Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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cus datus ſit _Q_uadrante maior, ſed ſemicirculo minor; </
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>
<
s
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xml:space
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">detracto _Q_uadrante, inqui-
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<
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xlink:label
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note-182-01a
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xml:space
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">modo eli-
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ciat̃ per par
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tẽ propor-
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tionalem.</
note
>
res reſidui arcus ſinum rectum per eandem regulam proportionum, eo modo, quem
<
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ſupra de ſinu recto tradidimus. </
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>
<
s
xml:id
="
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"
xml:space
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">_Q_uamuis _S_ecunda negligi poſsint, vt ſupra docui-
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mus, in hoc ſinuum negotio _E_xemplum. </
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>
<
s
xml:id
="
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xml:space
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">_S_it datus arcus grad. </
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>
<
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="
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xml:space
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">_69_. </
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<
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">_M_in. </
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<
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">_16._ </
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<
s
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">_S_ec. </
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<
s
xml:id
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">_40._
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</
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<
s
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">_A_ccipedifferentiam _2721_. </
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<
s
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">inter ſinum _3540190._ </
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<
s
xml:id
="
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xml:space
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">arcus grad. </
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<
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xml:id
="
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xml:space
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">_69_. </
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<
s
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xml:space
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">_M_in. </
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<
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xml:id
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xml:space
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">_16_. </
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<
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">proxime
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minoris in parte tabulæ inferiori deſcripti, & </
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<
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">ſinum _3537469_. </
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<
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xml:id
="
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"
xml:space
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">arcus grad. </
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>
<
s
xml:id
="
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xml:space
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">_69_. </
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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-s5990
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xml:space
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">
<
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_17._ </
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<
s
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="
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xml:space
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">proxime maioris in eadem parteinferiori tabulæ poſiti; </
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>
<
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xml:space
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">& </
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<
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<
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">_S_i _40._ </
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<
s
xml:id
="
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xml:space
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">_S_ecundæ
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requirunt differentiam _2721_. </
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>
<
s
xml:id
="
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xml:space
="
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">ſubtrahendam à ſinu _3540190_. </
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>
<
s
xml:id
="
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xml:space
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">arcus grad. </
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>
<
s
xml:id
="
echoid-s5998
"
xml:space
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">_69_. </
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>
<
s
xml:id
="
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xml:space
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">_M_in. </
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>
<
s
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="
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_16._ </
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>
<
s
xml:id
="
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"
xml:space
="
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">in i feriori parte tabulæ poſiti, vt relinquatur ſinus _3537469_. </
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>
<
s
xml:id
="
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"
xml:space
