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: 37
[Note]
Page: 37
[Note]
Page: 37
[Note]
Page: 37
[Note]
Page: 37
[Note]
Page: 37
[Note]
Page: 37
[Note]
Page: 37
[Note]
Page: 37
[Note]
Page: 37
[Note]
Page: 38
[Note]
Page: 38
[Note]
Page: 38
[Note]
Page: 38
[Note]
Page: 38
[Note]
Page: 38
[Note]
Page: 38
[Note]
Page: 39
[Note]
Page: 39
[Note]
Page: 39
[Note]
Page: 39
[Note]
Page: 39
[Note]
Page: 39
[Note]
Page: 39
[Note]
Page: 39
[Note]
Page: 40
[Note]
Page: 40
[Note]
Page: 40
[Note]
Page: 40
[Note]
Page: 40
<
1 - 3
[out of range]
>
page
|<
<
(180)
of 532
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div508
"
type
="
section
"
level
="
1
"
n
="
247
">
<
p
>
<
s
xml:id
="
echoid-s6736
"
xml:space
="
preserve
">
<
pb
o
="
180
"
file
="
192
"
n
="
192
"
rhead
="
"/>
quod diuiſum per diametrum AD, notam, cognitam faciet chordam BC. </
s
>
<
s
xml:id
="
echoid-s6737
"
xml:space
="
preserve
">Ex
<
lb
/>
datis ergo chordis duorum arcuum inæqualium chordam arcus, quo maior
<
lb
/>
arcus minorem ſuperat, inquiſiuimus. </
s
>
<
s
xml:id
="
echoid-s6738
"
xml:space
="
preserve
">Quod faciendum erat.</
s
>
<
s
xml:id
="
echoid-s6739
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div510
"
type
="
section
"
level
="
1
"
n
="
248
">
<
head
xml:id
="
echoid-head275
"
xml:space
="
preserve
">COROLLARIVM.</
head
>
<
p
>
<
s
xml:id
="
echoid-s6740
"
xml:space
="
preserve
">ITAQVE datis chordis duorum arcuum inæqualium, ſi maioris chorda multiplice-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-192-01
"
xlink:href
="
note-192-01a
"
xml:space
="
preserve
">Praxis.</
note
>
tur in chordam arcus, qui cum minori arcu ſemicirculum conficit, quæ quidem per 3. </
s
>
<
s
xml:id
="
echoid-s6741
"
xml:space
="
preserve
">pro-
<
lb
/>
poſ. </
s
>
<
s
xml:id
="
echoid-s6742
"
xml:space
="
preserve
">datur; </
s
>
<
s
xml:id
="
echoid-s6743
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s6744
"
xml:space
="
preserve
">ex producto ſubtrahatur numerus procreatus ex minoris arcus chorda in chor
<
lb
/>
dam arcus, qui cum arcu maiori ſemicirculum complet, quæ per eandem propoſ. </
s
>
<
s
xml:id
="
echoid-s6745
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s6746
"
xml:space
="
preserve
">dat@r;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s6747
"
xml:space
="
preserve
">reliquus autem numerus per diametrum diuidatur, reddetur chorda illius arcus, quo ma-
<
lb
/>
ior arcus minorem ſuperat, nota: </
s
>
<
s
xml:id
="
echoid-s6748
"
xml:space
="
preserve
">vt ex figura & </
s
>
<
s
xml:id
="
echoid-s6749
"
xml:space
="
preserve
">demonſtratione huius propoſ, manife-
<
lb
/>
ſtum eſt.</
s
>
<
s
xml:id
="
echoid-s6750
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div512
"
type
="
section
"
level
="
1
"
n
="
249
">
<
head
xml:id
="
echoid-head276
"
xml:space
="
preserve
">PROBL. 6. PROPOS. 14.</
head
>
<
note
position
="
left
"
xml:space
="
preserve
">Qua arte ex
