<
lb
/>
dato ſemi- tranſ-
<
lb
/>
uerſo, & </
s
>
<
s
xml:id
="
echoid-s3287
"
xml:space
="
preserve
">per ver-
<
lb
/>
ticem E, cum cẽ-
<
lb
/>
tro F adſeribatur
<
lb
/>
ſectioni A B
<
note
symbol
="
a
"
position
="
right
"
xlink:label
="
note-0121-01
"
xlink:href
="
note-0121-01a
"
xml:space
="
preserve
">6. huius.</
note
>
Hyperbole EG ſi-
<
lb
/>
milis datæ ABC;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3288
"
xml:space
="
preserve
">quæ (cum habeat
<
lb
/>
centrum F, velin
<
lb
/>
ipſo D, ſinempe datum ſemi-tran ſuerſum EF æquale fuerit iunctæ ED, vel
<
lb
/>
infra idem centrum D, ſi datum fuerit ipſa ED minus) erit datæ
<
note
symbol
="
b
"
position
="
right
"
xlink:label
="
note-0121-02
"
xlink:href
="
note-0121-02a
"
xml:space
="
preserve
">48. h.</
note
>
læ ABC inſcripta. </
s
>
<
s
xml:id
="
echoid-s3289
"
xml:space
="
preserve
">Dico hanc eſſe _MAXIMAM_ quæſitam.</
s
>
<
s
xml:id
="
echoid-s3290
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3291
"
xml:space
="
preserve
">Quoniam quælibet alia per verticem E, cum eodem tranſuerſo EF adſcri-
<
lb
/>
pta, ſed cum recto, quod ſit minus recto ſectionis EG, ipſa EG minor eſt;</
s
>
<
s
xml:id
="
echoid-s3292
"
xml:space
="
preserve
">
<
note
symbol
="
c
"
position
="
right
"
xlink:label
="
note-0121-03
"
xlink:href
="
note-0121-03a
"
xml:space
="
preserve
">2. Co-
<
lb
/>
roll. 19. h.</
note
>
quæ verò cum recto, quod ipſum excedat qualis eſt EL eſt quidem
<
note
symbol
="
d
"
position
="
right
"
xlink:label
="
note-0121-04
"
xlink:href
="
note-0121-04a
"
xml:space
="
preserve
">ibidem.</
note
>
eadem EG, ſed omnino ſecat circumſcriptam ABC. </
s
>
<
s
xml:id
="
echoid-s3293
"
xml:space
="
preserve
">Nam ducta FI aſym-
<
lb
/>
ptoto ſectionis EG, & </
s
>
<
s
xml:id
="
echoid-s3294
"
xml:space
="
preserve
">FM ſectionis EL, (quæ FM cadet extra E I, vt patet
<
lb
/>
ex vltima parte 37. </
s
>
<
s
xml:id
="
echoid-s3295
"
xml:space
="
preserve
">huius) ac DH ſectionis ABC: </
s
>
<
s
xml:id
="
echoid-s3296
"
xml:space
="
preserve
">erunt DH, FI inter ſe
<
note
symbol
="
e
"
position
="
right
"
xlink:label
="
note-0121-05
"
xlink:href
="
note-0121-05a
"
xml:space
="
preserve
">48. h.</
note
>
rallelę, ſed FM aſymptotos EL producta ſecatur à DH, cum ſecetur quoque
<
lb
/>
ab altera parallelarum in F, quare ipſa DH ſecabit Hyperbolen EL; </
s
>
<
s
xml:id
="
echoid-s3297
"
xml:space
="
preserve
">
<
note
symbol
="
f
"
position
="
right
"
xlink:label
="
note-0121-06
"
xlink:href
="
note-0121-06a
"
xml:space
="
preserve
">35. h.</
note
>
DH tota cadit extra ABC, cum ſit eius aſymptotos, ideò occurſus rectę DH
<
lb
/>
cum ſectione EL, erit extra ipſam ABC, vnde EL neceſſariò ſecabit priùs
<
lb
/>
circumſcriptam ABC. </
s
>
<
s
xml:id
="
echoid-s3298
"
xml:space
="
preserve
">Erit ergo EG _MAXIMA_ inſcripta quæſita, cum da-
<
lb
/>
to ſemi tranſuerſo EF. </
s
>
<
s
xml:id
="
echoid-s3299
"
xml:space
="
preserve
">Quod primò erat, &</
s
>
<
s
xml:id
="
echoid-s3300
"
xml:space
="
preserve
">c.</
s
>
<
s
xml:id
="
echoid-s3301
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>