Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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ſuperantium, reſpectu Sinus totius particularum 100000. </
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>
<
s
xml:id
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echoid-s4586
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xml:space
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">quotnimirum com
<
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muniter ab omnibus, & </
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>
<
s
xml:id
="
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"
xml:space
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">ànobis etiam conſtituitur, vt ſupra diximus. </
s
>
<
s
xml:id
="
echoid-s4588
"
xml:space
="
preserve
">Vt auté
<
lb
/>
accuratior ſiat ſupputatio, ponemus in hiſce ſupputationibus Sinum totum
<
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/>
<
note
position
="
right
"
xlink:label
="
note-131-01
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xlink:href
="
note-131-01a
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xml:space
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">Sinus totꝰ
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in cuiꝰ par
<
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/>
tibꝰ alij ſi-
<
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/>
nus ompu
<
lb
/>
tátur, quoe
<
lb
/>
particula
<
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/>
rú ponédus
<
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/>
ſit, vt alij
<
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/>
ſinus inue-
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/>
niátur ma-
<
lb
/>
gis exquiſi
<
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/>
ti reſp ectu
<
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/>
Sinus to-
<
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/>
tius pattiũ
<
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/>
100000. vel
<
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/>
pauciotum
<
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/>
pluriúve.</
note
>
partium 10000000. </
s
>
<
s
xml:id
="
echoid-s4589
"
xml:space
="
preserve
">Ita enim fiet, vt abiectis duabus primis figuris ad dexte-
<
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/>
rá ex ſingulis ſinubus inuentis, (addita tamen vnitate, ſi duæ figuræ abiectæ nu
<
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/>
merũ 50. </
s
>
<
s
xml:id
="
echoid-s4590
"
xml:space
="
preserve
">ſuperent) relinquãtur ſinus magis exquiſiti reſpectu ſinus totius par
<
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/>
tium 100000. </
s
>
<
s
xml:id
="
echoid-s4591
"
xml:space
="
preserve
">Quòd ſi quis ſinus deſideret plurium particularum, poſito ni-
<
lb
/>
mirũ ſinu toto partiũ 10000000. </
s
>
<
s
xml:id
="
echoid-s4592
"
xml:space
="
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">quot eum Ioan. </
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<
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">Regiom. </
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<
s
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">poſuit, & </
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>
<
s
xml:id
="
echoid-s4595
"
xml:space
="
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">nos in ſe
<
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/>
quẽti tabula ſtatuemus, conſtituendus erit Sinus totus partiũ 1000000000.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4596
"
xml:space
="
preserve
">Nam hac ratione, abiectis duabus primis figuris ad dexteram ex ſingulis ſinu-
<
lb
/>
bus inuentis, vt dictum eſt, remanebunt Sinus magis exquiſiti reſpectu Sinus
<
lb
/>
totius partium 10000000. </
s
>
<
s
xml:id
="
echoid-s4597
"
xml:space
="
preserve
">Ratio huius rei eſt, quòd in ſinuum inueſtigatio-
<
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ne error ſolum contingere poteſt in vna aut altera figura ad dextram: </
s
>
<
s
xml:id
="
echoid-s4598
"
xml:space
="
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">quare,
<
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/>
abiectis duabus figuris ad dextram, relinquentur ſinus reſpectu ſinus totius
<
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/>
minoris exquiſrtiſsimi. </
s
>
<
s
xml:id
="
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"
xml:space
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">Id quod in ſupputationibus ſinuum quiuis facile ex pe-
<
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rietur, & </
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>
<
s
xml:id
="
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xml:space
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">nos infra demonſtrabimus. </
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>
<
s
xml:id
="
echoid-s4601
"
xml:space
="
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">Pari ratione, ſi inueſtigandi ſint ſinus re-
<
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ſpectu alterius Sinus totius, qui plures, aut pauciores particulas contineat,
<
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/>
quàm 100000. </
s
>
<
s
xml:id
="
echoid-s4602
"
xml:space
="
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">vel 10000000. </
s
>
<
s
xml:id
="
echoid-s4603
"
xml:space
="
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">conſtituendus erit in ſupputatione Sinus to-
<
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/>
tus, qui ad dexteram illum ſuperet duabus figuris his, 00; </
s
>
<
s
xml:id
="
echoid-s4604
"
xml:space
="
preserve
">adeo vt illius ſit
<
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/>
centuplus, quemadmodum & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">hic 10000000. </
s
>
<
s
xml:id
="
echoid-s4606
"
xml:space
="
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">quem in calculo aſſumimus, cen-
<
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tuplus eſt illius 100000. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">quem nos cum alijs Aſtronomis in vſu recipimus.</
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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">SIT igitur in quadrante ABC, arcus CD, grad. </
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<
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">15. </
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<
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">CE, 30. </
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<
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">CF, 45. </
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<
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">ac
<
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proinde EB, 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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">DB, 75. </
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<
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">vtpote complementa arcuum grad. </
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<
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">30. </
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<
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">& </
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<
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">15.