<
lb
/>
datis dua-
<
lb
/>
bus chordis
<
lb
/>
cognoſcaf
<
lb
/>
chorda ar-
<
lb
/>
cus cõpoſiti
<
lb
/>
ex duobus
<
lb
/>
arcubus da
<
lb
/>
tarũ duarũ
<
lb
/>
chordarũ.</
note
>
<
p
>
<
s
xml:id
="
echoid-s6751
"
xml:space
="
preserve
">EX datis chordis duorum arcuum chordam
<
lb
/>
arcus, qui ex duobus illis arcubus componitur, in-
<
lb
/>
ueſtigare.</
s
>
<
s
xml:id
="
echoid-s6752
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s6753
"
xml:space
="
preserve
">IN circulo ABCDE, cuius centrum F, datæ ſint duæ chordæ AB, BC:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s6754
"
xml:space
="
preserve
">oporteatq́; </
s
>
<
s
xml:id
="
echoid-s6755
"
xml:space
="
preserve
">inueſtigare chordam AC, arcus ABC, ex duobus arcubus AB,
<
lb
/>
BC, compoſiti. </
s
>
<
s
xml:id
="
echoid-s6756
"
xml:space
="
preserve
">Ductis duabus diametris AD, BE, & </
s
>
<
s
xml:id
="
echoid-s6757
"
xml:space
="
preserve
">rectis BD, CE, CD,
<
lb
/>
DE; </
s
>
<
s
xml:id
="
echoid-s6758
"
xml:space
="
preserve
">quoniam data eſt chorda AB, dabitur quoq; </
s
>
<
s
xml:id
="
echoid-s6759
"
xml:space
="
preserve
">chorda BD, arcus BCD,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-192-03
"
xlink:href
="
note-192-03a
"
xml:space
="
preserve
">3.huius.</
note
>
<
figure
xlink:label
="
fig-192-01
"
xlink:href
="
fig-192-01a
"
number
="
143
">
<
image
file
="
192-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/192-01
"/>
</
figure
>
reliqui in ſemicirculo ABD. </
s
>
<
s
xml:id
="
echoid-s6760
"
xml:space
="
preserve
">Pariratione, quia
<
lb
/>
data eſt chorda BC, dabitur quoq; </
s
>
<
s
xml:id
="
echoid-s6761
"
xml:space
="
preserve
">chorda CE,
<
lb
/>
arcus CDE, reliqui in ſemicirculo BCE. </
s
>
<
s
xml:id
="
echoid-s6762
"
xml:space
="
preserve
">Et quia
<
lb
/>
anguli AFB, DFE, æquales ſunt, lateraq́; </
s
>
<
s
xml:id
="
echoid-s6763
"
xml:space
="
preserve
">FA,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-192-04
"
xlink:href
="
note-192-04a
"
xml:space
="
preserve
">15. primi.</
note
>
FB, lateribus FD, FE, æqualia, æquales quoque
<
lb
/>
erunt baſes AB, DE; </
s
>
<
s
xml:id
="
echoid-s6764
"
xml:space
="
preserve
">ac proinde cum AB, data
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-192-05
"
xlink:href
="
note-192-05a
"
xml:space
="
preserve
">4.primi.</
note
>
ſit, data quoq; </
s
>
<
s
xml:id
="
echoid-s6765
"
xml:space
="
preserve
">erit DE. </
s
>
<
s
xml:id
="
echoid-s6766
"
xml:space
="
preserve
">Quoniam igitur rectan-
<
lb
/>
gulum ſub datis rectis BD, CE, æquale eſt rectan
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-192-06
"
xlink:href
="
note-192-06a
"
xml:space
="
preserve
">11.huius.</
note
>
gulis ſub datis rectis BC, DE, & </
s
>
<
s
xml:id
="
echoid-s6767
"
xml:space
="
preserve
">ſub diametro
<
lb
/>
BE, ac recta CD: </
s
>
<
s
xml:id
="
echoid-s6768
"
xml:space
="
preserve
">ſi rectangulum ſub BC, DE,
<
lb
/>
