Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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<
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xml:space
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">EXPLICATIO, ATQVE VSVS TABVLAE</
head
>
<
head
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xml:space
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">præcedentis Sinuum rectorum.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
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"
xml:space
="
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">_IN_vertice præcedentis tabulæ ordine deſcripti ſunt 90. </
s
>
<
s
xml:id
="
echoid-s5733
"
xml:space
="
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">gradus Quadrantis, & </
s
>
<
s
xml:id
="
echoid-s5734
"
xml:space
="
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">
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-180-01
"
xlink:href
="
note-180-01a
"
xml:space
="
preserve
">Expoſitio
<
lb
/>
partium ta
<
lb
/>
bulęSinuũ.</
note
>
ad ſiniſtram deorſum verſus, 60. </
s
>
<
s
xml:id
="
echoid-s5735
"
xml:space
="
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">Minuta. </
s
>
<
s
xml:id
="
echoid-s5736
"
xml:space
="
preserve
">In infimo deinde latere ijdem 90. </
s
>
<
s
xml:id
="
echoid-s5737
"
xml:space
="
preserve
">gradus
<
lb
/>
Quadrantis repoſiti ſunt ordine retrogrado, & </
s
>
<
s
xml:id
="
echoid-s5738
"
xml:space
="
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">ad dexteram ſurſum verſus, 60. </
s
>
<
s
xml:id
="
echoid-s5739
"
xml:space
="
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">Mi-
<
lb
/>
nuta. </
s
>
<
s
xml:id
="
echoid-s5740
"
xml:space
="
preserve
">Quod ideofactum est à nobis, vt illico cuiuslibet arcus complementum cognoſca-
<
lb
/>
tur. </
s
>
<
s
xml:id
="
echoid-s5741
"
xml:space
="
preserve
">Nam quilibet gradus in vertice tabulæ poſitus cum quouis Minuto ad ſiniſtram
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-180-02
"
xlink:href
="
note-180-02a
"
xml:space
="
preserve
">Comple
<
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/>
mẽtum cu
<
lb
/>
iuſuis arcꝰ
<
lb
/>
quo pacto
<
lb
/>
ex hac ta-
<
lb
/>
bula elicia
<
lb
/>
tur.</
note
>
collocato, habet pro complemento gradum in infimo latere gradui accepto in vertice
<
lb
/>
reſpondentem cum Minuto, quod ad dextram Minuto ad ſiniſtram accepto reſpondet.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s5742
"
xml:space
="
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">Vt quomam gradui 46. </
s
>
<
s
xml:id
="
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xml:space
="
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">in vertice, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Minuto O ad ſiniſtram poſito, reſpondet in infi-
<
lb
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mo latere gradus 43. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s5746
"
xml:space
="
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">Minutum 60. </
s
>
<
s
xml:id
="
echoid-s5747
"
xml:space
="
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">ad dexteram collocatum; </
s
>
<
s
xml:id
="
echoid-s5748
"
xml:space
="
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">erit arcus grad. </
s
>
<
s
xml:id
="
echoid-s5749
"
xml:space
="
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">43. </
s
>
<
s
xml:id
="
echoid-s5750
"
xml:space
="
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">
<
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/>
Min. </
s
>
<
s
xml:id
="
echoid-s5751
"
xml:space
="
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">60. </
s
>
<
s
xml:id
="
echoid-s5752
"
xml:space
="
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">hoceſt, arcus grad. </
s
>
<
s
xml:id
="
echoid-s5753
"
xml:space
="
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">44. </
s
>
<
s
xml:id
="
echoid-s5754
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s5755
"
xml:space
="
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">o. </
s
>
<
s
xml:id
="
echoid-s5756
"
xml:space
="
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">complementum arcus grad. </
s
>
<
s
xml:id
="
echoid-s5757
"
xml:space
="
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">46. </
s
>
<
s
xml:id
="
echoid-s5758
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s5759
"
xml:space
="
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">o. </
s
>
<
s
xml:id
="
echoid-s5760
"
xml:space
="
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">Sic
<
lb
/>
quoque arcus grad. </
s
>
<
s
xml:id
="
echoid-s5761
"
xml:space
="
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">43. </
s
>
<
s
xml:id
="
echoid-s5762
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s5763
