Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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quàm ſphæricis, docebit, num accipiendus sit arcus quadrante maior proposito ſinui
<
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veſpondens, an vero minor, vt proprijs locis apparebit.</
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<
s
xml:id
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<
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<
s
xml:id
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xml:space
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">_SI_ vero sinus cognitus, eſt sinus complementi arcus quæsiti, ſumendierunt gra-
<
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<
note
position
="
left
"
xlink:label
="
note-184-01
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xlink:href
="
note-184-01a
"
xml:space
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">Arcus qua-
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dranre mi-
<
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/>
nor quo pa
<
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cto ex ſinu
<
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/>
complemẽ
<
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/>
ti cruatur.</
note
>
dus in parte inferiori tabulæ, & </
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>
<
s
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xml:space
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">_M_inuta ad dextram. </
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<
s
xml:id
="
echoid-s6276
"
xml:space
="
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">_I_ta enim habebitur arcus quæ-
<
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situs. </
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>
<
s
xml:id
="
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"
xml:space
="
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">_V_elcerte inueniendus erit arcus, vt prius diximus, ſinui dato, tanquam recto,
<
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/>
reſpondens, is que ex quadrante demendus, vt arcus quæsitus relinquatur. </
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>
<
s
xml:id
="
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"
xml:space
="
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">_V_t si co-
<
lb
/>
gnitus sit _7510767_. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">sinus complementi alicuius arcus. </
s
>
<
s
xml:id
="
echoid-s6280
"
xml:space
="
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">_I_nuenio sinum _7510722_. </
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>
<
s
xml:id
="
echoid-s6281
"
xml:space
="
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">pro-
<
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/>
xime minorem; </
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>
<
s
xml:id
="
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"
xml:space
="
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">quoniam paucioribus hic vnitatibus à sinu cognito diſtat, quàm sinus
<
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/>
_7512642_. </
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>
<
s
xml:id
="
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"
xml:space
="
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">proxime maior in tabula sinuum: </
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>
<
s
xml:id
="
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"
xml:space
="
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">_C_ui sinui proxime minori reſpondent in
<
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/>
ima ſede tabulæ grad. </
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<
s
xml:id
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xml:space
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">_41_. </
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>
<
s
xml:id
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"
xml:space
="
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">& </
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>
<
s
xml:id
="
echoid-s6287
"
xml:space
="
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">ad dexteram _M_inuta _19_. </
s
>
<
s
xml:id
="
echoid-s6288
"
xml:space
="
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">_A_rcus igitur grad. </
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>
<
s
xml:id
="
echoid-s6289
"
xml:space
="
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">_41_. </
s
>
<
s
xml:id
="
echoid-s6290
"
xml:space
="
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">_M_in. </
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>
<
s
xml:id
="
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"
xml:space
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">_19_.
