Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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<
s
xml:id
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"
xml:space
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">_CAETERVM_ _Q_uadrantist tam ſinus rectus, quàm verſus eſt ſinus totus; </
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>
<
s
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="
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xml:space
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">ſinus
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<
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="
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xlink:label
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note-183-01
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xlink:href
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note-183-01a
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xml:space
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">Sinus tã re
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ctus, q̃ ver-
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ſus Quadiã
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tis eſt ſinus
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totus, ſinus
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/>
vero cõple-
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menti ni-
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hil eſt.</
note
>
vero complementi nihil eſt, vt manifeſtum eſt ex prima figura in definitionibus poſita.</
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>
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<
s
xml:id
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xml:space
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">_IAM_ vero ex cognito ſinu recto ita arcum inuenies. </
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>
<
s
xml:id
="
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"
xml:space
="
preserve
">_Q_uære ſinum rectum propo-
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ſitum inter ſinus tabulæ; </
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>
<
s
xml:id
="
echoid-s6147
"
xml:space
="
preserve
">vel ſi eum non inueneris, ſume proxime maiorem, vel mino-
<
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rem, qui nimirum paucioribus vnitatibus à propoſito ſinu diſtat. </
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>
<
s
xml:id
="
echoid-s6148
"
xml:space
="
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">_N_am in vertice ta-
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bulæ reperies gradus, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">ad ſini ſtram è regione ſinus accepti, _M_inuta illius arcus, qui
<
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propoſito ſinut reſpondet. </
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>
<
s
xml:id
="
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xml:space
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">_V_t ſi cognitus ſit ſinus _7510767_. </
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<
s
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="
echoid-s6151
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xml:space
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">_I_nuenio ſinum _7510722_.
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</
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<
s
xml:id
="
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xml:space
="
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">proxime minorem, qui paucioribus vmtatibus à ſinu cognito diſtat, quàm ſinus
<
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<
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position
="
right
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xlink:label
="
note-183-02
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xlink:href
="
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xml:space
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">Arcus qua-
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drante mi-
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not quo pà
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cto ex ſinu
<
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/>
recto cogni
<
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to eliciat̃.</
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>
_7512642_. </
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>
<
s
xml:id
="
echoid-s6153
"
xml:space
="
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">proxime maior: </
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>
<
s
xml:id
="
echoid-s6154
"
xml:space
="
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">_C_ui ſinui proxime minori reſpõdent in vertice tabulæ grad.
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</
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>
<
s
xml:id
="
echoid-s6155
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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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">& </
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>
<
s
xml:id
="
echoid-s6157
"
xml:space
="
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">ad ſiniſtram _M_inuta _41_. </
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<
s
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="
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xml:space
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">_A_rcum ergo grad. </
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>
<
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xml:id
="
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xml:space
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">_48_. </
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<
s
xml:id
="
echoid-s6160
"
xml:space
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">& </
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>
<
s
xml:id
="
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xml:space
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">_M_in _41_ dico deberi ſinui pro-
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poſito. </
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>
<
s
xml:id
="
echoid-s6162
"
xml:space
="
preserve