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</
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<
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xml:space
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">Horum ergo arcuum ſinus rectos ita ſupputabimus. </
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<
s
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xml:space
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">Ducantur EH, DI, ad AB,
<
lb
/>
perpendiculares, quæ ſinus recti erunt arcuum grad. </
s
>
<
s
xml:id
="
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">60. </
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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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">grad. </
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<
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>
<
s
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xml:space
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">Ductam
<
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autem chordam BC, ſecet recta AF, in L, bi-
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<
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xlink:href
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number
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<
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="
131-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/131-01
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</
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>
fariam, ex lemmate in definitionibus demon-
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ſtrato; </
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>
<
s
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xml:space
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">ac proinde ad angulos rectos: </
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>
<
s
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">eritq̀ue
<
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<
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position
="
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xlink:label
="
note-131-02
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="
note-131-02a
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xml:space
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">3. tertij.</
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>
BL, ſinus rectus grad. </
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<
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">45. </
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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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">Ducatur rurſus EG, ad AC, perpendicula-
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ris pro ſinu grad. </
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>
<
s
xml:id
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xml:space
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">30. </
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>
<
s
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xml:space
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">Item ductam chordã CE,
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<
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xlink:label
="
note-131-03
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xlink:href
="
note-131-03a
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xml:space
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">Supputatio
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ſinuum ar
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cuũ gradi-
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bus 15. ſeſe
<
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ſuperantiũ
<
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quales ſunt
<
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/>
arcus grad.
<
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/>
15. 30. 45.
<
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/>
60. 75. &
<
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90.</
note
>
ſecet recta AD, in K, bifariam, ex dicto lem-
<
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mate; </
s
>
<
s
xml:id
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"
xml:space
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">ac propterea ad angulos rectos; </
s
>
<
s
xml:id
="
echoid-s4636
"
xml:space
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">eritq́ue
<
lb
/>
CK, ſinus rectus grad. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">15. </
s
>
<
s
xml:id
="
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"
xml:space
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">Denique rectæ iun-
<
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gantur AE, EB. </
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>
<
s
xml:id
="
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"
xml:space
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">Quoniam igitur arcus BE,
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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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">ſexta pars eſt totius circunferentiæ
<
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circuli, cum ſexies 60. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ſaciant 360. </
s
>
<
s
xml:id
="
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"
xml:space
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">grad. </
s
>
<
s
xml:id
="
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"
xml:space
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">erit
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recta BE, latus Hexagoni; </
s
>
<
s
xml:id
="
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"
xml:space
="
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">atque adeo, ex
<
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coroll. </
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>
<
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xml:space
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">propof. </
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>
<
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">15. </
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<
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xml:space
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">lib. </
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<
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">4. </
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<
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">Euel. </
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<
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="
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xml:space
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">ſemidiametro AE, æqualis. </
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>
<
s
xml:id
="
echoid-s4652
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xml:space
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">Anguliergo EAB,
<
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EBA, æquales erunt: </
s
>
<
s
xml:id
="
echoid-s4653
"
xml:space
="
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">Sunt autem & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">anguli ad H, æquales, vtpote recti. </
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>
<
s
xml:id
="
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"
xml:space
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">Igi-
<
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<
note
position
="
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xlink:label
="
note-131-04
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xlink:href
="
note-131-04a
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xml:space
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">5. primi.</
note
>
tur cum duo anguli EAH, EHA, trianguli AEH, æquales ſint duobus an-
<
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gulis EBH, EHB, trianguli BEH, latusq́ue AE, lateri BE, æquale; </
s
>
<
s
xml:id
="
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"
xml:space
="
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">erit la-
<
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tus AH, lateri BH, æquale; </
s
>
<
s
xml:id
="
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"
xml:space
="
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">ac proinde AH, medietas erit ſemidia metri AB.
<
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</
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>
<
s
xml:id
="
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xml:space
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">
<
note
position
="
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"
xlink:label
="
note-131-05
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xlink:href
="
note-131-05a
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xml:space
="
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">26. primi.</
note
>
Quare cum EG, ſinus rectus grad. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">30. </
s
>
<
s
xml:id
="
echoid-s4660
"
xml:space
="
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">ſit ipſi AH, æqualis, erit ſinus rectus
<
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/>
<
note
position
="
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"
xlink:label
="
note-131-06
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xlink:href
="
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xml:space
="
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">34. primi.</
note
>
grad. </
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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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">medietati ſemidiametri, ſiue ſinus totius, æqualis. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Cum ergo ſinus
<
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<
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position
="
right
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xlink:label
="
note-131-07
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xlink:href
="
note-131-07a
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xml:space
="
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">Sinus rectꝰ
<
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/>
grad. 30. æ-
<
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/>
qualis eſt
<
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/>
medietati
<
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/>
ſinus totiꝰ;</
note
>
totus ponatur 10000000. </
s
>
<
s
xml:id
="
echoid-s4664
"
xml:space
="
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">erit EG, ſinus grad. </
s
>
<
s
xml:id
="
echoid-s4665
"
xml:space
="
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">30. </
s
>
<
s
xml:id
="
echoid-s4666
"
xml:space
="
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">talium particularum
<
lb
/>
5000000. </
s
>
<
s
xml:id
="
echoid-s4667
"
xml:space
="
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">nempe medietas ſinus totius.</
s
>
<
s
xml:id
="
echoid-s4668
"
xml:space
="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4669
"
xml:space
="
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">EX hoc ſinu, per propof. </
s
>
<
s
xml:id
="
echoid-s4670
"
xml:space
="
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">3. </
s
>
<
s
xml:id
="
echoid-s4671
"
xml:space
="
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">cognoſcetur ſinus complementi arcus grad. </
s
>
<
s
xml:id
="
echoid-s4672
"
xml:space
="
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">30.</
s
>
<
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="
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"/>
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