Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

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    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div476" type="section" level="1" n="240">
          <p style="it">
            <s xml:id="echoid-s5970" xml:space="preserve">
              <pb o="170" file="182" n="182" rhead=""/>
            cus datus ſit _Q_uadrante maior, ſed ſemicirculo minor; </s>
            <s xml:id="echoid-s5971" xml:space="preserve">detracto _Q_uadrante, inqui-
              <lb/>
              <note position="left" xlink:label="note-182-01" xlink:href="note-182-01a" xml:space="preserve">modo eli-
                <lb/>
              ciat̃ per par
                <lb/>
              tẽ propor-
                <lb/>
              tionalem.</note>
            res reſidui arcus ſinum rectum per eandem regulam proportionum, eo modo, quem
              <lb/>
            ſupra de ſinu recto tradidimus. </s>
            <s xml:id="echoid-s5972" xml:space="preserve">_Q_uamuis _S_ecunda negligi poſsint, vt ſupra docui-
              <lb/>
            mus, in hoc ſinuum negotio _E_xemplum. </s>
            <s xml:id="echoid-s5973" xml:space="preserve">_S_it datus arcus grad. </s>
            <s xml:id="echoid-s5974" xml:space="preserve">_69_. </s>
            <s xml:id="echoid-s5975" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s5976" xml:space="preserve">_16._ </s>
            <s xml:id="echoid-s5977" xml:space="preserve">_S_ec. </s>
            <s xml:id="echoid-s5978" xml:space="preserve">_40._
              <lb/>
            </s>
            <s xml:id="echoid-s5979" xml:space="preserve">_A_ccipedifferentiam _2721_. </s>
            <s xml:id="echoid-s5980" xml:space="preserve">inter ſinum _3540190._ </s>
            <s xml:id="echoid-s5981" xml:space="preserve">arcus grad. </s>
            <s xml:id="echoid-s5982" xml:space="preserve">_69_. </s>
            <s xml:id="echoid-s5983" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s5984" xml:space="preserve">_16_. </s>
            <s xml:id="echoid-s5985" xml:space="preserve">proxime
              <lb/>
            minoris in parte tabulæ inferiori deſcripti, & </s>
            <s xml:id="echoid-s5986" xml:space="preserve">ſinum _3537469_. </s>
            <s xml:id="echoid-s5987" xml:space="preserve">arcus grad. </s>
            <s xml:id="echoid-s5988" xml:space="preserve">_69_. </s>
            <s xml:id="echoid-s5989" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s5990" xml:space="preserve">
              <lb/>
            _17._ </s>
            <s xml:id="echoid-s5991" xml:space="preserve">proxime maioris in eadem parteinferiori tabulæ poſiti; </s>
            <s xml:id="echoid-s5992" xml:space="preserve">& </s>
            <s xml:id="echoid-s5993" xml:space="preserve">dic. </s>
            <s xml:id="echoid-s5994" xml:space="preserve">_S_i _40._ </s>
            <s xml:id="echoid-s5995" xml:space="preserve">_S_ecundæ
              <lb/>
            requirunt differentiam _2721_. </s>
            <s xml:id="echoid-s5996" xml:space="preserve">ſubtrahendam à ſinu _3540190_. </s>
            <s xml:id="echoid-s5997" xml:space="preserve">arcus grad. </s>
            <s xml:id="echoid-s5998" xml:space="preserve">_69_. </s>
            <s xml:id="echoid-s5999" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6000" xml:space="preserve">
              <lb/>
            _16._ </s>
            <s xml:id="echoid-s6001" xml:space="preserve">in i feriori parte tabulæ poſiti, vt relinquatur ſinus _3537469_. </s>
            <s xml:id="echoid-s6002" xml:space="preserve">arcus grad. </s>
            <s xml:id="echoid-s6003" xml:space="preserve">_69_. </s>
            <s xml:id="echoid-s6004" xml:space="preserve">
              <lb/>
            _M_in. </s>
            <s xml:id="echoid-s6005" xml:space="preserve">_17_. </s>
            <s xml:id="echoid-s6006" xml:space="preserve">in eadem parte inferiori tabulæ deſcripti: </s>
            <s xml:id="echoid-s6007" xml:space="preserve">quantam differentiam poſtulãt
              <lb/>
            _40_. </s>
            <s xml:id="echoid-s6008" xml:space="preserve">_S_ecunda ſubtrahendam ab eodem ſinu _3540190_. </s>
            <s xml:id="echoid-s6009" xml:space="preserve">arcus grad _69_. </s>
            <s xml:id="echoid-s6010" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6011" xml:space="preserve">_16_. </s>
            <s xml:id="echoid-s6012" xml:space="preserve">poſiti
              <lb/>
            in part in feriori tabulæ, vt relinquatur ſinus arcus grad. </s>
            <s xml:id="echoid-s6013" xml:space="preserve">_69_. </s>
            <s xml:id="echoid-s6014" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6015" xml:space="preserve">_16._ </s>
            <s xml:id="echoid-s6016" xml:space="preserve">_S_ec. </s>
            <s xml:id="echoid-s6017" xml:space="preserve">_40_ in
              <lb/>
            eadẽ parte inferiori tabulæ contenti? </s>
            <s xml:id="echoid-s6018" xml:space="preserve">Inuenies enim differentiã ſiue partẽ proportio-
              <lb/>
            nalẽ _1814_. </s>
            <s xml:id="echoid-s6019" xml:space="preserve">quæ ſubtracta ex sinu _3540190_. </s>
            <s xml:id="echoid-s6020" xml:space="preserve">relinquet sinum _3538376_. </s>
            <s xml:id="echoid-s6021" xml:space="preserve">arcus grad. </s>
            <s xml:id="echoid-s6022" xml:space="preserve">
              <lb/>
            _69_. </s>
            <s xml:id="echoid-s6023" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6024" xml:space="preserve">_16_. </s>
            <s xml:id="echoid-s6025" xml:space="preserve">_S_ec. </s>
            <s xml:id="echoid-s6026" xml:space="preserve">_40_. </s>