<
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/>
</
s
>
<
s
xml:id
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"
xml:space
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">eſt is, qui quæritur. </
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<
s
xml:id
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xml:space
="
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">_H_uius enim complementum eſt arcus grad. </
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>
<
s
xml:id
="
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"
xml:space
="
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">_48_. </
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>
<
s
xml:id
="
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"
xml:space
="
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">_M_in. </
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>
<
s
xml:id
="
echoid-s6296
"
xml:space
="
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">_41_. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">cui sinus
<
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/>
datus debetur _I_dem arcus grad. </
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>
<
s
xml:id
="
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"
xml:space
="
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">_41_. </
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>
<
s
xml:id
="
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"
xml:space
="
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">_M_in. </
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>
<
s
xml:id
="
echoid-s6300
"
xml:space
="
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">_19_. </
s
>
<
s
xml:id
="
echoid-s6301
"
xml:space
="
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">reperietur, si arcus grad. </
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>
<
s
xml:id
="
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"
xml:space
="
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s
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<
s
xml:id
="
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"
xml:space
="
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">_M_in. </
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>
<
s
xml:id
="
echoid-s6304
"
xml:space
="
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">_41_. </
s
>
<
s
xml:id
="
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xml:space
="
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">
<
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sinui dato in vertice tabulæ, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">ad siniſtram reſpondens ex quadrante ſubducatur. </
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>
<
s
xml:id
="
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xml:space
="
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">
<
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/>
_Q_uòd si partem proportionalem ſupra inuentam, nimirum _S_ec. </
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<
s
xml:id
="
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"
xml:space
="
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">_1._ </
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>
<
s
xml:id
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="
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">detrahas ex arcure
<
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<
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="
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xlink:label
="
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xlink:href
="
note-184-02a
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xml:space
="
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">Arcus qua-
<
lb
/>
drante mi-
<
lb
/>
nor magis
<
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/>
pręcisꝰ, qua
<
lb
/>
via ex ſinu
<
lb
/>
cõplementi
<
lb
/>
@ognoſcat̃.</
note
>
perto grad. </
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<
s
xml:id
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xml:space
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">_41_. </
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<
s
xml:id
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xml:space
="
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">_M_in. </
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>
<
s
xml:id
="
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"
xml:space
="
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">_19_. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">(quia maiorem arcum, quàm par eſt, dato sinui _7510767_. </
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>
<
s
xml:id
