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 Notes
<
1 - 3
[out of range]
>
[Note]
Page: 19
[Note]
Page: 19
[Note]
Page: 19
[Note]
Page: 19
[Note]
Page: 19
[Note]
Page: 20
[Note]
Page: 20
[Note]
Page: 20
[Note]
Page: 20
[Note]
Page: 20
[Note]
Page: 20
[Note]
Page: 20
[Note]
Page: 20
[Note]
Page: 20
[Note]
Page: 20
[Note]
Page: 21
[Note]
Page: 21
[Note]
Page: 21
[Note]
Page: 21
[Note]
Page: 21
[Note]
Page: 21
[Note]
Page: 22
[Note]
Page: 22
[Note]
Page: 23
[Note]
Page: 23
[Note]
Page: 23
[Note]
Page: 23
[Note]
Page: 23
[Note]
Page: 24
[Note]
Page: 24
<
1 - 3
[out of range]
>
page
|<
<
(6)
of 532
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div18
"
type
="
section
"
level
="
1
"
n
="
18
">
<
pb
o
="
6
"
file
="
018
"
n
="
18
"
rhead
="
"/>
<
p
>
<
s
xml:id
="
echoid-s124
"
xml:space
="
preserve
">TRANSEAT deinde planum ſecans non per centrum ſphæræ. </
s
>
<
s
xml:id
="
echoid-s125
"
xml:space
="
preserve
">Du-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-018-01
"
xlink:href
="
note-018-01a
"
xml:space
="
preserve
">11. vndec.</
note
>
catur autem ex D, centro ſphæræ ad planum ſecans perpendicularis D H,
<
lb
/>
<
figure
xlink:label
="
fig-018-01
"
xlink:href
="
fig-018-01a
"
number
="
8
">
<
image
file
="
018-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/018-01
"/>
</
figure
>
emittãturq; </
s
>
<
s
xml:id
="
echoid-s126
"
xml:space
="
preserve
">ex H,
<
lb
/>
rectę vtcunq; </
s
>
<
s
xml:id
="
echoid-s127
"
xml:space
="
preserve
">H E,
<
lb
/>
H F, ad lineam B E
<
lb
/>
F C G, & </
s
>
<
s
xml:id
="
echoid-s128
"
xml:space
="
preserve
">cõnectan
<
lb
/>
tur rectæ D E, D F.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s129
"
xml:space
="
preserve
">Quoniã igitur an-
<
lb
/>
guli D H E, D H F,
<
lb
/>
recti ſunt, ex defin. </
s
>
<
s
xml:id
="
echoid-s130
"
xml:space
="
preserve
">
<
lb
/>
3. </
s
>
<
s
xml:id
="
echoid-s131
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s132
"
xml:space
="
preserve
">11. </
s
>
<
s
xml:id
="
echoid-s133
"
xml:space
="
preserve
">Euclid. </
s
>
<
s
xml:id
="
echoid-s134
"
xml:space
="
preserve
">
<
lb
/>
erit tam quadratũ
<
lb
/>
ex D E, quadratis
<
lb
/>
ex D H, H E, quàm
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-018-02
"
xlink:href
="
note-018-02a
"
xml:space
="
preserve
">47. primi.</
note
>
quadratũ ex D F,
<
lb
/>
quadratis ex D H,
<
lb
/>
H F, æ quale: </
s
>
<
s
xml:id
="
echoid-s135
"
xml:space
="
preserve
">Sunt autem quadrata ex D E, D F, inter ſe æqualia, quod & </
s
>
<
s
xml:id
="
echoid-s136
"
xml:space
="
preserve
">
<
lb
/>
rectæ D E, D F, ex centro ſphæræ in eius ſuperficiẽ cadentes inter ſe æqua-
<
lb
/>
les ſint. </
s
>
<
s
xml:id
="
echoid-s137
"
xml:space
="
preserve
">Quadrata igitur ex D H, H E, ſimul quadratis ex D H, H F, ſi-
<
lb
/>
mul æqualia erunt. </
s
>
<
s
xml:id
="
echoid-s138
"
xml:space
="
preserve
">Dempto igitur communi quadrato rectæ D H, reliquæ
<
lb
/>
quadrata rectarum H E, H F, inter ſe æqualia, & </
s
>
<
s
xml:id
="
echoid-s139
"
xml:space
="
preserve
">rectæ propterea H E, H F,
<
lb
/>
inter ſe æquales erunt. </
s
>
<
s
xml:id
="
echoid-s140
"
xml:space
="
preserve
">Eodem argumento oſtendemus, omnes lineas ex H, ad
<
lb
/>
lineam B E F C G, cadentes eſſe æquales & </
s
>
<
s
xml:id
="
echoid-s141
"
xml:space
="
preserve
">inter ſe, & </
s
>
<
s
xml:id
="
echoid-s142
"
xml:space
="
preserve
">dictis duabus H E,
<
lb
/>
H F. </
s
>
<
s
xml:id
="
echoid-s143
"
xml:space
="
preserve
">Linea ergo B E F C G, circum ſerentia erit circuli, ex defin. </
s
>
<
s
xml:id
="
echoid-s144
