Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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arcus grad. </
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<
s
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xml:space
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>
<
s
xml:id
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echoid-s6943
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xml:space
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">& </
s
>
<
s
xml:id
="
echoid-s6944
"
xml:space
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">ex chorda arcus grad. </
s
>
<
s
xml:id
="
echoid-s6945
"
xml:space
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">60. </
s
>
<
s
xml:id
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echoid-s6946
"
xml:space
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">cognoſcemus chordam arcus grad.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s6947
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xml:space
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">30. </
s
>
<
s
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"
xml:space
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">quo duo illi inter ſe differunt. </
s
>
<
s
xml:id
="
echoid-s6949
"
xml:space
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">Eodemq́; </
s
>
<
s
xml:id
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"
xml:space
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">modo plurimorum arcuum chor-
<
lb
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das inueſtigabimus.</
s
>
<
s
xml:id
="
echoid-s6951
"
xml:space
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"/>
</
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>
<
p
>
<
s
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xml:space
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">RVRSVS perea, quæ propoſ. </
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<
s
xml:id
="
echoid-s6953
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xml:space
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">14. </
s
>
<
s
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echoid-s6954
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xml:space
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">eiusq́; </
s
>
<
s
xml:id
="
echoid-s6955
"
xml:space
="
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">corollario demonſtrauimus,
<
lb
/>
reperiemus chordam cuiuſq; </
s
>
<
s
xml:id
="
echoid-s6956
"
xml:space
="
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">arcus compoſiti ex duobus, quorum chordæ no-
<
lb
/>
tæ ſint. </
s
>
<
s
xml:id
="
echoid-s6957
"
xml:space
="
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">Vt ex chorda arcus grad. </
s
>
<
s
xml:id
="
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xml:space
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">60. </
s
>
<
s
xml:id
="
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xml:space
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">& </
s
>
<
s
xml:id
="
echoid-s6960
"
xml:space
="
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">ex chorda arcus grad. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">90. </
s
>
<
s
xml:id
="
echoid-s6962
"
xml:space
="
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">nota red-
<
lb
/>
detur chorda arcus grad. </
s
>
<
s
xml:id
="
echoid-s6963
"
xml:space
="
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">150. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ex illis duobus compoſiti. </
s
>
<
s
xml:id
="
echoid-s6965
"
xml:space
="
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">Sic etiam ex chor-
<
lb
/>
da arcus grad. </
s
>
<
s
xml:id
="
echoid-s6966
"
xml:space
="
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">90. </
s
>
<
s
xml:id
="
echoid-s6967
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s6968
"
xml:space
="
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">ex chorda arcus grad. </
s
>
<
s
xml:id
="
echoid-s6969
"
xml:space
="
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">36. </
s
>
<
s
xml:id
="
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"
xml:space
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">cognoſcetur chorda arcus
<
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/>
grad. </
s
>
<
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<
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xml:space
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">&</
s
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<
s
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xml:space
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">c.</
s
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<
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</
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>
<
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>
<
s
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="
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xml:space
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">PRAETEREA per doctrinam propoſ. </
s
>
<
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="
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"
xml:space
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">15. </