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xml:space
="
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">tri-
<
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buimus.) </
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>
<
s
xml:id
="
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"
xml:space
="
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">inuenietur arcus magis præciſus grad. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">_41_. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">_M_in. </
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>
<
s
xml:id
="
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"
xml:space
="
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">_18_. </
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>
<
s
xml:id
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xml:space
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">_S_ec. </
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<
s
xml:id
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"
xml:space
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">_59_. </
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>
<
s
xml:id
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xml:space
="
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">_Q_ui etiam repe-
<
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rietur, si arcum grad. </
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<
s
xml:id
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xml:space
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">_48_. </
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<
s
xml:id
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xml:space
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">_M_in. </
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>
<
s
xml:id
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"
xml:space
="
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">_41_. </
s
>
<
s
xml:id
="
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xml:space
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">_S_ec. </
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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">eidem ſinui, tanquam recto, debitum, & </
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<
s
xml:id
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xml:space
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">ſe-
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cundum partem propertionalem inuentum, detrahas ex quadrante. </
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<
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xml:id
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xml:space
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">_R_urſus detur
<
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_455630_. </
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<
s
xml:id
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xml:space
="
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">sinus complementi alicuius arcus, quem in tabula quæsitum non inuenio.
<
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/>
</
s
>
<
s
xml:id
="
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"
xml:space
="
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">_A_ccipio ergo proxime maiorem _456536_. </
s
>
<
s
xml:id
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xml:space
="
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">(quoniam ab hoc minus diſtat, quàm à pro-
<
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/>
xime minore _453630_.) </
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>
<
s
xml:id
="
echoid-s6333
"
xml:space
="
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">cui in parte inferiori tabulæ reſpondet arcus grad. </
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>
<
s
xml:id
="
echoid-s6334
"
xml:space
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">_87_. </
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>
<
s
xml:id
="
echoid-s6335
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xml:space
="
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">_M_in. </
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<
s
xml:id
="
echoid-s6336
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xml:space
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<
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_23_. </
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<
s
xml:id
="
echoid-s6337
"
xml:space
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">quæſitus; </
s
>
<
s
xml:id
="
echoid-s6338
"
xml:space
="
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">cum huius complementum ſit arcus grad. </
