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
|<
<
(94)
of 347
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div296
"
type
="
section
"
level
="
1
"
n
="
130
">
<
p
>
<
s
xml:id
="
echoid-s3160
"
xml:space
="
preserve
">
<
pb
o
="
94
"
file
="
0118
"
n
="
118
"
rhead
="
"/>
nor ſit ſemi-tranſuerſo DB: </
s
>
<
s
xml:id
="
echoid-s3161
"
xml:space
="
preserve
">(ſi enim datum punctum eſſet in angulis, qui
<
lb
/>
deinceps ſunt, recta linea per ipſum datum punctum, & </
s
>
<
s
xml:id
="
echoid-s3162
"
xml:space
="
preserve
">centrum ſectionis
<
lb
/>
ducta non eſſet eius diameter, cum nunquam ſectioni occurreret, ac
<
note
symbol
="
a
"
position
="
left
"
xlink:label
="
note-0118-01
"
xlink:href
="
note-0118-01a
"
xml:space
="
preserve
">Monit.
<
lb
/>
poſt 11. h.</
note
>
problema, iuxta quintam ſecundarum definitionum inſolubile eſſet: </
s
>
<
s
xml:id
="
echoid-s3163
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3164
"
xml:space
="
preserve
">cum
<
lb
/>
fuerit in angulo ad verticem, vt in ſecunda, niſi diſtantia ED minor ſit ſemi-
<
lb
/>
tranſuerſo DB, Hyperbole ad regulam datæ adſcribi minimè poſſet, vt ſatis
<
lb
/>
patet) oportet per E _MINIMAM_ Hyperbolen circumſcribere, cuius regula
<
lb
/>
eadem ſit cum regula datæ ſectionis.</
s
>
<
s
xml:id
="
echoid-s3165
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3166
"
xml:space
="
preserve
">Iungatur ED, & </
s
>
<
s
xml:id
="
echoid-s3167
"
xml:space
="
preserve
">ad partes ſectionis producatur donec ei occurrat in B,
<
lb
/>
ſumptaq; </
s
>
<
s
xml:id
="
echoid-s3168
"
xml:space
="
preserve
">in directum DH æquali DB, erit HB tranſuerſum ſectionis
<
note
symbol
="
b
"
position
="
left
"
xlink:label
="
note-0118-02
"
xlink:href
="
note-0118-02a
"
xml:space
="
preserve
">47. pri-
<
lb
/>
mi conic.</
note
>
cuius vertex B: </
s
>
<
s
xml:id
="
echoid-s3169
"
xml:space
="
preserve
">ſit ergo BI eius rectum latus, & </
s
>
<
s
xml:id
="
echoid-s3170
"
xml:space
="
preserve
">regula HI; </
s
>
<
s
xml:id
="
echoid-s3171
"
xml:space
="
preserve
">ſitque EK æqui-
<
lb
/>
diſtans BI, & </
s
>
<
s
xml:id
="
echoid-s3172
"
xml:space
="
preserve
">per verticem B, cum tranſuerſo EH, & </
s
>
<
s
xml:id
="
echoid-s3173
"
xml:space
="
preserve
">recto EK, ſiue ad ean-
<
lb
/>
dem regulam HI adſcribatur Hyperbole LEM: </
s
>
<
s
xml:id
="
echoid-s3174
"
xml:space
="
preserve
">patet ipſam datæ ABC eſſe
<
lb
/>
inſcriptam, cum ſimul ſint nun quam coeuntes.</
s
>
<
s
xml:id
="
echoid-s3175
"
xml:space
="
preserve
"/>
</
p
>
<
note
symbol
="
c
"
position
="
left
"
xml:space
="
preserve
">45. h.</
note
>
<
figure
number
="
83
">
<
image
file
="
0118-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0118-01
"/>
</
figure
>
<
p
>
<
s
xml:id
="
echoid-s3176
"
xml:space
="
preserve
">Dico ampliùs ipſam LEM eſſe _MINIMAM_ quæſitam. </
s
>
<
s
xml:id
="
echoid-s3177
"
xml:space
="
preserve
