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 figures
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 372
[out of range]
>
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 372
[out of range]
>
page
|<
<
(390)
of 532
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div1056
"
type
="
section
"
level
="
1
"
n
="
528
">
<
p
>
<
s
xml:id
="
echoid-s13377
"
xml:space
="
preserve
">
<
pb
o
="
390
"
file
="
402
"
n
="
402
"
rhead
="
"/>
qui illi ad verticem æqualis eſt, maior erit angulo ACE: </
s
>
<
s
xml:id
="
echoid-s13378
"
xml:space
="
preserve
">Sed angulus ACE,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-402-01
"
xlink:href
="
note-402-01a
"
xml:space
="
preserve
">@4. huius.</
note
>
& </
s
>
<
s
xml:id
="
echoid-s13379
"
xml:space
="
preserve
">anguli ACB, & </
s
>
<
s
xml:id
="
echoid-s13380
"
xml:space
="
preserve
">B, duobus rectis ſuntæquales. </
s
>
<
s
xml:id
="
echoid-s13381
"
xml:space
="
preserve
">Igitur anguli BAC, ACB,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-402-02
"
xlink:href
="
note-402-02a
"
xml:space
="
preserve
">16. huius.</
note
>
& </
s
>
<
s
xml:id
="
echoid-s13382
"
xml:space
="
preserve
">B, maiores erunt duobus rectis. </
s
>
<
s
xml:id
="
echoid-s13383
"
xml:space
="
preserve
">Semper ergo tres anguli ſimul duobus re-
<
lb
/>
ctis ſunt maiores.</
s
>
<
s
xml:id
="
echoid-s13384
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s13385
"
xml:space
="
preserve
">QVIA verò omnis angulus ſphæricus, etiam obtuſus, minor eſt duobus
<
lb
/>
rectis; </
s
>
<
s
xml:id
="
echoid-s13386
"
xml:space
="
preserve
">perſpicuum eſt, tres angulos cuiusuis trianguli ſphærici ſimul minores
<
lb
/>
eſſe ſex rectis. </
s
>
<
s
xml:id
="
echoid-s13387
"
xml:space
="
preserve
">Cuiuſcunque ergo trianguli ſphærici tres anguli, &</
s
>
<
s
xml:id
="
echoid-s13388
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s13389
"
xml:space
="
preserve
">Quod
<
lb
/>
erat demonſtrandum.</
s
>
<
s
xml:id
="
echoid-s13390
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div1058
"
type
="
section
"
level
="
1
"
n
="
529
">
<
head
xml:id
="
echoid-head564
"
xml:space
="
preserve
">THEOR. 30. PROPOS. 32.</
head
>
<
p
>
<
s
xml:id
="
echoid-s13391
"
xml:space
="
preserve
">IN omni triangulo ſphærico, cuius vnus an-
<
lb
/>
gulus rectus ſit, & </
s
>
<
s
xml:id
="
echoid-s13392
"
xml:space
="
preserve
">alter reliquorum acutus, ſi qui-
<
lb
/>
dem arcus illis angulis adiacẽs fuerit quadians, erit
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s13393
"
xml:space
="
preserve
">arcus rectum ſubtendens angulum quadrans; </
s
>
<
s
xml:id
="
echoid-s13394
"
xml:space
="
preserve
">ſi
<
lb
/>
verò minor fuerit quadrante, quadrante quoque
<
lb
/>
minor erit: </
s
>
<
s
xml:id
="
echoid-s13395
"
xml:space
="
preserve
">ſi deniq; </
s
>
<
s
xml:id
="
echoid-s13396
"
xml:space
="
preserve
">quadrante fuerit maior, qua-
<
lb
/>
drante quoq; </
s
>
<
s
xml:id
="
echoid-s13397
"
xml:space
="
preserve
">maior erit: </
s
>
<
s
xml:id
="
echoid-s13398
"
xml:space
="
preserve
">Sem per autem arcus acu-
<
lb
/>
tum angulum ſubtendens minor erit quadrante.</
s
>
<
s
xml:id
="
echoid-s13399
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s13400
"
xml:space
="
preserve
">IN triangulo ABC, angulus C, rectus ſit, & </
s
>
<
s
xml:id
="
echoid-s13401
"
xml:space
="
preserve
">B, acutus, ſitque primum ar-
<
lb
/>
cus BC, quadrans, Dico & </
s
>
<
s
xml:id
="
echoid-s13402
"
xml:space
="
preserve
">AB, quadrantem eſſe. </
s
>
<
s
xml:id
="
echoid-s13403
"
xml:space
="
preserve
">Fiat enim angulus CBD,
<
lb
/>
<
figure
xlink:label
="
fig-402-01
"
xlink:href
="
fig-402-01a
"
number
="
248
">
<
image
file
="