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>
<
s
xml:id
="
echoid-s6339
"
xml:space
="
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">_2_. </
s
>
<
s
xml:id
="
echoid-s6340
"
xml:space
="
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">_M_in. </
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>
<
s
xml:id
="
echoid-s6341
"
xml:space
="
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">_37_. </
s
>
<
s
xml:id
="
echoid-s6342
"
xml:space
="
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">sinui dato, tanquã
<
lb
/>
recto, debitus. </
s
>
<
s
xml:id
="
echoid-s6343
"
xml:space
="
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">_Q_uòd si partem proportionalem ſupra inuentam, nimirum _S_ec. </
s
>
<
s
xml:id
="
echoid-s6344
"
xml:space
="
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">_19_. </
s
>
<
s
xml:id
="
echoid-s6345
"
xml:space
="
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">ad-
<
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/>
das arcui inuento grad. </
s
>
<
s
xml:id
="
echoid-s6346
"
xml:space
="
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">_87_. </
s
>
<
s
xml:id
="
echoid-s6347
"
xml:space
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">_M_in. </
s
>
<
s
xml:id
="
echoid-s6348
"
xml:space
="
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">_23_. </
s
>
<
s
xml:id
="
echoid-s6349
"
xml:space
="
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">(quia minorem arcum, quàm par eſt, dato sinui
<
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/>
_455630_. </
s
>
<
s
xml:id
="
echoid-s6350
"
xml:space
="
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">tribuimus.) </
s
>
<
s
xml:id
="
echoid-s6351
"
xml:space
="
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">inuenietur arcus magis præciſus grad. </
s
>
<
s
xml:id
="
echoid-s6352
"
xml:space
="
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">_87_. </
s
>
<
s
xml:id
="
echoid-s6353
"
xml:space
="
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">_M_in. </
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>
<
s
xml:id
="
echoid-s6354
"
xml:space
="
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">_23_. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">_S_ec. </
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>
<
s
xml:id
="
echoid-s6356
"
xml:space
="
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">_19_. </
s
>
<
s
xml:id
="
echoid-s6357
"
xml:space
="
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">_Q_uẽ
<
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/>
etiam reperies, si arcum grad. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">_2_. </
s
>
<
s
xml:id
="
echoid-s6359
"
xml:space
="
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">_M_in _36_. </
s
>
<
s
xml:id
="
echoid-s6360
"
xml:space
="
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">_S_ec. </
s
>
<
s
xml:id
="
echoid-s6361
"
xml:space
="
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">_41_. </
s
>
<
s
xml:id
="
echoid-s6362
"
xml:space
="
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">eidem sinui, tanquam recto, debitũ,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s6363
"
xml:space
="
preserve
">ſecundum partem proportionalem inuentum, ex quadrante ſubducas _I_am vero si
<
lb
/>
sinus propositus, eſt sinus complementi arcus quadrante maioris, (_Q_uod quãdo fiat,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-184-03
"
xlink:href
="
note-184-03a
"
xml:space
="
preserve
">Arcus qua-
<
lb
/>
drante ma-
<
lb
/>
ior quomo
<
lb
/>
do ex ſinu
<
lb
/>
cõplementi
<
lb
/>
inueſtiget̃.</
note
>
pulchre operatio in triãgulis ſiue rectilineis, ſiue ſphæricis docebit) ſumẽdus erit arcus
<
lb
/>
ei in vertice tabulæ, tanquàm ſinui recto reſpondens, & </
s
>
<
s
xml:id
="
echoid-s6364
"
xml:space
="
preserve
">quadrãti adijciendus, vt ar-
<
lb
/>
cus quæſitus conficiatur. </
s
>
<
s
xml:id
="
echoid-s6365
"
xml:space
="
preserve
">_V_t sisinus complementi alicuius arcus quadrante maioris
<
lb
/>
cognitus sit _7510722_. </
s
>
<
s
xml:id
="
echoid-s6366
"
xml:space
="
preserve
">ſumendus erit arcus ei reſpondens in vertice tabulæ vna cum
<
lb
/>
parte proportionali, grad. </
s
>
<
s
xml:id
="
echoid-s6367
"
xml:space
="
preserve
">_48_. </
s
>
<
s
xml:id
="
echoid-s6368
"
xml:space
="
preserve
">_M_in. </
s
>
<
s
xml:id
="
echoid-s6369
"
xml:space
="
preserve
">_41_. </
s
>
<
s
xml:id
="
echoid-s6370
"
xml:space
="
preserve
">_S_ec. </
s
>
<
s
xml:id
="
echoid-s6371
"
xml:space
="
preserve
">_1._ </
s
>
<
s
xml:id
="
echoid-s6372
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s6373
"
xml:space
="
preserve
">quadranti adijciendus. </
s
>
<
s
xml:id
="
echoid-s6374
"
xml:space
="
preserve
">_C_omponetur
<
lb
/>
enim arcus grad. </
s