"
xml:space
="
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">13. </
s
>
<
s
xml:id
="
echoid-s5764
"
xml:space
="
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">complementum habebit arcum grad. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">46 Min. </
s
>
<
s
xml:id
="
echoid-s5766
"
xml:space
="
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">47. </
s
>
<
s
xml:id
="
echoid-s5767
"
xml:space
="
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">Ea-
<
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/>
dem ratione quilibet gradus in infimo latere poſitus cum quouis Minuto ad dexteram
<
lb
/>
collocato, habet pro complemento gradum in vertice gradui acceptoin infimo latere
<
lb
/>
reſpondentem cum Minuto, quod ad ſiniſtram Minuto ad dextram accepto reſpondet. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">
<
lb
/>
Poſtremo ſub gradibus in vertice tabulæ deſcriptis poſiti ſunt ſinus recti omnium ar-
<
lb
/>
cuũ per ſingula Quadrãtis Minuta progredientiũ, quatenus ſinus totus eſt 10000000. </
s
>
<
s
xml:id
="
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xml:space
="
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">
<
lb
/>
Quòd ſi ex ſingulis ſinubus binæ priores figuræ ad dexter am abijciãtur, (addita tamen
<
lb
/>
vnitate, ſi duæ figuræ abiectæ numerum 50. </
s
>
<
s
xml:id
="
echoid-s5770
"
xml:space
="
preserve
">excedunt) reliqui erunt ſinus eorundem
<
lb
/>
arcuum, quatenus ſinus totus eſt 100000. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">vt ſupra diximus. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Vnde quicquid in vſu hu-
<
lb
/>
ius tabulæ præcipiemus de ſinubus reſpectu ſinus totius 10000000. </
s
>
<
s
xml:id
="
echoid-s5773
"
xml:space
="
preserve
">intelligendum quo-
<
lb
/>
que erit de ſinubus reſpectu ſinus totius 100000. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">abiectis nimirum duabus primis fi-
<
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/>
<
note
position
="
left
"
xlink:label
="
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"
xlink:href
="
note-180-03a
"
xml:space
="
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">Vſus tabu-
<
lb
/>
bulę ſinuũ
<
lb
/>
duplex.</
note
>
guris ad dexteram, vt diximus.</
s
>
<
s
xml:id
="
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</
p
>
<
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="
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<
s
xml:id
="
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xml:space
="
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">_HVIVS_tabulæ vſus duplex eſt. </
s
>
<
s
xml:id
="
echoid-s5777
"
xml:space
="
preserve
">Nam in ea vel cuiuslibet arcus inquiritur ſi-
<
lb
/>
nus, vel cuiuſuis ſinus cogniti arcus inueſtigatur. </
s
>
<
s
xml:id
="
echoid-s5778
"
xml:space
="
preserve
">Quando ergo dati arcus Quadrante
<
lb
/>
<
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position
="
left
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xlink:label
="
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xlink:href
="
note-180-04a
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xml:space
="
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">Sinus tectꝰ
<
lb
/>
cuiuſuis ar
<
lb
/>
cus quadrã
<
lb
/>
te minoris
<
lb
/>
quo pacto í
<
lb
/>
tabula repe
<
lb
/>
riatur.</
note
>
minoris ſinum rectum quæris, ſume gradus illius in vertice tabulæ, Minuta vero ad ſini
<
lb
/>
ſtram. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">In communi enim angulo, procedendo nimirum à Minutis dextram verſus, do-
<
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/>
nec adlocum ſub gradibus acceptis peruenias, illico ſinum rectum inuenies. </
s
>
<
s
xml:id
="
echoid-s5780
"
xml:space
="
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">Ita ſinum
<
lb
/>
rectum arcus grad 25. </
s
>
<
s
xml:id
="
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xml:space
="
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">ſub grad 25. </
s
>
<
s
xml:id
="
echoid-s5782
"
xml:space
="
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">è regione Minuti o ad ſinistram collocati repe-
<
lb
/>
ries 4226183. </
s
>
<
s
xml:id
="
echoid-s5783
"
xml:space
="
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">Sinum vero rectum arcus grad. </
s
>
<
s
xml:id
="
echoid-s5784
"
xml:space
="
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">25. </
s
>
<
s
xml:id
="
echoid-s5785
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s5786
"
xml:space
="
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">19. </
s
>
<
s
xml:id
="
echoid-s5787
"
xml:space
="
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">inuenies 4276209. </
s
>
<
s
xml:id
="