">_N_am vnitates illæ, quibus ſinus propoſitus à ſinu dicti arcus differt, non indu-
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cunt errorem notabilem. </
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>
<
s
xml:id
="
echoid-s6163
"
xml:space
="
preserve
">_S_i tamen arcum cupis præciſiorem, inueſtiganda erit pars
<
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proportionalis, hac arte. </
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>
<
s
xml:id
="
echoid-s6164
"
xml:space
="
preserve
">_C_ape differentiam inter ſinum proxime minorem, & </
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>
<
s
xml:id
="
echoid-s6165
"
xml:space
="
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">ſinum
<
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/>
proxime maiorem: </
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>
<
s
xml:id
="
echoid-s6166
"
xml:space
="
preserve
">_I_tem differentiam inter ſinum propoſitum, & </
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>
<
s
xml:id
="
echoid-s6167
"
xml:space
="
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">illum in tabula re-
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pertũ, à quo minus differt; </
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>
<
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xml:id
="
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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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">dic. </
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>
<
s
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="
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xml:space
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">_S_i differentia inter duos ſinus in tabula repertos dat
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<
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position
="
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xlink:label
="
note-183-03
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xlink:href
="
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xml:space
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">Arcus qua-
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drante mi-
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nor magis
<
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p̃ciſus, quo
<
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/>
pacto p par
<
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/>
tẽ propor-
<
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tionalẽ ex
<
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dato ſinu
<
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eliciatur.</
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>
_60_. </
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<
s
xml:id
="
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xml:space
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">_S_ecunda addenda arcui ſinus proxime minoris, vel auferenda ab arcu ſinus proxi-
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me maioris, (prout videlicet ſumpta fuerit differentia inter ſinum propoſitum, & </
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<
s
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<
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ſinum proxime minorem, vel proxime maiorem) vt habeatur arcus ſinus proxime ma-
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ioris, vel proxime minoris; </
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>
<
s
xml:id
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">quot _S_ecunda poſtulat differentia inter ſinum propoſitum
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& </
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<
s
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xml:space
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">ſinum proxime minorem, vel proxime maiorem, addenda arcui ſinus proxime mi-
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noris, vel auferenda ab arcu ſinus proxime maioris, vt habeatur arcus propoſiti ſinus?
<
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/>
</
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>
<
s
xml:id
="
echoid-s6175
"
xml:space
="
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">_N_am hæc ſecunda inuenta addita arcui ſinus proxime minoris, vel ablata ab arcu
<
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ſinus proxime maioris, dabunt arcum ſinus propoſiti. </
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<
s
xml:id
="
echoid-s6176
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xml:space
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">_V_t in dato exemplo, ſi dicas. </
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<
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_D_ifferẽtia _1920_. </
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<
s
xml:id
="
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">inter ſinum _7510722_. </
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<
s
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">proxime minorem, & </
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<
s
xml:id
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">ſinum _17512642_. </
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<
s
xml:id
="
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xml:space
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xime maiorẽ, dat _60_. </
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<
s
xml:id
="
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xml:space
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">_S_ecunda addenda arcui grad. </
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<
s
xml:id
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">_48_. </
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<
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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
="
echoid-s6186
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xml:space
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">qui ſinui proxime mi-
<
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nori reſpõdet, (quoniã propoſitus ſinus minus differt à ſinu proxime minori quàm à si
<
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nu proxime maiori) vt habeatur arcus grad. </