>
<
s
xml:id
="
echoid-s6375
"
xml:space
="
preserve
">_138_. </
s
>
<
s
xml:id
="
echoid-s6376
"
xml:space
="
preserve
">_M_in. </
s
>
<
s
xml:id
="
echoid-s6377
"
xml:space
="
preserve
">_41_. </
s
>
<
s
xml:id
="
echoid-s6378
"
xml:space
="
preserve
">_S_ec. </
s
>
<
s
xml:id
="
echoid-s6379
"
xml:space
="
preserve
">_1._ </
s
>
<
s
xml:id
="
echoid-s6380
"
xml:space
="
preserve
">qui quæritur, cuius nimirum complement@
<
lb
/>
datus sinus debetur.</
s
>
<
s
xml:id
="
echoid-s6381
"
xml:space
="
preserve
"/>
</
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>
<
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="
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<
s
xml:id
="
echoid-s6382
"
xml:space
="
preserve
">_
<
emph
style
="
sc
">DENIQVe</
emph
>
_ ex sinu verſo cognito ita arcum inquires. </
s
>
<
s
xml:id
="
echoid-s6383
"
xml:space
="
preserve
">_S_i datus sinus verſus
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-184-04
"
xlink:href
="
note-184-04a
"
xml:space
="
preserve
">Arcus quo
<
lb
/>
pacto ex ſi-
<
lb
/>
nu verſo
<
lb
/>
cruatur.</
note
>
minor eſt, quàm sinus totus, detrahe eum ex sinu toto. </
s
>
<
s
xml:id
="
echoid-s6384
"
xml:space
="
preserve
">_R_eliquus enim eritsinus com-
<
lb
/>
plementi arcus quæsiti. </
s
>
<
s
xml:id
="
echoid-s6385
"
xml:space
="
preserve
">_Q_uare ex hoc, vt proxime docuimus, arcum quæsitum inue-
<
lb
/>
nies. </
s
>
<
s
xml:id
="
echoid-s6386
"
xml:space
="
preserve
">_S_i vero datus sinus verſus sinum totum ſuperat, ſubtrahe ex eo sinum totum.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s6387
"
xml:space
="
preserve
">_R_emanebit enim sinus rectus arcus, qui quadranti adiectus arcum quæsitum conficiet-
<
lb
/>
_E_xemplum. </
s
>
<
s
xml:id
="
echoid-s6388
"
xml:space
="
preserve
">_D_etur ſinus verſus _9544370_. </
s
>
<
s
xml:id
="
echoid-s6389
"
xml:space
="
preserve
">_H_unc detraho ex sinu toto _10000000_. </
s
>
<
s
xml:id
="
echoid-s6390
"
xml:space
="
preserve
">re-
<
lb
/>
manebitq; </
s
>
<
s
xml:id
="
echoid-s6391
"
xml:space
="
preserve
">_455630_. </
s
>
<
s
xml:id
="
echoid-s6392
"
xml:space
="
preserve
">sinus complementi arcus quæsiti, ex quo inuenietur arcus grad. </
s
>
<
s
xml:id
="
echoid-s6393
"
xml:space
="
preserve
">
<
lb
/>
_87_. </
s
>
<
s
xml:id
="
echoid-s6394
"
xml:space
="
preserve
">_M_in. </
s
>
<
s
xml:id
="
echoid-s6395
"
xml:space
="
preserve
">_23_. </
s
>
<
s
xml:id
="
echoid-s6396
"
xml:space
="
preserve
">_V_el partem proportionalem magis præciſus, grad. </
s
>
<
s
xml:id
="
echoid-s6397
"
xml:space
="
preserve
">_87_. </
s
>
<
s
xml:id
="
echoid-s6398
"
xml:space
="
preserve
">_M_in. </
s
>
<
s
xml:id
="
echoid-s6399
"
xml:space
="
preserve
">_23_. </
s
>
<
s
xml:id
="
echoid-s6400
"
xml:space
="
preserve
">_S_ec. </
s
>
<
s
xml:id
="
echoid-s6401
"
xml:space
="
preserve
">_19_. </
s
>
<
s
xml:id
="
echoid-s6402
"
xml:space
="
preserve
">
<
lb
/>
_I_tem sit datus sinus verſus _10455630_. </
s
>
<
s
xml:id
="
echoid-s6403
"
xml:space
="
preserve
">
<
emph
style
="
sc
">E</
emph
>
xhoc ſubduco sinum totum _10000000_. </
s
>
<
s
xml:id
="
echoid-s6404
"
xml:space
="
preserve
">re-
<
lb
/>
linqueturq́; </
s
>
<
s
xml:id
="
echoid-s6405
"
xml:space
="
preserve
">_455630_. </
s
>
<
s
xml:id
="
echoid-s6406
"
xml:space
="
preserve
">sinus rectus, cuius arcus grad. </
s
>
<
s
xml:id
="
echoid-s6407
"
xml:space
="
preserve
">_2_. </
s
>
<
s
xml:id
="
echoid-s6408
"
xml:space
="
preserve
">_M_in. </
s
>
<
s
xml:id
="
echoid-s6409
"
xml:space
="
preserve
">_37_. </
s
>
<
s
xml:id
="
echoid-s6410
"
xml:space
="
preserve
">vel magis præciſus per
<
lb
/>
partem proportionalem inuentus, grad. </
s
>
<
s
xml:id
="
echoid-s6411
"
xml:space
="
preserve
">_2_. </
s
>
<
s
xml:id
="
echoid-s6412
"
xml:space
="
preserve
">_M_in. </
s
>
<
s
xml:id
="
echoid-s6413
"
xml:space
="
preserve
">_36_. </
s
>
<
s
xml:id
="
echoid-s6414
"
xml:space
="
preserve
">_S_ec. </
s
>
<
s
xml:id
="
echoid-s6415
"
xml:space
="
preserve
">_41_. </
s
>
<
s
xml:id
="
echoid-s6416
"
xml:space
="
preserve
">adiectus quadranti efficiet
<
lb
/>
arcum quæsitum grad. </
s
>
<
s
xml:id
="
echoid-s6417
"
xml:space
="
preserve
">_92_. </
s
>
<
s
xml:id
="
echoid-s6418
"
xml:space
="
preserve
">_M_in. </
s
>
<
s
xml:id
="
echoid-s6419
"
xml:space
="
preserve
">_37_. </
s
>
<
s
xml:id
="
echoid-s6420
"
xml:space
="
preserve
">vel magis præciſum, grad. </
s
>
<
s
xml:id
="
echoid-s6421
"
xml:space
="
preserve
">_2_. </
s
>
<
s
xml:id
="
echoid-s6422
"
xml:space
="
preserve
">_M_in. </
s
>
<
s
xml:id
="
echoid-s6423
"
xml:space
="
preserve
">_36_. </
s
>
<
s
xml:id
="
echoid-s6424
"
xml:space
="
preserve
">_S_ec. </
s
>
<
s
xml:id
="
echoid-s6425
"
xml:space
="
preserve
">_41_. </
s
>
<
s
xml:id
="
echoid-s6426
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>