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">arcus grad. </
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>
<
s
xml:id
="
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"
xml:space
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">_69_. </
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>
<
s
xml:id
="
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xml:space
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">
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_M_in. </
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<
s
xml:id
="
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"
xml:space
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">_17_. </
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<
s
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="
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xml:space
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">in eadem parte inferiori tabulæ deſcripti: </
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>
<
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xml:space
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">quantam differentiam poſtulãt
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_40_. </
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>
<
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xml:space
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">_S_ecunda ſubtrahendam ab eodem ſinu _3540190_. </
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>
<
s
xml:id
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xml:space
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">arcus grad _69_. </
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>
<
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xml:id
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xml:space
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">_M_in. </
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<
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xml:id
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xml:space
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">_16_. </
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<
s
xml:id
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xml:space
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">poſiti
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in part in feriori tabulæ, vt relinquatur ſinus arcus grad. </
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>
<
s
xml:id
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xml:space
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">_69_. </
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<
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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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">_16._ </
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>
<
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">_S_ec. </
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<
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xml:space
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">_40_ in
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eadẽ parte inferiori tabulæ contenti? </
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<
s
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">Inuenies enim differentiã ſiue partẽ proportio-
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nalẽ _1814_. </
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>
<
s
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="
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">quæ ſubtracta ex sinu _3540190_. </
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>
<
s
xml:id
="
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"
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">relinquet sinum _3538376_. </
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>
<
s
xml:id
="
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"
xml:space
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">arcus grad. </
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>
<
s
xml:id
="
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">
<
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_69_. </
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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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">_16_. </
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>
<
s
xml:id
="
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"
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">_S_ec. </
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<
s
xml:id
="
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"
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">_40_. </
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<
s
xml:id
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">in inferiori parte tabulæ collocati: </
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>
<
s
xml:id
="
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">qui quidem eſt sinus rectus
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arcus grad. </
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>
<
s
xml:id
="
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">_20_ _M_in. </
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<
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<
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">_20_. </
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<
s
xml:id
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">hoc eſt, complementi arcus datigrad. </
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<
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xml:space
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">_69._ </
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<
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xml:id
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<
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xml:id
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"
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">_16_. </
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<
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<
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_S_ec. </
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<
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xml:id
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">_40_. </
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>
<
s
xml:id
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xml:space
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">_S_it rurſum datus arcus grad. </
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>
<
s
xml:id
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xml:space
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">_110_. </