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<
s
xml:id
="
echoid-s6187
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xml:space
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">_48_. </
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<
s
xml:id
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<
s
xml:id
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">_41_. </
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<
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<
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">_60_. </
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<
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">hoc eſt, grad. </
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<
s
xml:id
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xml:space
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<
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xml:id
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xml:space
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<
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<
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_42_. </
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<
s
xml:id
="
echoid-s6196
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xml:space
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">reſpõdens ſinui proxime maiori. </
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>
<
s
xml:id
="
echoid-s6197
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xml:space
="
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">_Q_uot ergo Secũda poſtulat differẽtia _45_. </
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>
<
s
xml:id
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xml:space
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<
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propoſitũ, & </
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<
s
xml:id
="
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xml:space
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">ſinũ proxime minorẽ, addenda eidẽ arcui ſinus proxime minoris, vt fiat
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arcus dati ſinus? </
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<
s
xml:id
="
echoid-s6200
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xml:space
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">_I_nuenies enim _S_ecundũ _1._ </
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<
s
xml:id
="
echoid-s6201
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xml:space
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">& </
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<
s
xml:id
="
echoid-s6202
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">paulo amplius addendũ arcui grad. </
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<
s
xml:id
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echoid-s6203
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xml:space
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">_48_. </
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<
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_M_in. </
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<
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xml:id
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echoid-s6205
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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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">ita vt ſinui propoſito _7510767_. </
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<
s
xml:id
="
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">reſpondeat 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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<
s
xml:id
="
echoid-s6210
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xml:space
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">_41_. </
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<
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xml:id
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<
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">_1._ </
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<
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xml:id
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xml:space
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">& </
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<
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xml:id
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<
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paulo amplius. </
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<
s
xml:id
="
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xml:space
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">_R_u-ſus ſit datus ſinus _455630_. </
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>
<
s
xml:id
="
echoid-s6216
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xml:space
="
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">quem in tabula quæſitum non inuenio. </
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<
s
xml:id
="
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<
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_A_ccipio ergo proxime maiorem _456536_. </
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<
s
xml:id
="
echoid-s6218
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xml:space
="
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">(_A_b hoc enim minus diſtat, quàm à proxime
<
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minori _453630_.) </
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>
<
s
xml:id
="
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xml:space
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">cui reſpondet arcus grad. </
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<
s
xml:id
="
echoid-s6220
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xml:space
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">_2_. </
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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-s6222
"
xml:space
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">_37_. </
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>
<
s
xml:id
="