            <s xml:id="echoid-s6027" xml:space="preserve">in inferiori parte tabulæ collocati: </s>
            <s xml:id="echoid-s6028" xml:space="preserve">qui quidem eſt sinus rectus
              <lb/>
            arcus grad. </s>
            <s xml:id="echoid-s6029" xml:space="preserve">_20_ _M_in. </s>
            <s xml:id="echoid-s6030" xml:space="preserve">_43_ _S_ec. </s>
            <s xml:id="echoid-s6031" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s6032" xml:space="preserve">hoc eſt, complementi arcus datigrad. </s>
            <s xml:id="echoid-s6033" xml:space="preserve">_69._ </s>
            <s xml:id="echoid-s6034" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6035" xml:space="preserve">_16_. </s>
            <s xml:id="echoid-s6036" xml:space="preserve">
              <lb/>
            _S_ec. </s>
            <s xml:id="echoid-s6037" xml:space="preserve">_40_. </s>
            <s xml:id="echoid-s6038" xml:space="preserve">_S_it rurſum datus arcus grad. </s>
            <s xml:id="echoid-s6039" xml:space="preserve">_110_. </s>
            <s xml:id="echoid-s6040" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6041" xml:space="preserve">_43_. </s>
            <s xml:id="echoid-s6042" xml:space="preserve">_S_ec. </s>
            <s xml:id="echoid-s6043" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s6044" xml:space="preserve">_D_etrahe _Q_uadrantem,
              <lb/>
            id eſt, grad. </s>
            <s xml:id="echoid-s6045" xml:space="preserve">_90_ & </s>
            <s xml:id="echoid-s6046" xml:space="preserve">residui arcus grad. </s>
            <s xml:id="echoid-s6047" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s6048" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6049" xml:space="preserve">_43_. </s>
            <s xml:id="echoid-s6050" xml:space="preserve">_S_ec. </s>
            <s xml:id="echoid-s6051" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s6052" xml:space="preserve">quære sinum rectum, vt
              <lb/>
            ſupra tradidimus. </s>
            <s xml:id="echoid-s6053" xml:space="preserve">_I_nuenies enim per partem proportionalem, sinum _3538376_. </s>
            <s xml:id="echoid-s6054" xml:space="preserve">qui
              <lb/>
            eſt sinus complementi arcus propositi.</s>
            <s xml:id="echoid-s6055" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6056" xml:space="preserve">_HOC_ etiam modo sinum complemẽti arcus propositi quadrante minoris reperies.
              <lb/>
            </s>
            <s xml:id="echoid-s6057" xml:space="preserve">
              <note position="left" xlink:label="note-182-02" xlink:href="note-182-02a" xml:space="preserve">@lia rõ in.
                <lb/>
              ueſtigãdi ſi
                <lb/>
              nũ comple
                <lb/>
              menti arcꝰ
                <lb/>
              quad rante
                <lb/>
              minoris.</note>
            _S_ubtrahe propositũ arcum ex quadrante, vt habeas eius complementum _S_inus enim
              <lb/>
            rectus eius complementi inuentus, vt de sinu recto diximus, eſt is, qui quæritur. </s>
            <s xml:id="echoid-s6058" xml:space="preserve">_V_t
              <lb/>
            si quæratur sinus complementi arcus grad. </s>
            <s xml:id="echoid-s6059" xml:space="preserve">_69_. </s>
            <s xml:id="echoid-s6060" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6061" xml:space="preserve">_16_. </s>
            <s xml:id="echoid-s6062" xml:space="preserve">_S_ec. </s>
            <s xml:id="echoid-s6063" xml:space="preserve">_40_. </s>
            <s xml:id="echoid-s6064" xml:space="preserve">detrahe hunc ar-
              <lb/>
            cum ex grad. </s>
            <s xml:id="echoid-s6065" xml:space="preserve">_90_. </s>
            <s xml:id="echoid-s6066" xml:space="preserve">& </s>
            <s xml:id="echoid-s6067" xml:space="preserve">residui arcus grad. </s>
            <s xml:id="echoid-s6068" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s6069" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6070" xml:space="preserve">_43_. </s>
            <s xml:id="echoid-s6071" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s6072" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s6073" xml:space="preserve">(qui complementum
              <lb/>
            eſt dati arcus grad. </s>
            <s xml:id="echoid-s6074" xml:space="preserve">_69_. </s>
            <s xml:id="echoid-s6075" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6076" xml:space="preserve">_16_. </s>
            <s xml:id="echoid-s6077" xml:space="preserve">_S_ec. </s>
            <s xml:id="echoid-s6078" xml:space="preserve">_40_) sinum rectum quære, quem inuenies eſſe
              <lb/>
            _3538376_. </s>
            <s xml:id="echoid-s6079" xml:space="preserve">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="preserve">_S_ec. </s>
            <s xml:id="echoid-s6084" xml:space="preserve">_40_.
              <lb/>
            </s>
            <s xml:id="echoid-s6085" xml:space="preserve">
              <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>
          <p 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="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6088" xml:space="preserve">_QVANDO_ deniq; </s>
            <s xml:id="echoid-s6089" xml:space="preserve">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-
              <lb/>
            ior, ſed ſemicirculo minor, adde eius sinum complementi sinui toti. </s>
            <s xml:id="echoid-s6092" xml:space="preserve">_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>
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