Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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quidem ſinus eſt arcus BD. </
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<
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<
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note-137-01
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ſinus grad.
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1.</
note
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BH. </
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<
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">Sit ergo propoſitum inuenire ſinum OK, arcus BD, grad. </
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<
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<
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xml:space
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NK, ſinus grad. </
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<
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">0. </
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<
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<
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<
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xml:space
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<
s
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xml:space
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">erit eius tertia pars, nempe
<
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43632. </
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<
s
xml:id
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xml:space
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">maior, quàm MN: </
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<
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<
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xml:space
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">1. </
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<
s
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xml:space
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">maior eſt KL, quàm
<
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LM, & </
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<
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">LM, maior, quàm MN, adeo vt MN, mi-
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<
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nor ſit, quàm tertia pars ipſius NK, hoc eſt, minor,
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quàm 43632. </
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<
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="
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xml:space
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">Multo igitur maior erit eadem tertia
<
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pars rectæ NK, nempe 43632. </
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<
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="
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">quàm NO: </
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>
<
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xml:id
="
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"
xml:space
="
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">quod, per
<
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eandẽ propof. </
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>
<
s
xml:id
="
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"
xml:space
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">1. </
s
>
<
s
xml:id
="
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xml:space
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">maior quoque ſit MN, quàm NO.
<
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</
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>
<
s
xml:id
="
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xml:space
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">Quare ſi addamus 43632. </
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<
s
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xml:space
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">ad 130896. </
s
>
<
s
xml:id
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xml:space
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">id eſt, ad NK,
<
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ſinum Minutorum 45. </
s
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<
s
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="
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"
xml:space
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">efficiemus numerum 174528. </
s
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<
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qui maior erit, quàm OK, ſinus rectus grad. </
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<
s
xml:id
="
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"
xml:space
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">1. </
s
>
<
s
xml:id
="
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"
xml:space
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">quan
<
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/>
doquidem ad NK, plus addimus, quàm rectã NO,
<
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/>
vt dictum eſt. </
s
>
<
s
xml:id
="
echoid-s5037
"
xml:space
="
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">Rurſus quia EK, ſinus grad. </
s
>
<
s
xml:id
="
echoid-s5038
"
xml:space
="
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">1. </
s
>
<
s
xml:id
="
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"
xml:space
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">Min. </
s
>
<
s
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="
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"
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">
<
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30. </
s
>
<
s
xml:id
="
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"
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">inuentus eſt 261769. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ſi ex eo detrahamus ſinum NK, Minutorum 45. </
s
>
<
s
xml:id
="
echoid-s5043
"
xml:space
="
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">nem
<
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/>
pe 130896. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">relinquetur recta EN, partium 130873. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">cuius tertia pars, nempe
<
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/>
43624. </
s
>
<
s
xml:id
="
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xml:space
="
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">fere, minor erit, quàm NO: </
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>
<
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">propterea quod, per propof. </
s
>
<
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xml:id
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xml:space
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">1. </
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>
<
s
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">maior eſt
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NO, quàm OP, & </
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<
s
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xml:space
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">OP, maior, quàm PE, adeo vt NO, maior ſit, quàm ter-
<
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tia parsipſius EN, hoc eſt, maior, quàm 43624. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Quare ſi addamus 43624. </
s
>
<
s
xml:id
="
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xml:space
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">ad
<
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/>
130896. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">id eſt, ad NK, ſinum Min. </
s
>
<
s
xml:id
="
echoid-s5054
"
xml:space
="
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">45. </
s
>
<
s
xml:id
="
echoid-s5055
"
xml:space
="
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">efficiemus numerum 174520. </
s
>
<
s
xml:id
="
echoid-s5056
"
xml:space
="
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">qui minor
<
lb
/>
erit, quàm OK, ſinus re ctus grad. </
s
>
<
s
xml:id
="
echoid-s5057
"
xml:space
="
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">1. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">quandoquidem ad NK, minus addimus,
<
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quàm rectam NO. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Conſtatigitur, ſinum rectum grad. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">1. </
s
>
<
s
xml:id
="
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"
xml:space
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">conſiſtere inter hos
<
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duos numeros, 174528. </
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>
<
s
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"
xml:space
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">174520. </
s
>
<
s
xml:id
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xml:space
="
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">cum ille maior ſit, hic auté minor. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Statuamus
<
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/>
ergo eum eſſe, 174524. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">inter illos numeros omnino medium. </
s
>
<
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xml:id
="
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"
xml:space
="
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">Ita enim non dif-
<
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feret ſenſibiliter hic numerus à vero ſinu grad. </
s
>
<
s
xml:id
="
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xml:space
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">1.</
s
>
<
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</
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<
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<
s
xml:id
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xml:space
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">EX hoc ſinu grad. </
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<
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xml:space
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">1. </
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>
<
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">inueniemus, per propoſ. </
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<
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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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">ſinum eius cõplementi, hoc
<
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<
note
position
="
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xlink:label
="
note-137-02
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xlink:href
="
note-137-02a
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xml:space
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">Supputatio
<
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ſinus grad.
