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: 83
[Note]
Page: 83
[Note]
Page: 83
[Note]
Page: 83
[Note]
Page: 83
[Note]
Page: 83
[Note]
Page: 83
[Note]
Page: 83
[Note]
Page: 84
[Note]
Page: 84
[Note]
Page: 84
[Note]
Page: 84
[Note]
Page: 84
[Note]
Page: 84
[Note]
Page: 84
[Note]
Page: 84
[Note]
Page: 84
[Note]
Page: 84
[Note]
Page: 84
[Note]
Page: 85
[Note]
Page: 85
[Note]
Page: 85
[Note]
Page: 87
[Note]
Page: 87
[Note]
Page: 88
[Note]
Page: 88
[Note]
Page: 88
[Note]
Page: 88
[Note]
Page: 88
[Note]
Page: 89
<
1 - 14
[out of range]
>
page
|<
<
(77)
of 347
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div757
"
type
="
section
"
level
="
1
"
n
="
300
">
<
pb
o
="
77
"
file
="
0261
"
n
="
261
"
rhead
="
"/>
<
p
>
<
s
xml:id
="
echoid-s7212
"
xml:space
="
preserve
">Ducatur enim in plano ſecante D A E, per punctum F ſectionem con-
<
lb
/>
tingens G F H, quæ, (vtielicitur ex propoſitionibus 20. </
s
>
<
s
xml:id
="
echoid-s7213
"
xml:space
="
preserve
">22. </
s
>
<
s
xml:id
="
echoid-s7214
"
xml:space
="
preserve
">ac 23. </
s
>
<
s
xml:id
="
echoid-s7215
"
xml:space
="
preserve
">huius)
<
lb
/>
cum _MINIMA_ C F rectos an-
<
lb
/>
gulos efficiet. </
s
>
<
s
xml:id
="
echoid-s7216
"
xml:space
="
preserve
">Concipiatur
<
lb
/>
<
figure
xlink:label
="
fig-0261-01
"
xlink:href
="
fig-0261-01a
"
number
="
217
">
<
image
file
="
0261-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0261-01
"/>
</
figure
>
denique per contingentem G
<
lb
/>
H, ductum planũ L M, quod
<
lb
/>
ad planum D A E, in quo iam
<
lb
/>
ponitur eſſe C F, rectum ſit.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7217
"
xml:space
="
preserve
">Cum ergo plana L M, D A E,
<
lb
/>
ſe mutuò ſecent per rectam G
<
lb
/>
H, cui in plano D A E ducta
<
lb
/>
eſt perpendicularis C F, erit
<
lb
/>
ipſa C F, recta quoque
<
note
symbol
="
a
"
position
="
right
"
xlink:label
="
note-0261-01
"
xlink:href
="
note-0261-01a
"
xml:space
="
preserve
">4. def.
<
lb
/>
II. Elem.</
note
>
planum L M, ſiue ad idem planum ex puncto C erit _MINIMA_; </
s
>
<
s
xml:id
="
echoid-s7218
"
xml:space
="
preserve
">ſed
<
note
symbol
="
b
"
position
="
right
"
xlink:label
="
note-0261-02
"
xlink:href
="
note-0261-02a
"
xml:space
="
preserve
">52. h.</
note
>
num L M conuexam ſolidi ſuperficiem contingit in puncto tantùm F, quę
<
lb
/>
cadit tota infra idem planum, ergo recta C F eò magis eſt _MINIMA_
<
note
symbol
="
c
"
position
="
right
"
xlink:label
="
note-0261-03
"
xlink:href
="
note-0261-03a
"
xml:space
="
preserve
">55. h.</
note
>
conuexam ſolidi ſuperficiem D A E. </
s
>
<
s
xml:id
="
echoid-s7219
"
xml:space
="
preserve
">Quod erat, &</
s
>
<
s
xml:id
="
echoid-s7220
"
xml:space
="
preserve
">c.</
s
>
<
s
xml:id
="
echoid-s7221
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div760
"
type
="
section
"
level
="
1
"
n
="
301
">
<
head
xml:id
="
echoid-head310
"
xml:space
="
preserve
">PROBL. X. PROP. LIX.</
head
>
<
p
>
<
s
xml:id
="
echoid-s7222
"
xml:space
="
preserve
">A puncto non intra ſphæram dato, ad eius ſuperficiem, MA-
<
lb
/>
XIMAM rectam lineam ducere.</
s
>
<
s
xml:id
="
echoid-s7223
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s7224
"
xml:space
="
preserve
">SIt data ſphæra, cuius centrum A, & </
s
>
<
s
xml:id
="
echoid-s7225
"
xml:space
="
preserve
">oporteat per punctum B non intra
<
lb
/>
ſphæram datum, ad eius ſuperficiẽ, _MAXIMAM_ rectam lineam ducere.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7226
"
xml:space
="
preserve
">Iungatur B A, & </
s
>
<
s
xml:id
="
echoid-s7227
"
xml:space
="
preserve
">producatur, donec
<
lb
/>
<
figure
xlink:label
="
fig-0261-02
"
xlink:href
="
fig-0261-02a
"
number
="
218
">
<
image
file
="
0261-02
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0261-02
"/>
</
figure
>
ſphæricæ ſuperficiei occurrat in D, & </
s
>
<
s
xml:id
="
echoid-s7228
"
xml:space
="
preserve
">E.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7229
"
xml:space
="
preserve
">Dico B E, in qua eſt centrum, eſſe _MAXI_-
<
lb
/>
_MAM._</
s
>
<
s
xml:id
="
echoid-s7230
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s7231
"
xml:space
="
preserve
">Concipiatur per B E ductum planum,
<
lb
/>
quod in ſpæræ ſuperficie maximum circu-
<
lb
/>
lum deſignabit D F E, ad cuius periphe-
<
lb
/>
riam eſt recta B E _MAXIMA._</
s
>
<
s
xml:id
="
echoid-s7232
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s7233
"
xml:space
="
preserve
">Iam in plano circuli D F E, cum radio
<
lb
/>
B E deſcripto circulo G E H, & </
s
>
<
s
xml:id
="
echoid-s7234
"
xml:space
="
preserve
">circa im-
<
lb
/>
motum axim B E reuoluto, ab ipſo deſcri-
<
lb
/>
betur ſphæra G E H, quæ datam ſphæram
<
lb
/>
D F E circa eundem axim deſcriptam comprehendet, ac ſe ſimul contingét
<
lb
/>
in ipſo circulorum contactu E, ſed quæ à centro B ad ſphæricam
<
note
symbol
="
d
"
position
="
right
"
xlink:label
="
note-0261-04
"
xlink:href
="
note-0261-04a
"
xml:space
="
preserve
">56. h.</
note
>
ciem G E H ducuntur omnes ſunt æquales rectæ B E, ergo quæ ab eodem
<
lb
/>
puncto B ad interioris ſphæræ D F E ſuperficiem ducentur ipſa B E mino-
<
lb
/>
res erunt. </
s
>
<
s
xml:id
="
echoid-s7235
"
xml:space
="
preserve
">Vnde B E eſt _MAXIMA_ quæſita, &</
s
>
<
s
xml:id
="
echoid-s7236
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s7237
"
xml:space
="
preserve
">Quod erat, &</
s
>
<
s
xml:id
="
echoid-s7238
"
xml:space
="
preserve
">c.</
s
>
<
s
xml:id
="
echoid-s7239
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>