s
>
<
s
xml:id
="
echoid-s6977
"
xml:space
="
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">eiusq́; </
s
>
<
s
xml:id
="
echoid-s6978
"
xml:space
="
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">coroll. </
s
>
<
s
xml:id
="
echoid-s6979
"
xml:space
="
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">cognita chor-
<
lb
/>
da cuiuſuis arcus, cognoſcemus & </
s
>
<
s
xml:id
="
echoid-s6980
"
xml:space
="
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">chordam dimidiati arcus. </
s
>
<
s
xml:id
="
echoid-s6981
"
xml:space
="
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">Vt ex chorda ar-
<
lb
/>
cus grad. </
s
>
<
s
xml:id
="
echoid-s6982
"
xml:space
="
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">60. </
s
>
<
s
xml:id
="
echoid-s6983
"
xml:space
="
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">notam efficiemus chordam arcus grad. </
s
>
<
s
xml:id
="
echoid-s6984
"
xml:space
="
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">30. </
s
>
<
s
xml:id
="
echoid-s6985
"
xml:space
="
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">Ex hac chordam ar-
<
lb
/>
cus grad. </
s
>
<
s
xml:id
="
echoid-s6986
"
xml:space
="
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">15. </
s
>
<
s
xml:id
="
echoid-s6987
"
xml:space
="
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">Ex hac vero chordam arcus grad. </
s
>
<
s
xml:id
="
echoid-s6988
"
xml:space
="
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">7. </
s
>
<
s
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xml:space
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">Min. </
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<
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">30. </
s
>
<
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="
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"
xml:space
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">& </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ex hac chordam
<
lb
/>
arcus grad. </
s
>
<
s
xml:id
="
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xml:space
="
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">3. </
s
>
<
s
xml:id
="
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xml:space
="
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">Min. </
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>
<
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xml:id
="
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"
xml:space
="
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">45. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Item ex chorda arcus grad. </
s
>
<
s
xml:id
="
echoid-s6997
"
xml:space
="
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">72. </
s
>
<
s
xml:id
="
echoid-s6998
"
xml:space
="
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">explorabimus chordam
<
lb
/>
arcus grad. </
s
>
<
s
xml:id
="
echoid-s6999
"
xml:space
="
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">36. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Et ex hac chordã arcus grad. </
s
>
<
s
xml:id
="
echoid-s7001
"
xml:space
="
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">18. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Et ex hac chordã arcus grad. </
s
>
<
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"
xml:space
="
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">9.
<
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</
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<
s
xml:id
="
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"
xml:space
="
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">Et ex hac chordã arcus grad. </
s
>
<
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xml:id
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"
xml:space
="
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">4. </
s
>
<
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xml:space
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">Min. </
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<
s
xml:id
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xml:space
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">30. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Et ex hac chordam arcus grad. </
s
>
<
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xml:id
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"
xml:space
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">2. </
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>
<
s
xml:id
="
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xml:space
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">Min. </
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<
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<
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15. </
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<
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xml:space
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<
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<
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xml:id
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xml:space
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>
<
s
xml:id
="
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"
