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
|<
<
(510)
of 532
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div1493
"
type
="
section
"
level
="
1
"
n
="
665
">
<
p
>
<
s
xml:id
="
echoid-s18778
"
xml:space
="
preserve
">
<
pb
o
="
510
"
file
="
522
"
n
="
522
"
rhead
="
"/>
_& </
s
>
<
s
xml:id
="
echoid-s18779
"
xml:space
="
preserve
">arcu_
<
emph
style
="
sc
">BD</
emph
>
, _inuento indagetur angulus oppoſitus_ BA:</
s
>
<
s
xml:id
="
echoid-s18780
"
xml:space
="
preserve
">D _qui duplicatus offeres_
<
lb
/>
_totum_
<
emph
style
="
sc
">BA</
emph
>
C, _quæſitum._</
s
>
<
s
xml:id
="
echoid-s18781
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s18782
"
xml:space
="
preserve
">IN hoc porro caſu non poteſt datus arcus AB, eſſe quadrans.</
s
>
<
s
xml:id
="
echoid-s18783
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s18784
"
xml:space
="
preserve
">22. </
s
>
<
s
xml:id
="
echoid-s18785
"
xml:space
="
preserve
">DATIS duobus arcubus trianguli non
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-522-01
"
xlink:href
="
note-522-01a
"
xml:space
="
preserve
">Quætũtur
<
lb
/>
luo angu-
<
lb
/>
li cum vno
<
lb
/>
ercu.</
note
>
rectanguli, cum angulo, qui alteri eorum
<
lb
/>
opponitur, reliquos angulos, cum reliquo
<
lb
/>
arcu ſcrutari: </
s
>
<
s
xml:id
="
echoid-s18786
"
xml:space
="
preserve
">ſi modo conſter, num angu-
<
lb
/>
lus alteri arcui dato oppoſitus acutus ſit, aut
<
lb
/>
obtuſus.</
s
>
<
s
xml:id
="
echoid-s18787
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s18788
"
xml:space
="
preserve
">SINT in triangulo ABC, dati duo arcus AB, AC, cum angulo B, qui
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-522-02
"
xlink:href
="
note-522-02a
"
xml:space
="
preserve
">Quãdo da-
<
lb
/>
ti duo ar-
<
lb
/>
cus sũt inę
<
lb
/>
quales, &
<
lb
/>
neuter eo-
<
lb
/>
rum qua-
<
lb
/>
drans.</
note
>
arcui AC, opponitur: </
s
>
<
s
xml:id
="
echoid-s18789
"
xml:space
="
preserve
">ſint autem primum illi arcus inæquales, & </
s
>
<
s
xml:id
="
echoid-s18790
"
xml:space
="
preserve
">neuter qua-
<
lb
/>
drans, conſtetq́; </
s
>
<
s
xml:id
="
echoid-s18791
"
xml:space
="
preserve
">præterea ſpecies anguli C, alteri arcui dato AB, oppoſiti.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s18792
"
xml:space
="
preserve
">Ducatur ex angulo A, à datis arcubus comprehenſo ad arcum BC, arcus per-
<
lb
/>
<
figure
xlink:label
="
fig-522-01
"
xlink:href
="
fig-522-01a
"
number
="
370
">
<
image
file
="
522-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/522-01
"/>
</
figure
>
pendicularis, qui intra triangulum cadet, ſi
<
lb
/>
vterque angulus B, C, ſit acutus, vel obtu-
<
lb
/>
ſus; </
s
>
<
s
xml:id
="
echoid-s18793
"
xml:space
="
preserve
">extra vero, ſi vnus acutus ſit, & </
s
>
<
s
xml:id
="
echoid-s18794
"
xml:space
="
preserve
">alter ob-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-522-03
"
xlink:href
="
note-522-03a
"
xml:space
="
preserve
">Propoſ. 67.
