Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Table of handwritten notes
<
1 - 3
[out of range]
>
<
1 - 3
[out of range]
>
page
|<
<
(11)
of 532
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div36
"
type
="
section
"
level
="
1
"
n
="
28
">
<
p
>
<
s
xml:id
="
echoid-s317
"
xml:space
="
preserve
">
<
pb
o
="
11
"
file
="
023
"
n
="
23
"
rhead
="
"/>
maximi ſunt, qui per ſphæræ centrũ ducũtur, &</
s
>
<
s
xml:id
="
echoid-s318
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s319
"
xml:space
="
preserve
">Quod erat demonſtrandũ.</
s
>
<
s
xml:id
="
echoid-s320
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div41
"
type
="
section
"
level
="
1
"
n
="
29
">
<
head
xml:id
="
echoid-head40
"
xml:space
="
preserve
">THEOREMA 6. PROPOS. 7.</
head
>
<
note
position
="
right
"
xml:space
="
preserve
">8.</
note
>
<
p
>
<
s
xml:id
="
echoid-s321
"
xml:space
="
preserve
">SI in ſphæra ſit circulus, à centro autem ſphæ-
<
lb
/>
ræ ad centrum circuli connectatur recta linea, con
<
lb
/>
nexa linea ad circuli planum recta erit.</
s
>
<
s
xml:id
="
echoid-s322
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s323
"
xml:space
="
preserve
">IN ſphæra A B C, cuius centrum D, ſit circulus B F C G, cuius centrũ
<
lb
/>
E: </
s
>
<
s
xml:id
="
echoid-s324
"
xml:space
="
preserve
">Et recta D E, connectat duo centra D, E. </
s
>
<
s
xml:id
="
echoid-s325
"
xml:space
="
preserve
">Dico D E, rectam eſſe ad planũ
<
lb
/>
circuli B F C G. </
s
>
<
s
xml:id
="
echoid-s326
"
xml:space
="
preserve
">Ductis enim duabus diametris vtcunque B C, F G, in circu
<
lb
/>
lo, ducantur ab earum extremis ad D, centrum ſphæræ rectæ lineæ, B D,
<
lb
/>
<
figure
xlink:label
="
fig-023-01
"
xlink:href
="
fig-023-01a
"
number
="
15
">
<
image
file
="
023-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/023-01
"/>
</
figure
>
C D, F D, G D, quæ omnes inter ſe æqua-
<
lb
/>
les erunt, cum à centro ſphæræ ad eius ſuper
<
lb
/>
ficiem cadant: </
s
>
<
s
xml:id
="
echoid-s327
"
xml:space
="
preserve
">Sunt autem & </
s
>
<
s
xml:id
="
echoid-s328
"
xml:space
="
preserve
">B E, C E, F E,
<
lb
/>
G E, ſemidiametri circuli B F C G, æquales.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s329
"
xml:space
="
preserve
">Igitur duo triangula D E B, D E C, duo la-
<
lb
/>
tera D E, E B, duobus lateribus D E, E C,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s330
"
xml:space
="
preserve
">baſim D B, baſi D C, æqualem habent; </
s
>
<
s
xml:id
="
echoid-s331
"
xml:space
="
preserve
">ex
<
lb
/>
quo fit, angulos D E B, D E C, æquales, at-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-023-02
"
xlink:href
="
note-023-02a
"
xml:space
="
preserve
">8. primi.</
note
>
que adeò rectos eſſe. </
s
>
<
s
xml:id
="
echoid-s332
"
xml:space
="
preserve
">Recta igitur D E, rectę
<
lb
/>
B C, ad rectos inſiſtet angulos. </
s
>
<
s
xml:id
="
echoid-s333
"
xml:space
="
preserve
">Non aliter
<
lb
/>
oſtendemus, rectam D E, rectæ F G, ad re-
<
lb
/>
ctos angulos inſiſtere. </
s
>
<
s
xml:id
="
echoid-s334
"
xml:space
="
preserve
">Quamobrem & </
s
>
<
s
xml:id
="
echoid-s335
"
xml:space
="
preserve
">pla-
<
lb
/>
no circuli B F C G, per rectas B C, F G, du-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-023-03
"
xlink:href
="
note-023-03a
"
xml:space
="
preserve
">4. vndec.</
note
>
cto ad rectos angulos inſiſtet. </
s
>
<
s
xml:id
="
echoid-s336
"
xml:space
="
preserve
">Si igitur in ſphæra ſit circulus, &</
s
>
<
s
xml:id
="
echoid-s337
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s338
"
xml:space
="
preserve
">Quod oſten
<
lb
/>
dendum erat.</
s
>
<
s
xml:id
="
echoid-s339
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div43
"
type
="
section
"
level
="
1
"
n
="
30
">
<
head
xml:id
="
echoid-head41
"
xml:space
="
preserve
">THEOREMA 7. PROPOS. 8.</
head
>
<
note
position
="
right
"
xml:space
="
preserve
">9.</
note
>
<
p
>
<
s
xml:id
="
echoid-s340
"
xml:space
="
preserve
">SI ſit in ſphæra circulus, & </
s
>
<
s
xml:id
="
echoid-s341
"
xml:space
="
preserve
">à centro ſphæræ ad
<
lb
/>
circulũ ducatur perpendicularis, quæ ad vtramq;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s342
"
xml:space
="
preserve
">partẽ producatur, cadet ea in polos ipſius circuli.</
s
>
<
s
xml:id
="
echoid-s343
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s344
"
xml:space
="
preserve
">IN ſphæra A B C D,
<
lb
/>
<
figure
xlink:label
="
fig-023-02
"
xlink:href
="
fig-023-02a
"
number
="
16
">
<
image
file
="
023-02
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/023-02
"/>
</
figure
>
cuius centrum E, ſit cir-
<
lb
/>
culus B G D H, in cuius
<
lb
/>
planum à centro ſphæræ
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-023-05
"
xlink:href
="
note-023-05a
"
xml:space
="
preserve
">11. vndec.</
note
>
E, per pendicularis dedu
<
lb
/>
cta ſit E F, quæ in vtram-
<
lb
/>
que partem protracta ca
<
lb
/>
dat in ſuperficiem ſphæ-
<
lb
/>
ræ ad puncta A, C. </
s
>
<
s
xml:id
="
echoid-s345
"
xml:space
="
preserve
">Dico
<
lb
/>
A, C, polos eſſe circuli
<
lb
/>
BGDH. </
s
>
<
s
xml:id
="
echoid-s346
"
xml:space
="
preserve
">Cadet em̃ per-
<
lb
/>
pendicularis E F, in </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>