echoid-s5788
"
xml:space
="
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">Sinum
<
lb
/>
denique rectum arcus grad. </
s
>
<
s
xml:id
="
echoid-s5789
"
xml:space
="
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">25. </
s
>
<
s
xml:id
="
echoid-s5790
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s5791
"
xml:space
="
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">50. </
s
>
<
s
xml:id
="
echoid-s5792
"
xml:space
="
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">offendes 4357549. </
s
>
<
s
xml:id
="
echoid-s5793
"
xml:space
="
preserve
">Si vero ſinum rectum ar-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-180-05
"
xlink:href
="
note-180-05a
"
xml:space
="
preserve
">Sinꝰ rectus
<
lb
/>
cuiuſuis ar
<
lb
/>
cus quadrã
<
lb
/>
te maioris,
<
lb
/>
qua rõne
<
lb
/>
inueniatur</
note
>
cus Quadrante maioris, ſed ſemicirculo minoris deſideras, detrabe arcum datum ex
<
lb
/>
ſemicirculo, & </
s
>
<
s
xml:id
="
echoid-s5794
"
xml:space
="
preserve
">reſidui arcus ſinum rectum cape, vt prius. </
s
>
<
s
xml:id
="
echoid-s5795
"
xml:space
="
preserve
">Hic enim ſinus erit etiam
<
lb
/>
ſinus rectus arcus quadrante maioris: </
s
>
<
s
xml:id
="
echoid-s5796
"
xml:space
="
preserve
">propterea quòd duo arcus ſemicirculum con-
<
lb
/>
ficientes eundem ſinũ rectum habent, vtin definitionũ expoſitione diximus. </
s
>
<
s
xml:id
="
echoid-s5797
"
xml:space
="
preserve
">Vt ſi da-
<
lb
/>
tus ſit arcus grad. </
s
>
<
s
xml:id
="
echoid-s5798
"
xml:space
="
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">138. </
s
>
<
s
xml:id
="
echoid-s5799
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s5800
"
xml:space
="
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">47. </
s
>
<
s
xml:id
="
echoid-s5801
"
xml:space
="
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">detrabe eum ex ſemicirculo, hoc eſt, ex grad. </
s
>
<
s
xml:id
="
echoid-s5802
"
xml:space
="
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">180.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s5803
"
xml:space
="
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">Sinus namq; </
s
>
<
s
xml:id
="
echoid-s5804
"
xml:space
="
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">rectus 6589082. </
s
>
<
s
xml:id
="
echoid-s5805
"
xml:space
="
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">reſidui arcus grad. </
s
>
<
s
xml:id
="
echoid-s5806
"
xml:space
="
preserve
">41. </
s
>
<
s
xml:id
="
echoid-s5807
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s5808
"
xml:space
="
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">13. </
s
>
<
s
xml:id
="
echoid-s5809
"
xml:space
="
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">eſt quoq; </
s
>
<
s
xml:id
="
echoid-s5810
"
xml:space
="
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">ſinus rectus
<
lb
/>
arcus grad. </
s
>
<
s
xml:id
="
echoid-s5811
"
xml:space
="
preserve
">138. </
s
>
<
s
xml:id
="
echoid-s5812
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s5813
"
xml:space
="
preserve
">47. </
s
>
<
s
xml:id
="
echoid-s5814
"
xml:space
="
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">cum illo arcu grad. </
s
>
<
s
xml:id
="
echoid-s5815
"
xml:space
="
preserve
">41. </
s
>
<
s
xml:id
="
echoid-s5816
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s5817
"
xml:space
="
preserve
">13. </
s
>
<
s
xml:id
="
echoid-s5818
"
xml:space
="
preserve
">ſemicirculũ coficientis.</
s
>
<
s
xml:id
="
echoid-s5819
"
xml:space
="
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"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s5820
"
xml:space
="
preserve
">_QVOD_ſiarcus datus præter gradus, ac minuta habeat etiam Secunda, inquiren-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-180-06
"
xlink:href
="
note-180-06a
"
xml:space
="
preserve
">Sinꝰ rectus
<
lb
/>
cuiuſuis ar
<
lb
/>
cus habẽtis
<
lb
/>
Secũda, prę
<
lb
/>
ter Minuta
<
lb
/>
quomodo
<
lb
/>
eliciat̃ per</
note
>
da erit pars proportionalis, hoc modo. </
s
>
<
s
xml:id
="
echoid-s5821
"
xml:space
="
preserve
">Accipe differentiam inter ſinum rectum arcus
<
lb
/>
proxime minoris, & </
s
>
<
s
xml:id
="
echoid-s5822
"
xml:space
="
preserve
">ſinũ arcus proxime maioris, & </
s
>
<
s
xml:id
="
echoid-s5823
"
xml:space
="
preserve
">dic. </
s
>
<
s
xml:id
="
echoid-s5824
"
xml:space
="
preserve
">Si 60. </
s
>
<
s
xml:id
="
echoid-s5825
"
xml:space
="
preserve
">ſecunda (qui-
<
lb
/>
bus ſinguli arcus proximiin hae tabula inter ſe differunt) requirũt tota eam differen
<
lb
/>
tiam addendam ſinui arcus proxime minoris, vt componatur ſinus arcus proxime
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maioris, quantam differentiam requirunt propoſita ſecunda addendam eidem </
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