datum auferatur ex rectangulo dato ſub BD, CE; </
s
>
<
s
xml:id
="
echoid-s6769
"
xml:space
="
preserve
">notum relinquetur rectan
<
lb
/>
gulum ſub BE, CD. </
s
>
<
s
xml:id
="
echoid-s6770
"
xml:space
="
preserve
">quo diuiſo per diametrum notam BE, nota fiet chor-
<
lb
/>
da CD; </
s
>
<
s
xml:id
="
echoid-s6771
"
xml:space
="
preserve
">ac proinde & </
s
>
<
s
xml:id
="
echoid-s6772
"
xml:space
="
preserve
">chorda AC, reliqui arcus ABC, in ſemicirculo ACD,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-192-07
"
xlink:href
="
note-192-07a
"
xml:space
="
preserve
">3. huius.</
note
>
nota erit.</
s
>
<
s
xml:id
="
echoid-s6773
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s6774
"
xml:space
="
preserve
">ALITER. </
s
>
<
s
xml:id
="
echoid-s6775
"
xml:space
="
preserve
">Quoniam data eſt chorda AB, dabitur etiam BD, reliqui ar-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-192-08
"
xlink:href
="
note-192-08a
"
xml:space
="
preserve
">3.huius.</
note
>
cus BCD, in ſemicirculo ABD: </
s
>
<
s
xml:id
="
echoid-s6776
"
xml:space
="
preserve
">Data eſt autem & </
s
>
<
s
xml:id
="
echoid-s6777
"
xml:space
="
preserve
">BC. </
s
>
<
s
xml:id
="
echoid-s6778
"
xml:space
="
preserve
">Igitur cum chordæ
<
lb
/>
BD, BC, datæ ſint, dabitur quoq; </
s
>
<
s
xml:id
="
echoid-s6779
"
xml:space
="
preserve
">chorda CD, arcus CD, quo maior arcus
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-192-09
"
xlink:href
="
note-192-09a
"
xml:space
="
preserve
">13. huius.</
note
>
BD, minorem arcum BC, ſuperat; </
s
>
<
s
xml:id
="
echoid-s6780
"
xml:space
="
preserve
">ac proinde rurſus chorda AC, reliqui
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-192-10
"
xlink:href
="
note-192-10a
"
xml:space
="
preserve
">3.huius.</
note
>
arcus ABC, in ſemicirculo ACD, dabitur. </
s
>
<
s
xml:id
="
echoid-s6781
"
xml:space
="
preserve
">Ex datis ergo chordis duorum ar
<
lb
/>
cuum chordam arcus, qui ex duobus illis arcubus componitur, inueſtigaui-
<
lb
/>
mus. </
s
>
<
s
xml:id
="
echoid-s6782
"
xml:space
="
preserve
">Quod erat faciendum.</
s
>
<
s
xml:id
="
echoid-s6783
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div515
"
type
="
section
"
level
="
1
"
n
="
250
">
<
head
xml:id
="
echoid-head277
"
xml:space
="
preserve
">COROLLARIVM.</
head
>
<
p
>
<
s
xml:id
="
echoid-s6784
"
xml:space
="
preserve
">ITAQVE datis chordis duorum arcuum, ſi chordæ arcuum duorum, qui cum illis ſe-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-192-11
"
xlink:href
="
note-192-11a
"
xml:space
="
preserve
">Praxis.</
note
>
micirculos complent, quæ quidem per propoſ. </
s
>
<
s
xml:id
="
echoid-s6785
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s6786
"
xml:space
="
preserve
">dantur, inter ſe multiplicentur; </
s
>
<
s
xml:id
="
echoid-s6787
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s6788
"
xml:space
="
preserve
">ex </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>