402-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/402-01
"/>
</
figure
>
rectus, coëatq́ue arcus BD, cum arcu CA,
<
lb
/>
producto in D. </
s
>
<
s
xml:id
="
echoid-s13404
"
xml:space
="
preserve
">Erit igitur vterque arcus BD,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-402-03
"
xlink:href
="
note-402-03a
"
xml:space
="
preserve
">25. huius.</
note
>
CD, quadrans: </
s
>
<
s
xml:id
="
echoid-s13405
"
xml:space
="
preserve
">Ponitur autem & </
s
>
<
s
xml:id
="
echoid-s13406
"
xml:space
="
preserve
">BC, qua-
<
lb
/>
drans. </
s
>
<
s
xml:id
="
echoid-s13407
"
xml:space
="
preserve
">Ergo B, polus eſt arcus CD; </
s
>
<
s
xml:id
="
echoid-s13408
"
xml:space
="
preserve
">atque
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-402-04
"
xlink:href
="
note-402-04a
"
xml:space
="
preserve
">26. huius.</
note
>
adeo rectus erit angulus ad A. </
s
>
<
s
xml:id
="
echoid-s13409
"
xml:space
="
preserve
">Quare vterque
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-402-05
"
xlink:href
="
note-402-05a
"
xml:space
="
preserve
">15. 1 Theod.</
note
>
arcus BC, BA, quadrans erit. </
s
>
<
s
xml:id
="
echoid-s13410
"
xml:space
="
preserve
">Quadrans igi-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-402-06
"
xlink:href
="
note-402-06a
"
xml:space
="
preserve
">25. huius.</
note
>
tur eſt arcus AB, angulo recto C, oppoſitus.</
s
>
<
s
xml:id
="
echoid-s13411
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s13412
"
xml:space
="
preserve
">SIT deinde arcus BC, quadrante minor.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s13413
"
xml:space
="
preserve
">Dico & </
s
>
<
s
xml:id
="
echoid-s13414
"
xml:space
="
preserve
">arcum AB, quadrante eſſe minorem. </
s
>
<
s
xml:id
="
echoid-s13415
"
xml:space
="
preserve
">
<
lb
/>
Fiat enim rurſus angulus CBD, rectus, oc-
<
lb
/>
curratq́ue arcus BD, arcui CA, producto in
<
lb
/>
D; </
s
>
<
s
xml:id
="
echoid-s13416
"
xml:space
="
preserve
">eritque vt prius, vterque arcus BD, CD,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-402-07
"
xlink:href
="
note-402-07a
"
xml:space
="
preserve
">25. huius.</
note
>
quadrans. </
s
>
<
s
xml:id
="
echoid-s13417
"
xml:space
="
preserve
">Producto autem BC, ad E, vt ſit
<
lb
/>
BE, quadrans, ducatur per puncta D, E, arcus circuli maximi DE, quem BA,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-402-08
"
xlink:href
="
note-402-08a
"
xml:space
="
preserve
">20. 1 Theod.</
note
>
productus ſecet in F. </
s
>
<
s
xml:id
="
echoid-s13418
"
xml:space
="
preserve
">Quoniam igitur arcus BE, BD, quadrantes ſunt, erit
<
lb
/>
vterque angulus BDE, BED, rectus, & </
s
>
<
s
xml:id
="
echoid-s13419
"
xml:space
="
preserve
">B, polus arcus DE. </
s
>
<
s
xml:id
="
echoid-s13420
"
xml:space
="
preserve
">Rectus ergo
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-402-09
"
xlink:href
="
note-402-09a
"
xml:space
="
preserve
">25. & 26.
<
lb
/>
huius.</
note
>
erit angulus ad F; </
s
>
<
s
xml:id
="
echoid-s13421
"
xml:space
="
preserve
">atque adeò vterque arcus BE, BF, quadrans erit. </
s
>
<
s
xml:id
="
echoid-s13422
"
xml:space
="
preserve
">Igitur
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-402-10
"
xlink:href
="
note-402-10a
"
xml:space
="
preserve
">15. 1 Theod.</
note
>
arcus BA, quadrante erit minor.</
s
>
<
s
xml:id
="
echoid-s13423
"
xml:space
="
preserve
"/>
</
p
>
<
note
position
="
left
"
xml:space
="
preserve
">25. huius.</
note
>
<
p
>
<
s
xml:id
="
echoid-s13424
"
xml:space
="
preserve
">SIT denique arcus BC, quadrante maior. </
s
>
<
s
xml:id
="
echoid-s13425
"
xml:space
="
preserve
">Dico & </
s
>
<
s
xml:id
="
echoid-s13426
"
xml:space
="
preserve
">arcum AB, </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>