xml:space
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">coroll. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ex chordis arcuum
<
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/>
grad. </
s
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<
s
xml:id
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xml:space
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">36. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">& </
s
>
<
s
xml:id
="
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"
xml:space
="
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">grad. </
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>
<
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xml:id
="
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"
xml:space
="
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">48. </
s
>
<
s
xml:id
="
echoid-s7021
"
xml:space
="
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">cognoſcitur chorda arcus grad. </
s
>
<
s
xml:id
="
echoid-s7022
"
xml:space
="
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">12. </
s
>
<
s
xml:id
="
echoid-s7023
"
xml:space
="
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">quo illi duo inter ſe
<
lb
/>
differunt, cognoſcemus ex chorda arcus grad. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">12. </
s
>
<
s
xml:id
="
echoid-s7025
"
xml:space
="
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">chordam arcus grad. </
s
>
<
s
xml:id
="
echoid-s7026
"
xml:space
="
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">6. </
s
>
<
s
xml:id
="
echoid-s7027
"
xml:space
="
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">Et ex
<
lb
/>
hac chordam arcus grad. </
s
>
<
s
xml:id
="
echoid-s7028
"
xml:space
="
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">3. </
s
>
<
s
xml:id
="
echoid-s7029
"
xml:space
="
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">Ex hac chordam arcus grad. </
s
>
<
s
xml:id
="
echoid-s7030
"
xml:space
="
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">1. </
s
>
<
s
xml:id
="
echoid-s7031
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s7032
"
xml:space
="
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">30. </
s
>
<
s
xml:id
="
echoid-s7033
"
xml:space
="
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">Et ex hac
<
lb
/>
chordam arcus grad. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">0. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s7036
"
xml:space
="
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">45. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Deinde ſi per ea, quæ demonſtrata ſunt, ar-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-195-01
"
xlink:href
="
note-195-01a
"
xml:space
="
preserve
">Supputa-
<
lb
/>
tio chorda-
<
lb
/>
rũ arcuum
<
lb
/>
Min. 45. ſe-
<
lb
/>
ſe ſnperan-
<
lb
/>
tium.</
note
>
cuum cæterorum chordas diligẽter ex inuentis inquiramus, inueniemus chor
<
lb
/>
das omnium arcuum, qui ſe ordine continuo ſuperant Minutis 45. </
s
>
<
s
xml:id
="
echoid-s7038
"
xml:space
="
preserve
">ita vt pri-
<
lb
/>
mus arcus contineat grad. </
s
>
<
s
xml:id
="
echoid-s7039
"
xml:space
="
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">0. </
s
>
<
s
xml:id
="
echoid-s7040
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s7041
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s7042
"
xml:space
="
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">ſecundus grad. </
s
>
<
s
xml:id
="
echoid-s7043
"
xml:space
="
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">1. </
s
>
<
s
xml:id
="
echoid-s7044
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s7045
"
xml:space
="
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">30. </
s
>
<
s
xml:id
="
echoid-s7046
"
xml:space
="
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">tertius grad. </
s
>
<
s
xml:id
="
echoid-s7047
"
xml:space
="
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">2.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7048
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s7049
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s7050
"
xml:space
="
preserve
">vltimus deniq; </
s
>
<
s
xml:id
="
echoid-s7051
"
xml:space
="
preserve
">ſit totus ſemicirculus grad. </
s
>
<
s
xml:id
="
echoid-s7052
"
xml:space
="
preserve
">180. </
s
>
<
s
xml:id
="
echoid-s7053
"
xml:space
="
preserve
">Immo vero, ſi, vt
<
lb
/>
proxime docuimus, inuenta fuerit chorda arcus grad. </
s
>
<
s
xml:id
="
echoid-s7054
"
xml:space
="
preserve
">0. </
s
>
<
s
xml:id
="
echoid-s7055
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s7056
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s7057
"
xml:space
="
preserve
">inueniemus
<
lb
/>
ex hac, per doctrinam propoſ. </
s
>
<
s
xml:id
="
echoid-s7058
"
xml:space
="
preserve
">14. </
s
>
<
s
xml:id
="
echoid-s7059
"
xml:space
="
preserve
">eiusq́; </
s
>
<
s
xml:id
="
echoid-s7060
"
xml:space
="
preserve
">coroll. </
s
>
<
s
xml:id
="
echoid-s7061
"
xml:space
="
preserve
">chordas omnium arcuum ſe-
<
lb
/>
ſe continue Minutis 45. </
s
>
<
s
xml:id
="
echoid-s7062
"
xml:space
="
preserve
">ſuperantium, ſi primo inueſtigemus chordam arcus
<
lb
/>
grad. </
s
>
<
s
xml:id
="
echoid-s7063
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s7064
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s7065
