Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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24 # 45 # 4186597 # 56 # 15 # 8314696 # 87 # 45 # 9992290 # 75 # 0 # 965925
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27 # 0 # 4539905 # 58 # 30 # 8526402 # 3 # 45 # 654031 # 82 # 30 # 9914449
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9 # 15 # 4886212 # 60 # 45 # 8724960 # 7 # 30 # 1305262 # 86 # 15 # 9978589
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31 # 30 # 5224986 # 63 # 0 # 8910065 # 15 # 0 # 2588190 # 90 # 0 # 10000000
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ſtum eſt, ſinum grad. </
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<
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<
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<
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<
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xml:space
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">componi præciſe ex ſinubus grad. </
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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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<
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xml:space
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ſi ſinus totius, vt ſupra oſtenſum eſt, liquet ſinum grad. </
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<
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<
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ex ſemiſſe ſinus totius, & </
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<
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monſtratum.</
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<
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<
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<
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<
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<
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<
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<
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xml:space
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ſinus arcus
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grad. 12.</
note
>
noti facti ſunt, ita inueſtigabimus. </
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<
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<
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135-01
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/135-01
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te ABC, arcus BD, grad. </
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<
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<
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">& </
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<
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">BE, grad. </
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<
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<
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que adeò arcus DE, eorum differentia, grad. </
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<
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</
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<
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"
xml:space
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">ducanturque rectæ DF, EG, ad AB, perpendi-
<
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culares, quæ ſinus recti erunt arcuum BD, BE; </
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<
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<
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Item rectæ DH, EI, ad AC, perpendiculares,
<
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quæ finus recti erunt arcuum CD, CE, grad. </
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<
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60. </
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<
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<
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<
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">qui complementa ſunt arcuum BD,
<
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BE. </
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<
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">Secet autem recta DH, rectam EG, in K. </
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<
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<
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Et quoniam ſinus DF, hoc eſt, KG, illi æqua-
<
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<
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note
>
lis, & </
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<
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">EG, noti ſunt; </
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<
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">erit quoque eorum diffe-
<
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rentia EK, nota. </
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<
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">Similiter quia ſinus EI, hoc
<
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eſt, KH, illi æqualis, & </
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<
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">DH, noti quoque ſunt, per propof. </
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<
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<
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">cum ſint ſinus
<
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<
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xml:space
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">34. primi.</
note
>
complementorum arcuum BE, BD; </
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<
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xml:space
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">erit etiam eorum differentia DK, nota;
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</
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<
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xml:space
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">ac proinde duo quadrata rectarum notarum Ek, DK, nota erunt: </
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<
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xml:id
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xml:space
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">quæ cum
<
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æqualia ſint quadrato rectæ DE, notum quoque erit quadratum rectæ DE,
<
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<
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proptereaque & </
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<
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xml:space
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">ipſarecta DE, nota erit, nem pe chorda arcus grad. </
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<
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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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">eius medietas nota erit, nimirum ſinus rectus arcus grad. </
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<
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>
<
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<
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">Ex duorũ
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arcuũ ſinu
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bus notis
<
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notus quo-
<
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/>
que ſit ſinꝰ
<
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/>
medietatis
<
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/>
differentiæ
<
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/>
arcuum.</
note
>
particulas 2079117. </
s
>
<
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xml:space
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">Hac eadem arte; </
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<
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xml:space
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">ſi duorum arcuum quorumcumque ſinus
<
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/>
cogniti ſint, cognoſcetur etiam ſinus medietatis differentiæ illorum arcuum.
<
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/>
</
s
>
<
s
xml:id
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xml:space
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">Vt ſi ſinus arcuum BD, BE, quorumcumque etiam ſi non contineant grad. </
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>
<
s
xml:id
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">30. </
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>
<
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& </
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<
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">54. </
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<
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">noti ſint, erunt & </
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<
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">ſinus complementorum CD, CE, per propof. </
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<
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xml:space
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">3. </
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<
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">noti. </
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<
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<
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Quare, vt modo demon ſtrauimus, nota ſiet chorda DE; </
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<
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xml:space
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">ac proinde eius me-
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dietas nota quoque erit, nempe ſinus medietatis arcus DE.</
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<
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</
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<
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<
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<
emph
style
="
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">Cae</
emph
>
<
emph
style
="
sc
">Tervm</
emph
>
ex ſinu arcus grad. </
s
>
<
s
xml:id
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xml:space
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">12. </
s
>
<
s
xml:id
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xml:space
="
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">(ſi hunc arcum bifariam ſecemus
<
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<
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xlink:label
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xlink:href
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xml:space
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">Supputatio
<
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ſinuu ar-
<
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cuum Mi-
<
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nutis 45. ſe
<
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/>
ſe ſupeian-
<
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tium.</
note
>
continue, quoad poſſumus, medietatumq́; </
s
>
<
s
xml:id
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xml:space
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">complementa accipiamus, vnà cum
<
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ſinu complementi arcus grad. </
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<
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xml:id
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xml:space
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">12. </
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>
<
s
xml:id
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xml:space
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">quæ rurſus ſecemus bifariam continue, &</
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<
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xml:id
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xml:space
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">c.)
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</
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<
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">reperiemus per coroll. </
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>
<
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xml:id
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xml:space
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">propof. </
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>
<
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">4. </
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>
<
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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">per propoſ. </
s
>
<
s
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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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">ſinus omnium hor um arcuũ,
<
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qui in hac tabella continentur. </
s
>
<
s
xml:id
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xml:space
="
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">Quos ſinus ſi cum ſinubus proxime antece-
<
lb
/>
dentis tabellæ in ordinem redigamus, habebimus ſinus arcuum numero 120. </
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>
<
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<
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/>
## Arcus # Sinus # ## Arcus # Sinus # ## Arcus # Sinus # ## Arcus # Sinus
<
lb
/>
G # M # # G # M # # G # M # # G # M
<
lb
/>
12 # 0 # 2079117 # 42 # 0 # 6691306 # 12 # 45 # 2206974 # 33 # 0 # 5446390
<
lb
/>
78 # 0 # 9781476 # 48 # 0 # 7431448 # 77 # 15 # 9753423 # 57 # 0 # 8386706
<
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/>
</
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>
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