Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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minores ſint arcu grad. </
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<
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xml:space
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">60. </
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<
s
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xml:space
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">detraherentur ex ſinubus omnium arcuum maiorũ, quàm
<
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grad. </
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<
s
xml:id
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xml:space
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">60. </
s
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<
s
xml:id
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echoid-s5550
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xml:space
="
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">remanerent ſinus omnium arcuum à principio quadrantis vſque ad arcum
<
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grad. </
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<
s
xml:id
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echoid-s5551
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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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">Denique ſi ſinus omnium arcuum à principio quadrantis vſque ad arcum
<
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grad. </
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<
s
xml:id
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xml:space
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">60. </
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<
s
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xml:space
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">inuenti eſſent, & </
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>
<
s
xml:id
="
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xml:space
="
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">ſinus omnium arcuum minorum, quàm grad. </
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<
s
xml:id
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xml:space
="
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">30. </
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<
s
xml:id
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xml:space
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">ſinubus
<
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omnium arcuum maiorum, quàm grad. </
s
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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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">adijcerentur, componerentur ſinus omnium
<
lb
/>
arcuum maiorum, quàm grad. </
s
>
<
s
xml:id
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xml:space
="
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">60.</
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<
s
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xml:space
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</
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<
s
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xml:space
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">_SED_ iam ſubijciamus tabulam ſinuum omnium arcuum quadrantis per ſingula
<
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/>
Minuta extenſorumà Ioanne Regiom. </
s
>
<
s
xml:id
="
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xml:space
="
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">ſupputatam, quam tamen pleriſque in locis ab
<
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/>
erroribus, qui incuria typographorum irrepſerant, purgauimus. </
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>
<
s
xml:id
="
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xml:space
="
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">Cõtinet autem in hac
<
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tabula ſinus totus particulas 10000000. </
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>
<
s
xml:id
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"
xml:space
="
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">ratione cuius omnes alij ſinus inuenti ſunt.
<
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/>
</
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<
s
xml:id
="
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xml:space
="
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">Quòd ſi à ſingulis reijciantur primæ duæ figuræ ad dexteram, (addita tamen vnita-
<
lb
/>
te, ſi duæ figuræ abiectæ numerum maiorem conſtituant, quàm 50.) </
s
>
<
s
xml:id
="
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xml:space
="
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">relinquetur ſinus
<
lb
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reſpectu ſinus totius 100000. </
s
>
<
s
xml:id
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xml:space
="
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">Si tamen quis eandem tabulam per præcepta tradita
<
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<
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position
="
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xlink:label
="
note-141-01
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xlink:href
="
note-141-01a
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xml:space
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">Quid ageu
<
lb
/>
dum, vt ſe-
<
lb
/>
quens tabu
<
lb
/>
la ſinuum
<
lb
/>
exquiſite có
<
lb
/>
ſtruat, poſi-
<
lb
/>
to ſinu to-
<
lb
/>
to partium
<
lb
/>
10000000.</
note
>
proprio Marte conſtrnere velit, poſito ſinu toto partium 10000000. </
s
>
<
s
xml:id
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xml:space
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">conſtituendus
<
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ei erit ſinus totus in ſupputatione partium 1000000000. </
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<
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xml:space
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">_N_am ſi ex ſingulis ſinubus
<
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inuentis abijciantur duæ primæ figuræ ad dexteram, vt diximus, reliqui erunt ſinus
<
lb
/>
reſpectu ſinus totius 10000000. </
s
>
<
s
xml:id
="
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xml:space
="
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">ijdem omnino, qui in tabula Ioannis Regiom. </
s
>
<
s
xml:id
="
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xml:space
="
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">de-
<
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ſcripti ſunt. </
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<
s
xml:id
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xml:space
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">_H_oc idcirco dico, ne mireris, non omnes ſinus per regulam proportionũ
<
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inuentos ex ſinubus arcuum Minutis 45. </
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<
s
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xml:space
="
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">ſe ordine ſuperantium, poſito ſinu toto
<
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/>
10000000. </
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>
<
s
xml:id
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xml:space
="
preserve
">ad vnguem reſpondere ſinubus huius tabulæ. </
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<
s
xml:id
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xml:space
="
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">Vt enim ſinus exquiſitere-
<
lb
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periatur reſpectu alicuius ſinus totius, conſtituendus eſt in ſupputatione ſinus totus
<
lb
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centies maior, vt ſupra dictum eſt.</
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<
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</
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<
s
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xml:space
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">_QVOD_ autẽ, abiectis duabus primis figuris ad dexterã ex ſingulis ſinubus, rema
<
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<
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position
="
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xlink:label
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xlink:href
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note-141-02a
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xml:space
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">Ratio,
<
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/>
cur abtectis
<
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/>
duabus pri
<
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/>
mis figuris
<
lb
/>
ex ſinu
<
lb
/>
quocũque
<
lb
/>
reſpectu ſi-
<
lb
/>
nus totius
<
lb
/>
10000000.
<
lb
/>
relinqua -
<
lb
/>
tut idé ſi-
<
lb
/>
nus reſpe-
<
lb
/>
ctu ſinꝰ to-
<
lb
/>
tiꝰ 100000.