<
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/>
89.</
note
>
eſt, ſinum arcus grad. </
s
>
<
s
xml:id
="
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"
xml:space
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">89. </
s
>
<
s
xml:id
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xml:space
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">eſſe 9998477. </
s
>
<
s
xml:id
="
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"
xml:space
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">Quem hoc etiã modo reperiemus. </
s
>
<
s
xml:id
="
echoid-s5077
"
xml:space
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">Quo-
<
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/>
niam numerus 174528. </
s
>
<
s
xml:id
="
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xml:space
="
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">maior eſt, quam ſinus grad. </
s
>
<
s
xml:id
="
echoid-s5079
"
xml:space
="
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">1. </
s
>
<
s
xml:id
="
echoid-s5080
"
xml:space
="
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">vt diximus: </
s
>
<
s
xml:id
="
echoid-s5081
"
xml:space
="
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">ſit, vt per eum
<
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/>
inueſtigatus, iuxta doctrinam propof. </
s
>
<
s
xml:id
="
echoid-s5082
"
xml:space
="
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">3. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ſinus cóplementi grad. </
s
>
<
s
xml:id
="
echoid-s5084
"
xml:space
="
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">1. </
s
>
<
s
xml:id
="
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xml:space
="
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">hoc eſt, ſinus
<
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/>
grad. </
s
>
<
s
xml:id
="
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"
xml:space
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">89. </
s
>
<
s
xml:id
="
echoid-s5087
"
xml:space
="
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">ſit numerus 9998476. </
s
>
<
s
xml:id
="
echoid-s5088
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s5089
"
xml:space
="
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">paulo amplius, qui minor erit neceſſario,
<
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/>
quàm verus ſinus arcus grad. </
s
>
<
s
xml:id
="
echoid-s5090
"
xml:space
="
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">89. </
s
>
<
s
xml:id
="
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"
xml:space
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">quandoquidem pro ſinu grad. </
s
>
<
s
xml:id
="
echoid-s5092
"
xml:space
="
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">1. </
s
>
<
s
xml:id
="
echoid-s5093
"
xml:space
="
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">numerum
<
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/>
ſumpſimus vero ſinu maiorem. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Rurſus quia numerus 174520. </
s
>
<
s
xml:id
="
echoid-s5095
"
xml:space
="
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">minor eſt, quàm
<
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/>
ſinus grad. </
s
>
<
s
xml:id
="
echoid-s5096
"
xml:space
="
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">1. </
s
>
<
s
xml:id
="
echoid-s5097
"
xml:space
="
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">vt diximus; </
s
>
<
s
xml:id
="
echoid-s5098
"
xml:space
="
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">fit, vt per eum inueſtigatus, iuxta doctrinam propof.
<
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/>
</
s
>
<
s
xml:id
="
echoid-s5099
"
xml:space
="
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">3. </
s
>
<
s
xml:id
="
echoid-s5100
"
xml:space
="
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">ſinus eius complementi, nimirum ſinus grad. </
s
>
<
s
xml:id
="
echoid-s5101
"
xml:space
="
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">89. </
s
>
<
s
xml:id
="
echoid-s5102
"
xml:space
="
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">ſit numerus 9998477. </
s
>
<
s
xml:id
="
echoid-s5103
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s5104
"
xml:space
="
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">pau
<
lb
/>
lo amplius, qui maior erit neceſſario, quàm verus ſinus grad. </
s
>
<
s
xml:id
="
echoid-s5105
"
xml:space
="
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">89. </
s
>
<
s
xml:id
="
echoid-s5106
"
xml:space
="