echoid-s6223
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xml:space
="
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">_Q_uòd ſi magis præciſum arcum
<
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deſiderem, inquiram partem proportionalem, hoc modo. </
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>
<
s
xml:id
="
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"
xml:space
="
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">_D_ifferentia _2906_. </
s
>
<
s
xml:id
="
echoid-s6225
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xml:space
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">inter ſinũ
<
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_456536_. </
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>
<
s
xml:id
="
echoid-s6226
"
xml:space
="
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">proxime maiorem, & </
s
>
<
s
xml:id
="
echoid-s6227
"
xml:space
="
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">ſinum _453630_. </
s
>
<
s
xml:id
="
echoid-s6228
"
xml:space
="
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">proxime minorem, dat _60_. </
s
>
<
s
xml:id
="
echoid-s6229
"
xml:space
="
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">_S_ecũda au-
<
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ferenda ab arcu grad. </
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>
<
s
xml:id
="
echoid-s6230
"
xml:space
="
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">_2_. </
s
>
<
s
xml:id
="
echoid-s6231
"
xml:space
="
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">_M_in. </
s
>
<
s
xml:id
="
echoid-s6232
"
xml:space
="
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">_37_. </
s
>
<
s
xml:id
="
echoid-s6233
"
xml:space
="
preserve
">qui ſinui proxime maiori reſpondet, vt reliquus sit
<
lb
/>
arcus grad. </
s
>
<
s
xml:id
="
echoid-s6234
"
xml:space
="
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">_2_. </
s
>
<
s
xml:id
="
echoid-s6235
"
xml:space
="
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">_M_in. </
s
>
<
s
xml:id
="
echoid-s6236
"
xml:space
="
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">_36_. </
s
>
<
s
xml:id
="
echoid-s6237
"
xml:space
="
preserve
">reſpondens sinui proxime minori: </
s
>
<
s
xml:id
="
echoid-s6238
"
xml:space
="
preserve
">_Q_uot ergo _S_ecunda poſtulat
<
lb
/>
differentia _906_. </
s
>
<
s
xml:id
="
echoid-s6239
"
xml:space
="
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">inter sinum propositum, & </
s
>
<
s
xml:id
="
echoid-s6240
"
xml:space
="
preserve
">sinum proxime maiorem, auferenda ab
<
lb
/>
eodem arcu ſinus proxime maioris, vt fiat arcus dati sinus? </
s
>
<
s
xml:id
="
echoid-s6241
"
xml:space
="
preserve
">_I_nuenio enim _S_ecunda _19_. </
s
>
<
s
xml:id
="
echoid-s6242
"
xml:space
="
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">
<
lb
/>
fere, quæ ablata ex arcu grad. </
s
>
<
s
xml:id
="
echoid-s6243
"
xml:space
="
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">_2_. </
s
>
<
s
xml:id
="
echoid-s6244
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xml:space
="
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">_M_in. </
s
>
<
s
xml:id
="
echoid-s6245
"
xml:space
="
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">_37_. </
s
>
<
s
xml:id
="
echoid-s6246
"
xml:space
="
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">relinquunt arcum grad. </
s
>
<
s
xml:id
="
echoid-s6247
"
xml:space
="
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">_2_. </
s
>
<
s
xml:id
="
echoid-s6248
"
xml:space
="
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">_M_in. </
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>
<
s
xml:id
="
echoid-s6249
"
xml:space
="
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">_36_. </
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>
<
s
xml:id
="
echoid-s6250
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xml:space
="
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">_S_ec. </
s
>
<
s
xml:id
="
echoid-s6251
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xml:space
="
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">
<
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/>
_41_. </
s
>
<
s
xml:id
="
echoid-s6252
"
xml:space
="
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">sinui dato _455630_. </
s
>
<
s
xml:id
="
echoid-s6253
"
xml:space
="
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">debitum. </
s
>
<
s
xml:id
="
echoid-s6254
"
xml:space
="
preserve
">_Q_uoniam veroidem sinus rectus reſpondet duobus
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-183-04
"
xlink:href
="
note-183-04a
"
xml:space
="
preserve
">Atcus qu@-
<
lb
/>
drante ma
<
lb
/>
tor qua ar-
<
lb
/>
te ex ſinu
<
lb
/>
recto etua-
<
lb
/>
tur.</
note
>
arcubus ſemicirculum conficientibus, vt ſupra diximus, si arcus dicta arte ex sinu
<
lb
/>
recto inuentus ſubducatur ex ſemicirculo, ideſt, ex grad. </
s
>
<
s
xml:id
="
echoid-s6255
"
xml:space
="
preserve
">_180_. </
s
>
<
s
xml:id
="
echoid-s6256
"
xml:space
="
preserve
">reliquus erit alter ar-
<
lb
/>
cus quadrante maior, qui dicto etiam ſinui debetur. </
s
>
<
s
xml:id
="
echoid-s6257
"
xml:space
="
preserve
">_V_t ſi arcus grad. </
s
>
<
s
xml:id
="
echoid-s6258
"
xml:space
="
preserve
">_48._ </
s
>
<
s
xml:id
="
echoid-s6259
"
xml:space
="
preserve
">_M_in. </
s
>
<
s
xml:id
="
echoid-s6260
"
xml:space
="
preserve
">_41_.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s6261
"
xml:space
="
preserve
">_S_ec. </
s
>
<
s
xml:id
="
echoid-s6262
"
xml:space
="
preserve
">_1._ </
s
>
<
s
xml:id
="
echoid-s6263
"
xml:space
="
preserve
">inuentus dematur ex grad. </
s
>
<
s
xml:id
="
echoid-s6264
"
xml:space
="
preserve
">_180_. </
s
>
<
s
xml:id
="
echoid-s6265
"
xml:space
="
preserve
">remanebit arcus grad _131_. </
s
>
<
s
xml:id
="
echoid-s6266
"
xml:space
="
preserve
">_M_in. </
s
>
<
s
xml:id
="
echoid-s6267
"
xml:space
="
preserve
">_18_. </
s
>
<
s
xml:id
="
echoid-s6268
"
xml:space
="
preserve
">_S_ec. </
s
>
<
s
xml:id
="
echoid-s6269
"
xml:space
="
preserve
">_59_. </
s
>
<
s
xml:id
="
echoid-s6270
"
xml:space
="
preserve
">eidẽ
<
lb
/>
sinui recto _7510767_. </
s
>
<
s
xml:id
="
echoid-s6271
"
xml:space
="
preserve
">debitus. </
s
>
<
s
xml:id
="
echoid-s6272
"
xml:space
="
preserve
">_P_ulchre autem operatio in triangulis tam </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>