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<
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xml:id
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<
s
xml:id
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"
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">_43_. </
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>
<
s
xml:id
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>
<
s
xml:id
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">_20_. </
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>
<
s
xml:id
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xml:space
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">_D_etrahe _Q_uadrantem,
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id eſt, grad. </
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<
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">_90_ & </
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>
<
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xml:id
="
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"
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">residui arcus grad. </
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>
<
s
xml:id
="
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"
xml:space
="
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">_20_. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">_M_in. </
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>
<
s
xml:id
="
echoid-s6049
"
xml:space
="
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">_43_. </
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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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"
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">_20_. </
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>
<
s
xml:id
="
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">quære sinum rectum, vt
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ſupra tradidimus. </
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>
<
s
xml:id
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xml:space
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">_I_nuenies enim per partem proportionalem, sinum _3538376_. </
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>
<
s
xml:id
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">qui
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eſt sinus complementi arcus propositi.</
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>
<
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</
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<
s
xml:id
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">_HOC_ etiam modo sinum complemẽti arcus propositi quadrante minoris reperies.
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</
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<
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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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xml:space
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">@lia rõ in.
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ueſtigãdi ſi
<
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/>
nũ comple
<
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/>
menti arcꝰ
<
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/>
quad rante
<
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/>
minoris.</
note
>
_S_ubtrahe propositũ arcum ex quadrante, vt habeas eius complementum _S_inus enim
<
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/>
rectus eius complementi inuentus, vt de sinu recto diximus, eſt is, qui quæritur. </
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>
<
s
xml:id
="
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xml:space
="
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">_V_t
<
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si quæratur sinus complementi arcus grad. </
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>
<
s
xml:id
="
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"
xml:space
="
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">_69_. </
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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-s6061
"
xml:space
="
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">_16_. </
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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
="
echoid-s6063
"
xml:space
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">_40_. </
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>
<
s
xml:id
="
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"
xml:space
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">detrahe hunc ar-
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cum ex grad. </
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>
<
s
xml:id
="
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">_90_. </
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>
<
s
xml:id
="
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xml:space
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">& </
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>
<
s
xml:id
="
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"
xml:space
="
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">residui arcus grad. </
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>
<
s
xml:id
="
echoid-s6068
"
xml:space
="
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">_20_. </
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>
<
s
xml:id
="
echoid-s6069
"
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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">_43_. </
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>
<
s
xml:id
="
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"
xml:space
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">ſec. </
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>
<
s
xml:id
="
echoid-s6072
"
xml:space
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">_20_. </
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>
<
s
xml:id
="
echoid-s6073
"
xml:space
="
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">(qui complementum
<
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/>
eſt dati arcus grad. </
s
>
<
s
xml:id
="
echoid-s6074
"
xml:space
="
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">_69_. </
s
>
<
s
xml:id
="
echoid-s6075
"
xml:space
="
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">_M_in. </
s
>
<
s
xml:id
="
echoid-s6076
"
xml:space
="
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">_16_. </
s
>
<
s
xml:id
="
echoid-s6077
"
xml:space
="
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">_S_ec. </
s
>
<
s
xml:id
="
echoid-s6078
"
xml:space
="
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">_40_) sinum rectum quære, quem inuenies eſſe