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">quandoqui-
<
lb
/>
dem pro ſinu grad. </
s
>
<
s
xml:id
="
echoid-s5107
"
xml:space
="
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">1. </
s
>
<
s
xml:id
="
echoid-s5108
"
xml:space
="
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">numerum accepimus vero ſinu minorem. </
s
>
<
s
xml:id
="
echoid-s5109
"
xml:space
="
preserve
">Conſtitutus er-
<
lb
/>
go erit ſinus grad. </
s
>
<
s
xml:id
="
echoid-s5110
"
xml:space
="
preserve
">89. </
s
>
<
s
xml:id
="
echoid-s5111
"
xml:space
="
preserve
">inter duos hos numeros 9998476. </
s
>
<
s
xml:id
="
echoid-s5112
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s5113
"
xml:space
="
preserve
">paulo amplius, at-
<
lb
/>
que 9998477. </
s
>
<
s
xml:id
="
echoid-s5114
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s5115
"
xml:space
="
preserve
">paulo amplius: </
s
>
<
s
xml:id
="
echoid-s5116
"
xml:space
="
preserve
">ac proinde ſine notabili errore eum ſtatuemus
<
lb
/>
eſſe 9998477. </
s
>
<
s
xml:id
="
echoid-s5117
"
xml:space
="
preserve
">quantum videlicet eundem inuenimus ex ſinugrad. </
s
>
<
s
xml:id
="
echoid-s5118
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s5119
"
xml:space
="
preserve
">Ex quo
<
lb
/>
conſtat, recte conſtitutum eſſe ſinum grad. </
s
>
<
s
xml:id
="
echoid-s5120
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s5121
"
xml:space
="
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">partium 174524. </
s
>
<
s
xml:id
="
echoid-s5122
"
xml:space
="
preserve
">cum ex eo, per
<
lb
/>
propoſ. </
s
>
<
s
xml:id
="
echoid-s5123
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s5124
"
xml:space
="
preserve
">repertus ſit ſinus complementiipſius tot particularum, quot vere ac
<
lb
/>
reipſa continere debet.</
s
>
<
s
xml:id
="
echoid-s5125
"
xml:space
="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s5126
"
xml:space
="
preserve
">PRAETEREA ex finu arcus grad. </
s
>
<
s
xml:id
="
echoid-s5127
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s5128
"
xml:space
="
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">reperiemus, per coroll. </
s
>
<
s
xml:id
="
echoid-s5129
"
xml:space
="
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">propoſ. </
s
>
<
s
xml:id
="
echoid-s5130
"
xml:space
="
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">4.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s5131
"
xml:space
="
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">
<
note
position
="
right
"
xlink:label
="
note-137-03
"
xlink:href
="
note-137-03a
"
xml:space
="
preserve
">Supputatie
<
lb
/>
ſinus Min.
<
lb
/>
30. & ſinus
<
lb
/>
grad. 89.
<
lb
/>
Min. 30. It@
<
lb
/>
ſinus Min.
<
lb
/>
15. & ſinus
<
lb
/>
grad. 89.
<
lb
/>
Min. 45.</
note
>
ſinum rectum arcus Min. </
s
>
<
s
xml:id
="
echoid-s5132
"
xml:space
="
preserve
">30. </
s
>
<
s
xml:id
="
echoid-s5133
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s5134
"
xml:space
="
preserve
">ex hoc, per propoſ. </
s
>
<
s
xml:id
="
echoid-s5135
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s5136
"
xml:space
="
preserve
">ſinum complementi, nem-
<
lb
/>
pe ſinum grad. </
s
>
<
s
xml:id
="
echoid-s5137
"
xml:space
="
preserve
">89. </
s
>
<
s
xml:id
="
echoid-s5138
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s5139
"
xml:space
="
preserve
">30. </
s
>
<
s
xml:id
="
echoid-s5140
"
xml:space
="
preserve
">Item ex ſinu arcus Min. </
s
>
<
s
xml:id
="
echoid-s5141
"
xml:space
="
preserve
">30. </
s
>
<
s
xml:id
="
echoid-s5142
"
xml:space
="
preserve
">inueniemus, per coroll.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s5143
"
xml:space
="
preserve
">propoſ. </
s
>
<
s
xml:id
="
echoid-s5144
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s5145
"
xml:space
="
preserve
">ſinum arcus Min. </
s
>
<
s
xml:id
="
echoid-s5146
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s5147
"
xml:space
="
preserve
">atque ex hoe ſinum complementi, hoc eſt, ſi-
<
lb
/>
num grad. </
s
>
<
s
xml:id
="
echoid-s5148
"
xml:space
="
preserve
">89. </
s
>
<
s
xml:id
="
echoid-s5149
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s5150
"
xml:space
="
preserve
">45.</
s
>
<
s
xml:id
="
echoid-s5151
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s5152
"
xml:space
="
preserve
">QVEMADMODVM autem ſupra ex ſinubus rectis grad. </
s
>
<
s
xml:id
="
echoid-s5153
"
xml:space
="
preserve
">30. </
s
>
<
s
xml:id
="
echoid-s5154
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s5155
"
xml:space
="
preserve
">54.</
s
>
<
s
xml:id
="
echoid-s5156
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>