<
lb
/>
triãg. ſphęr.</
note
>
tuſus. </
s
>
<
s
xml:id
="
echoid-s18795
"
xml:space
="
preserve
">Conſtat autem, an vterque angulus
<
lb
/>
acutus ſit, obtuſusve, an non; </
s
>
<
s
xml:id
="
echoid-s18796
"
xml:space
="
preserve
">quia angulus
<
lb
/>
B, datus eſt, cum ſpecie anguli C. </
s
>
<
s
xml:id
="
echoid-s18797
"
xml:space
="
preserve
">inquiratur
<
lb
/>
ergo, per problema 2. </
s
>
<
s
xml:id
="
echoid-s18798
"
xml:space
="
preserve
">triang. </
s
>
<
s
xml:id
="
echoid-s18799
"
xml:space
="
preserve
">ſphær. </
s
>
<
s
xml:id
="
echoid-s18800
"
xml:space
="
preserve
">ex dato
<
lb
/>
arcu AB, angulum rectum D, ſubtendente, & </
s
>
<
s
xml:id
="
echoid-s18801
"
xml:space
="
preserve
">
<
lb
/>
angulo dato B, arcus oppoſitus AD. </
s
>
<
s
xml:id
="
echoid-s18802
"
xml:space
="
preserve
">Et hinc,
<
lb
/>
per problema 8. </
s
>
<
s
xml:id
="
echoid-s18803
"
xml:space
="
preserve
">triang. </
s
>
<
s
xml:id
="
echoid-s18804
"
xml:space
="
preserve
">ſphær. </
s
>
<
s
xml:id
="
echoid-s18805
"
xml:space
="
preserve
">ex eodem ar-
<
lb
/>
cu dato AB, & </
s
>
<
s
xml:id
="
echoid-s18806
"
xml:space
="
preserve
">arcu inuento AD, eliciatur
<
lb
/>
tertius arcus BD. </
s
>
<
s
xml:id
="
echoid-s18807
"
xml:space
="
preserve
">Hinc rurſus, per proble-
<
lb
/>
ma 1. </
s
>
<
s
xml:id
="
echoid-s18808
"
xml:space
="
preserve
">triang. </
s
>
<
s
xml:id
="
echoid-s18809
"
xml:space
="
preserve
">ſphær. </
s
>
<
s
xml:id
="
echoid-s18810
"
xml:space
="
preserve
">ex dato arcu AB, rectum
<
lb
/>
angulum D, ſubtendente, & </
s
>
<
s
xml:id
="
echoid-s18811
"
xml:space
="
preserve
">arcu BD, inuen-
<
lb
/>
to reperiatur angulus BAD, arcui BD, oppoſitus: </
s
>
<
s
xml:id
="
echoid-s18812
"
xml:space
="
preserve
">Et per problema 13. </
s
>
<
s
xml:id
="
echoid-s18813
"
xml:space
="
preserve
">triãg.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s18814
"
xml:space
="
preserve
">ſphær. </
s
>
<
s
xml:id
="
echoid-s18815
"
xml:space
="
preserve
">ex dato arcu AC, rectum angulum D, ſubtendente, & </
s
>
<
s
xml:id
="
echoid-s18816
"
xml:space
="
preserve
">arcu AD, in-
<
lb
/>
uento eruatur angulus CAD, à dictis arcubus comprehenſus. </
s
>
<
s
xml:id
="
echoid-s18817
"
xml:space
="
preserve
">Nam hic an-
<
lb
/>
gulus adiectus ad inuentum angulum BAD, vel ab eodem ſubtractus, (prout
<
lb
/>
arcus AD, cadit intra, vel extra triangulum) dabit quæſitum angulum BAC. </
s
>
<
s
xml:id
="
echoid-s18818
"
xml:space
="
preserve
">
<
lb
/>
Inueniatur præterea, per problema 15. </
s
>
<
s
xml:id
="
echoid-s18819
"
xml:space
="
preserve
">triang. </
s
>
<
s
xml:id
="
echoid-s18820
"
xml:space
="
preserve
">ſphær. </
s
>
<
s
xml:id
="
echoid-s18821
"
xml:space
="
preserve
">ex dato arcu AC, re-
<
lb
/>
ctum angulum D, ſubtendente, & </
s
>
<
s
xml:id
="
echoid-s18822
"
xml:space
="
preserve
">inuento angulo CAD, angulus ACD: </
s
>
<
s
xml:id
="
echoid-s18823
"
xml:space
="
preserve
">qui
<
lb
/>
erit is, quem quærimus, ſi arcus AD, intra triangulum cadit, ſi vero extra,
<
lb
/>
ablatus ex duobus rectis dabit angulum ACB, quæſitum: </
s
>
<
s
xml:id
="
echoid-s18824
"
xml:space
="
preserve
">ſicq́; </
s
>
<
s
xml:id
="
echoid-s18825
"
xml:space
="
preserve
">duo reliqui
<
lb
/>
anguli BAC, ACB, erunt cogniti.</
s
>
<
s
xml:id
="
echoid-s18826
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s18827
"
xml:space
="
preserve
">DEINDE, per problema 8. </
s
>
<
s
xml:id
="
echoid-s18828
"
xml:space
="
preserve
">triang. </
s
>
<
s
xml:id
="
echoid-s18829
"
xml:space
="
preserve
">ſphær. </
s
>
<
s
xml:id
="
echoid-s18830
"
xml:space
="
preserve
">ex dato arcu AC, angulum
<
lb
/>
rectum D, ſubtendente, & </
s
>
<
s
xml:id
="
echoid-s18831
"
xml:space
="
preserve
">inuento arcu AD, inquira tur arcus CD. </
s
>
<
s
xml:id
="
echoid-s18832
"
xml:space
="
preserve
">Hic enim
<
lb
/>
additus arcui inuento BD, vel ab eodem ſubductus (prout arcus AD, intra
<
lb
/>
triangulum cadit, vel extra) notum offeret quæſitum arcum BC.</
s
>
<
s
xml:id
="
echoid-s18833
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s18834
"
xml:space
="
preserve
">IN hoc porro caſu, nullus arcuum AD, BD, CD; </
s
>
<
s
xml:id
="
echoid-s18835
"
xml:space
="
preserve
">quadrans eſſe poteſt.</
s
>
<
s
xml:id
="
echoid-s18836
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s18837
"
xml:space
="
preserve
">PER _ſolos ſinus ita erit agendum. </
s
>
<
s
xml:id
="
echoid-s18838
"
xml:space
="
preserve
">Per problema_ 2. </
s
>
<
s
xml:id
="
echoid-s18839
"
xml:space
="
preserve
">_triang. </
s
>
<
s
xml:id
="
echoid-s18840
"
xml:space
="
preserve
">ſphær. </
s
>
<
s
xml:id
="
echoid-s18841
"
xml:space
="
preserve
">ex dato </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>