"
xml:space
="
preserve
">30. </
s
>
<
s
xml:id
="
echoid-s7066
"
xml:space
="
preserve
">ex duobus arcubus Min. </
s
>
<
s
xml:id
="
echoid-s7067
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s7068
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s7069
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s7070
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s7071
"
xml:space
="
preserve
">compoſiti: </
s
>
<
s
xml:id
="
echoid-s7072
"
xml:space
="
preserve
">Deinde ve
<
lb
/>
ro chordam arcus grad. </
s
>
<
s
xml:id
="
echoid-s7073
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s7074
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s7075
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s7076
"
xml:space
="
preserve
">qui ex duobus arcubus grad. </
s
>
<
s
xml:id
="
echoid-s7077
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s7078
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s7079
"
xml:space
="
preserve
">30. </
s
>
<
s
xml:id
="
echoid-s7080
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s7081
"
xml:space
="
preserve
">
<
lb
/>
Min. </
s
>
<
s
xml:id
="
echoid-s7082
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s7083
"
xml:space
="
preserve
">componitur: </
s
>
<
s
xml:id
="
echoid-s7084
"
xml:space
="
preserve
">Et poſtea chordam arcus grad. </
s
>
<
s
xml:id
="
echoid-s7085
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s7086
"
xml:space
="
preserve
">qui componitur ex
<
lb
/>
arcu grad. </
s
>
<
s
xml:id
="
echoid-s7087
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s7088
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s7089
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s7090
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s7091
"
xml:space
="
preserve
">ex arcu Min. </
s
>
<
s
xml:id
="
echoid-s7092
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s7093
"
xml:space
="
preserve
">atq; </
s
>
<
s
xml:id
="
echoid-s7094
"
xml:space
="
preserve
">ita deinceps, apponendo ſemper
<
lb
/>
arcui antecedenti arcum Min. </
s
>
<
s
xml:id
="
echoid-s7095
"
xml:space
="
preserve
">45.</
s
>
<
s
xml:id
="
echoid-s7096
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s7097
"
xml:space
="
preserve
">POSTREMO aliorum arcuum chordas inueſtigabimus hac arte. </
s
>
<
s
xml:id
="
echoid-s7098
"
xml:space
="
preserve
">Sit in
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-195-02
"
xlink:href
="
note-195-02a
"
xml:space
="
preserve
">Supputatio
<
lb
/>
chordæ ar-
<
lb
/>
cus grad. 1.</
note
>
ſemicirculo ABCDE, chorda AB, arcus Min.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7099
"
xml:space
="
preserve
">
<
figure
xlink:label
="
fig-195-01
"
xlink:href
="
fig-195-01a
"
number
="
146
">
<
image
file
="
195-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/195-01
"/>
</
figure
>
45. </
s
>
<
s
xml:id
="
echoid-s7100
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s7101
"
xml:space
="
preserve
">AD, chorda arcus grad. </
s
>
<
s
xml:id
="
echoid-s7102
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s7103
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s7104
"
xml:space
="
preserve
">30. </
s
>
<
s
xml:id
="
echoid-s7105
"
xml:space
="
preserve
">at AC,
<
lb
/>
chorda arcus grad. </
s
>
<
s
xml:id
="
echoid-s7106
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s7107
"
xml:space
="
preserve
">quæ inueſtiganda propo-
<
lb
/>
natur. </
s
>
<
s
xml:id
="
echoid-s7108
"
xml:space
="
preserve
">Quoniam igitur maior eſt proportio arcus
<
lb
/>
AC, ad arcum AB, quam chordæ AC, ad chor-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-195-03
"
xlink:href
="
note-195-03a
"
xml:space
="
preserve
">10. huius.</
note
>
dam AB: </
s
>
<
s
xml:id
="
echoid-s7109
"
xml:space
="
preserve
">Habet autem arcus AC, ad arcum AB,
<
lb
/>
proportionẽ ſesquitertiam; </
s
>
<
s
xml:id
="
echoid-s7110
"
xml:space
="
preserve
">habebit chorda AC,
<
lb
/>
ad chordam AB, proportionem minorem, quàm
<
lb
/>
ſeſquitertiam. </
s
>
<
s
xml:id
="
echoid-s7111
"
xml:space
="
preserve
">Cum ergo chorda AB, arcus Min.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7112
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s7113
"
xml:space
="
preserve
">ex præcedentibus inuenta ſit partium ferè 130899. </
s
>
<
s
xml:id
="
echoid-s7114
"
xml:space
="
preserve
">erit chorda AC, ar-
<
lb
/>
cus grad. </
s
>
<
s
xml:id
="
echoid-s7115
"
xml:space
="
preserve
">1 (quæ nimirum ad chordam AB, hoc eſt, ad 130899. </
s
>
<
s
xml:id
="
echoid-s7116
"
xml:space
="
preserve
">minorem pro-
<
lb
/>
portionem habet, quam ſeſquitertiam.) </
s
>
<
s
xml:id
="
echoid-s7117
"
xml:space
="
preserve
">minor, quàm 174532. </
s
>
<
s
xml:id
="
echoid-s7118
"
xml:space
="
preserve
">cum hic nume
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-195-04
"
xlink:href
="
note-195-04a
"
xml:space
="
preserve
">10. quinti.</
note
>
rus ad illum proportionem habeat ſeſquitertiam. </
s
>
<
s
xml:id
="
echoid-s7119
"
xml:space
="
preserve
">Rurſus quia maior eſt pro-
<
lb
/>
portio arcus AD, ad arcum AC, quam chordæ AD, ad chordam AC: </
s
>
<
s
xml:id
="
echoid-s7120
"
xml:space
="
preserve
">Habet
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-195-05
"
xlink:href
="
note-195-05a
"
xml:space
="
preserve
">10. huius.</
note
>
</
s
>
</
p
>
</
div
>
</
text
>
</
echo
>