">Quoniam quęlibet
<
lb
/>
alia adſcripta per verticem E, cum eodem verſo HE, ſed cum recto, quod
<
lb
/>
excedat EK, maior eſt ipſa LEM; </
s
>
<
s
xml:id
="
echoid-s3178
"
xml:space
="
preserve
">quæ verò cum recto EN, quod minus
<
note
symbol
="
d
"
position
="
left
"
xlink:label
="
note-0118-04
"
xlink:href
="
note-0118-04a
"
xml:space
="
preserve
">2. Co-
<
lb
/>
roll. 19. h.</
note
>
EK, qualis OEQ, eſt quidem minor eadem LEM, ſed omnino ſecat
<
note
symbol
="
e
"
position
="
left
"
xlink:label
="
note-0118-05
"
xlink:href
="
note-0118-05a
"
xml:space
="
preserve
">ibidem.</
note
>
ABC. </
s
>
<
s
xml:id
="
echoid-s3179
"
xml:space
="
preserve
">Nam ad productam regulam HN, ſecan@ BI in R adſcribatur per B
<
lb
/>
Hyperbole SBT; </
s
>
<
s
xml:id
="
echoid-s3180
"
xml:space
="
preserve
">hæc tota cadet intra ABC, eruntque SBT, OEQ duæ
<
note
symbol
="
f
"
position
="
left
"
xlink:label
="
note-0118-06
"
xlink:href
="
note-0118-06a
"
xml:space
="
preserve
">ibidem.</
note
>
miles Hyperbolæ per diuerſos vertices adſcriptæ ad eandem regulam HR,
<
lb
/>
eſtque ABC ipſi SBT, per eundem verticem, & </
s
>
<
s
xml:id
="
echoid-s3181
"
xml:space
="
preserve
">cum maiori recto latere BI
<
lb
/>
adſcripta, quare per præce dentem ſectiones ABC, OEQ ſe mutuò
<
note
symbol
="
g
"
position
="
left
"
xlink:label
="
note-0118-07
"
xlink:href
="
note-0118-07a
"
xml:space
="
preserve
">52. h.</
note
>
bunt: </
s
>
<
s
xml:id
="
echoid-s3182
"
xml:space
="
preserve
">Vnde Hyperbole LEM eſt _MINIMA_ circumſcripta quæſita. </
s
>
<
s
xml:id
="
echoid-s3183
"
xml:space
="
preserve
">Quod
<
lb
/>
faciendum, & </
s
>
<
s
xml:id
="
echoid-s3184
"
xml:space
="
preserve
">demonſtrandum erat.</
s
>
<
s
xml:id
="
echoid-s3185
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div300
"
type
="
section
"
level
="
1
"
n
="
131
">
<
head
xml:id
="
echoid-head136
"
xml:space
="
preserve
">ALITER.</
head
>
<
p
>
<
s
xml:id
="
echoid-s3186
"
xml:space
="
preserve
">SEcetur EH bifariam in X: </
s
>
<
s
xml:id
="
echoid-s3187
"
xml:space
="
preserve
">erit X centrum vtriuſque LEM, OEQ: </
s
>
<
s
xml:id
="
echoid-s3188
"
xml:space
="
preserve
">ſi ergo
<
lb
/>
ex centris X, D, ducantur XY, XZ, DF ſectionum LEM, OEQ, ABC
<
lb
/>
aſymptoti, hoc eſt XY circumſcriptæ LEM; </
s
>
<
s
xml:id
="
echoid-s3189
"
xml:space
="
preserve
">XZ inſcriptæ OEQ, quæ infra
<
lb
/>
XY cadet; </
s
>
<
s
xml:id
="
echoid-s3190
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3191
"
xml:space
="
preserve
">DF ſectionis ABC, quæ ipſi XY æquidiſtabit; </
s
>
<
s
xml:id
="
echoid-s3192
"
xml:space
="
preserve
">cum XZ
<
note
symbol
="
h
"
position
="
left
"
xlink:label
="
note-0118-08
"
xlink:href
="
note-0118-08a
"
xml:space
="
preserve
">Ex vlti-
<
lb
/>
ma partre
<
lb
/>
37. huius.</
note
>
<
handwritten
xlink:label
="
hd-0118-2
"
xlink:href
="
hd-0118-2a
"
number
="
11
"/>
</
s
>
</
p
>
</
div
>
</
text
>
</
echo
>