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s145
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s146
"
xml:space
="
preserve
">1.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s147
"
xml:space
="
preserve
">Euclid. </
s
>
<
s
xml:id
="
echoid-s148
"
xml:space
="
preserve
">cuius centrum eſt punctum H, in quod perpendicularis D H, cadit. </
s
>
<
s
xml:id
="
echoid-s149
"
xml:space
="
preserve
">
<
lb
/>
Quare ſi ſphærica ſuperficies Plano aliquo ſecetur, &</
s
>
<
s
xml:id
="
echoid-s150
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s151
"
xml:space
="
preserve
">Quod erat demon-
<
lb
/>
ſtrandum.</
s
>
<
s
xml:id
="
echoid-s152
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div21
"
type
="
section
"
level
="
1
"
n
="
19
">
<
head
xml:id
="
echoid-head30
"
xml:space
="
preserve
">COROLLARIVM.</
head
>
<
p
>
<
s
xml:id
="
echoid-s153
"
xml:space
="
preserve
">ITAQVE ſi planum ſecans per centrum ſphæræ tranſierit’, efficietur circulus idem
<
lb
/>
centrum habens, quod ſphæra. </
s
>
<
s
xml:id
="
echoid-s154
"
xml:space
="
preserve
">Si verò non per centrum tranſierit, efficientur circulus aliud
<
lb
/>
habens centrum, quàm ſphæra, illud videlicet punctum, in quod cadit perpendicularis ex
<
lb
/>
centro ſphæræ ad planum ſecans deducta. </
s
>
<
s
xml:id
="
echoid-s155
"
xml:space
="
preserve
">Nam ſemper demonſtrabuntur lineæ rectæ caden
<
lb
/>
tes ex hoc puncto in circum ferentiam circuli eſſe æquales.</
s
>
<
s
xml:id
="
echoid-s156
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div22
"
type
="
section
"
level
="
1
"
n
="
20
">
<
head
xml:id
="
echoid-head31
"
xml:space
="
preserve
">HOCEST.</
head
>
<
p
>
<
s
xml:id
="
echoid-s157
"
xml:space
="
preserve
">IDEM eſt ſphæræ centrum, & </
s
>
<
s
xml:id
="
echoid-s158
"
xml:space
="
preserve
">circuli per ſphæræ centrum traiecti. </
s
>
<
s
xml:id
="
echoid-s159
"
xml:space
="
preserve
">Et perpendiculatis
<
lb
/>
ducta à centro ſphæræ in planum circuli per centrum ſphæræ non traiecti, cadit in centrum
<
lb
/>
circuli: </
s
>
<
s
xml:id
="
echoid-s160
"
xml:space
="
preserve
">quia punctum H, in quod perpendicularis D H, cadit, demonſtratum cſt centrum
<
lb
/>
eſſe circuli.</
s
>
<
s
xml:id
="
echoid-s161
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div23
"
type
="
section
"
level
="
1
"
n
="
21
">
<
head
xml:id
="
echoid-head32
"
xml:space
="
preserve
">PROBL. 1. PROPOS. 2.</
head
>
<
note
position
="
left
"
xml:space
="
preserve
">2.</
note
>
</
div
>
<
div
xml:id
="
echoid-div24
"
type
="
section
"
level
="
1
"
n
="
22
">
<
head
xml:id
="
echoid-head33
"
xml:space
="
preserve
">DATAE Sphæræ centrum inuenire.</
head
>
<
p
>
<
s
xml:id
="
echoid-s162
"
xml:space
="
preserve
">SIT centrum inueniendum Sphæræ A B C D. </
s
>
<
s
xml:id
="
echoid-s163
"
xml:space
="
preserve
">Secetur eius ſuperficies
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-018-04
"
xlink:href
="
note-018-04a
"
xml:space
="
preserve
">1. huius.
<
lb
/>
1. tertij.
<
lb
/>
Coroll. 1.
<
lb
/>
huius.</
note
>
plano quopiam faciente in ipſa lineam B D E, quæ circuli circumferentia
<
lb
/>
crit. </
s
>
<
s
xml:id
="
echoid-s164
"
xml:space
="
preserve
">Sit huius circuli centrum F. </
s
>
<
s
xml:id
="
echoid-s165
"
xml:space
="
preserve
">Siigitur circulus B D E, per centrum ſphæ
<
lb
/>
ræ traijcitur, erit punctum F, centrum quoque ſphæræ. </
s
>
<
s
xml:id
="
echoid-s166
"
xml:space
="
preserve
">Si verò per centrum
<
lb
/>
ſphæræ non traijcitur, erigatur ex F, ad planum circuli B D E, </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>