<
lb
/>
licet prior
<
lb
/>
ille Ron ſit
<
lb
/>
exquiſitein
<
lb
/>
uentus.</
note
>
neant ſinus exquiſiti reſpectu ſinus totius 100000. </
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>
<
s
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xml:space
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">quàmuis priores illi nõ ſint exqui
<
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ſite inuenti, manifeſtũ eſt. </
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>
<
s
xml:id
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xml:space
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">Quoniã enim ſinus totus, ſiue ſemidiameter ad ſinum rectũ
<
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quemcumq; </
s
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<
s
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">determinatã quandã proportionẽ habet; </
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<
s
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xml:space
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">fit, vt omnes partes illius, quot-
<
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cunq; </
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<
s
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xml:space
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">illæ ſint, ad partes huius inuẽtas reſpectu illarũ partiũ ſinus totius eandẽ habeãt
<
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/>
proportionem, quam omnes partes eiusdẽ ſinus totius pauciores, quàm illæ priores, ha
<
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/>
bent ad partes eiuſdem ſinus reſpectu illarum partium ſinus totius pauciorum : </
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<
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quin ſinus totus non haberet ſemper ad eundem ſinum eandem proportionem, ſed ali-
<
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quando eſſet maioris quantitatis reſpectu illius, & </
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<
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xml:space
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">ali quando minoris : </
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<
s
xml:id
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xml:space
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">quod eſt ab-
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ſurdum. </
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<
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xml:id
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xml:space
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">Quocirca ſi ſinus cuiuslibet arcus, vt v. </
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<
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xml:id
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">g illius, qui continet grad. </
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<
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xml:space
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">28. </
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<
s
xml:id
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xml:space
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">inuen-
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tus ſit reſpectu ſinus totius in quotuis particulas diſtributi, facile per regulam pro-
<
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/>
portionum inueniemus eundem ſinũ reſpectu eiuſdem ſinus totius in pauciores partes
<
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/>
diuiſi, ſi ita dicamus. </
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<
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xml:id
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xml:space
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">Si ſinus totus partium 10000000. </
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<
s
xml:id
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xml:space
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">dat ſinum arcus grad. </
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<
s
xml:id
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xml:space
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">28. </
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<
s
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">par
<
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tium 4694716. </
s
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<
s
xml:id
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xml:space
="
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">Idem ſinus totus partium 100000. </
s
>
<
s
xml:id
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xml:space
="
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">quot partium dabit ſinam eiuſdẽ
<
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arcus grad. </
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<
s
xml:id
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">28? </
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<
s
xml:id
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xml:space
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">Inueniemus enim ſinum partium 46947 {1600000/10000000}. </
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<
s
xml:id
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xml:space
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">Omiſ-
<
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ſa autem hac fractione, (quòd minor ſit, quàm vnitas.) </
s
>
<
s
xml:id
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xml:space
="
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">continebit idem ſinus partes
<
lb
/>
duntaxat 46947. </
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>
<
s
xml:id
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xml:space
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">quemadmodum in tabulis ſinuum ponitur, in quibus ſinus totus
<
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/>
continet partes 100000. </
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>
<
s
xml:id
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xml:space
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">Vbi vides, ſinum hunc relinqui, ſi ex illo duæ primæ figuræ
<
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ad dexteram abijciantur. </
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>
<
s
xml:id
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xml:space
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">Ratio huius abiectionis eſt; </
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<
s
xml:id
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xml:space
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">quia vt ſinus ille grad. </
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<
s
xml:id
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">28. </
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>
<
s
xml:id
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xml:space
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">mul-
<
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tiplicatus per ſinum totum 100000 (quæ multiplicatio fit per appoſitionem quinque
<
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/>
cifrarũ, hoc modo; </
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>
<
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">469471600000. </
s
>
<
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xml:id
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xml:space
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">vt in cap. </
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>
<
s
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xml:space
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">4. </
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>
<
s
xml:id
="
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xml:space
="
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">Arithmeticæ diximus.) </
s
>
<
s
xml:id
="
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"
xml:space
="
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">diuidatur per
<
lb
/>
ſinum totum 10000000. </
s
>
<
s
xml:id
="
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xml:space
="
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">vt regula proportionnm præcipit; </
s
>
<
s
xml:id
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"
xml:space
="
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">ſatis eſt, ſi ex numero pro-
<
lb
/>
ducto reijciantur ſeptem figuræ, quotnimirum cifræ ſunt in diuiſore 10000000.
<
lb
/>
</
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<
s
xml:id
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">vt in cap. </
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<
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xml:id
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">5. </
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>
<
s
xml:id
="
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xml:space
="
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">Arithmeticæ docuimus. </
s
>
<
s
xml:id
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"
xml:space
="
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">Quare reijciendæ ſunt quing; </
s
>
<
s
xml:id
="
echoid-s5618
"
xml:space
="
preserve
">illæ cifræ appoſitæ,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s5619
"
xml:space
="
preserve
">præterea duæ figuræ primæ, nẽpe hic numerus 1600000. </
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>
<
s
xml:id
="
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"
xml:space
="
preserve
">qui cum diuiſore hanc </
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