<
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/>
_3538376_. </
s
>
<
s
xml:id
="
echoid-s6079
"
xml:space
="
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">atque hic eſt sinus complementi dati arcus grad. </
s
>
<
s
xml:id
="
echoid-s6080
"
xml:space
="
preserve
">_69_. </
s
>
<
s
xml:id
="
echoid-s6081
"
xml:space
="
preserve
">_M_in. </
s
>
<
s
xml:id
="
echoid-s6082
"
xml:space
="
preserve
">_16_. </
s
>
<
s
xml:id
="
echoid-s6083
"
xml:space
="
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">_S_ec. </
s
>
<
s
xml:id
="
echoid-s6084
"
xml:space
="
preserve
">_40_.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s6085
"
xml:space
="
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">
<
note
position
="
left
"
xlink:label
="
note-182-03
"
xlink:href
="
note-182-03a
"
xml:space
="
preserve
">Sinꝰ cõple
<
lb
/>
mẽti ſemi-
<
lb
/>
circuli, aut
<
lb
/>
arcus maio
<
lb
/>
ris, q̃rendus
<
lb
/>
non eſt.</
note
>
</
s
>
</
p
>
<
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style
="
it
">
<
s
xml:id
="
echoid-s6086
"
xml:space
="
preserve
">_HIC_ quoque ſemicirculi, atque arcus ſemicirculo matoris sinus complementi
<
lb
/>
quærendus non eſt, ob rationem ſupra dictam.</
s
>
<
s
xml:id
="
echoid-s6087
"
xml:space
="
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"/>
</
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>
<
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="
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<
s
xml:id
="
echoid-s6088
"
xml:space
="
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">_QVANDO_ deniq; </
s
>
<
s
xml:id
="
echoid-s6089
"
xml:space
="
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">propositi arcus sinum verſum desideras; </
s
>
<
s
xml:id
="
echoid-s6090
"
xml:space
="
preserve
">si quidem _Q_uadrante
<
lb
/>
minor eſt, detrahe eius sinum complementi ex sinu toto: </
s
>
<
s
xml:id
="
echoid-s6091
"
xml:space
="
preserve
">si vero _Q_uadrante eſt ma-
<
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/>
ior, ſed ſemicirculo minor, adde eius sinum complementi sinui toti. </
s
>
<
s
xml:id
="
echoid-s6092
"
xml:space
="
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">_N_umerus enim
<
lb
/>
reliquus, vel compositus, erit sinus verſus dati arcus: </
s
>
<
s
xml:id
="
echoid-s6093
"
xml:space
="
preserve
">propterea quod sinus comple-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-182-04
"
xlink:href
="
note-182-04a
"
xml:space
="
preserve
">Sinꝰ verſus
<
lb
/>
cuiuſuis ar
<
lb
/>
cꝰ ſiue qua
<
lb
/>
d@ãte mino
<
lb
/>
ris ſiue ma
<
lb
/>
ioris, qu
<
unsure
/>
o
<
lb
/>
pacto colli
<
lb
/>
gatur.</
note
>
menti cuiusuis arcus æqualis est complemento sinus versi eiuſdem arcus, vt ſupra
<
lb
/>
in definitionibus oſtendimus. </
s
>
<
s
xml:id
="
echoid-s6094
"
xml:space
="
preserve
">
<
emph
style
="
sc
">E</
emph
>
x quo fit, vt sinus complementi arcus cuiusuis abla-
<
lb
/>
tus ex sinu toto, vel ad eum adiectus relinquat, vel componat eiuſdem arcus sinum
<
lb
/>
verſum: </
s
>
<
s
xml:id
="
echoid-s6095
"
xml:space
="
preserve
">_I_d quod perſpicuum eſt ex prima figura, quam in expositione definitionum
<
lb
/>
poſuimus. </
s
>
<
s
xml:id
="
echoid-s6096
"
xml:space
="
preserve
">_E_xemplum. </
s
>
<
s
xml:id
="
echoid-s6097
"
xml:space
="
preserve
">_S_it quærendus sinus verſus arcus grad. </
s
>
<
s
xml:id
="
echoid-s6098
"
xml:space
="
preserve
">_20_. </
s
>
<
s
xml:id
="
echoid-s6099
"
xml:space
="
preserve
">_M_in. </
s
>
<
s
xml:id
="
echoid-s6100
"
xml:space
="
preserve
">_57_. </
s
>
<
s
xml:id
="
echoid-s6101
"
xml:space
="
preserve
">_H_uius
<
lb
/>
sinuscomplementi eſt _9338928_ qui detractus ex sinu toto _10000000_. </
s
>
<
s
xml:id
="
echoid-s6102
"
xml:space
="
preserve
">relinquet
<
lb
/>
sinum verſum _661072_. </
s
>
<
s
xml:id
="
echoid-s6103
"
xml:space
="
preserve
">dati arcus grad. </
s
>
<
s
xml:id
="
echoid-s6104
"
xml:space
="
preserve
">_20_. </
s
>
<
s
xml:id
="
echoid-s6105
"
xml:space
="
preserve
">_M_in. </
s
>
<
s
xml:id
="
echoid-s6106
"
xml:space
="
preserve
">_57_. </
s
>
<
s
xml:id
="
echoid-s6107
"
xml:space
="
preserve
">_R_urſus sit inueſtigandus sinus
<
lb
/>
verſus arcus grad. </
s
>
<
s
xml:id
="
echoid-s6108
"
xml:space
="
preserve
">_138_. </
s
>
<
s
xml:id
="
echoid-s6109
"
xml:space
="
preserve
">_M_in. </
s
>
<
s
xml:id
="
echoid-s6110
"
xml:space
="
preserve
">_31_. </
s
>
<
s
xml:id
="
echoid-s6111
"
xml:space
="
preserve
">_H_uius sinus complementi eſt _7491484_. </
s
>
<
s
xml:id
="
echoid-s6112
"
xml:space
="
preserve
">qui additus
<
lb
/>
sinui toti _10000000_. </
s
>
<
s
xml:id
="
echoid-s6113
"
xml:space
="
preserve
">efficiet sinum verſum _17491484_. </
s
>
<
s
xml:id
="
echoid-s6114
"
xml:space
="
preserve
">arcus propositi grad. </
s
>
<
s
xml:id
="
echoid-s6115
"
xml:space
="
preserve
">_138_.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s6116
"
xml:space
="
preserve
">_M_in. </
s
>
<
s
xml:id
="
echoid-s6117
"
xml:space
="
preserve
">_31_. </
s
>
<
s
xml:id
="
echoid-s6118
"
xml:space
="
preserve
">_P_oſtremo sit inueniendus sinus verſus arcus grad. </
s
>
<
s
xml:id
="
echoid-s6119
"
xml:space
="
preserve
">_69_. </
s
>
<
s
xml:id
="
echoid-s6120
"
xml:space
="
preserve
">_M_in. </
s
>
<
s
xml:id
="
echoid-s6121
"
xml:space
="
preserve
">_16_. </
s
>
<
s
xml:id
="
echoid-s6122
"
xml:space
="
preserve
">_S_ec. </
s
>
<
s
xml:id
="
echoid-s6123
"
xml:space
="
preserve
">_40_. </
s
>
<
s
xml:id
="
echoid-s6124
"
xml:space
="
preserve
">
<
lb
/>
_H_uius complementi sinus eſt _3538376_. </
s
>
<
s
xml:id
="
echoid-s6125
"
xml:space
="
preserve
">inuentus per partem proportionalem; </
s
>
<
s
xml:id
="
echoid-s6126
"
xml:space
="
preserve
">qui
<
lb
/>
ſubtractus ex ſinu toto _10000000_. </
s
>
<
s
xml:id
="
echoid-s6127
"
xml:space
="
preserve
">relinquet ſinũ verſum _6461624_. </
s
>
<
s
xml:id
="
echoid-s6128
"
xml:space
="
preserve
">dati arcus grad. </
s
>
<
s
xml:id
="
echoid-s6129
"
xml:space
="
preserve
">
<
lb
/>
_69_ _M_in. </
s
>
<
s
xml:id
="
echoid-s6130
"
xml:space
="
preserve
">_16_. </
s
>
<
s
xml:id
="
echoid-s6131
"
xml:space
="
preserve
">_S_ec. </
s
>
<
s
xml:id
="
echoid-s6132
"
xml:space
="
preserve
">_40_. </
s
>
<
s
xml:id
="
echoid-s6133
"
xml:space
="
preserve
">_S_ic quoque ſinus verſus arcus grad. </
s
>
<
s
xml:id
="
echoid-s6134
"
xml:space
="
preserve
">_159_. </
s
>
<
s
xml:id
="
echoid-s6135
"
xml:space
="
preserve
">_M_in. </
s
>
<
s
xml:id
="
echoid-s6136
"
xml:space
="
preserve
">_16_. </
s
>
<
s
xml:id
="
echoid-s6137
"
xml:space
="
preserve
">_S_ec. </
s
>
<
s
xml:id
="
echoid-s6138
"
xml:space
="
preserve
">_40_. </
s
>
<
s
xml:id
="
echoid-s6139
"
xml:space
="
preserve
">reperie-
<
lb
/>
tur _13538376_. </
s
>
<
s
xml:id
="
echoid-s6140
"
xml:space
="
preserve
">per partem proportionalem.</
s
>
<
s
xml:id
="
echoid-s6141
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>