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-s6272" xml:space="preserve">
              <pb o="172" file="184" n="184" rhead=""/>
            quàm ſphæricis, docebit, num accipiendus sit arcus quadrante maior proposito ſinui
              <lb/>
            veſpondens, an vero minor, vt proprijs locis apparebit.</s>
            <s xml:id="echoid-s6273" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6274" xml:space="preserve">_SI_ vero sinus cognitus, eſt sinus complementi arcus quæsiti, ſumendierunt gra-
              <lb/>
              <note position="left" xlink:label="note-184-01" xlink:href="note-184-01a" xml:space="preserve">Arcus qua-
                <lb/>
              dranre mi-
                <lb/>
              nor quo pa
                <lb/>
              cto ex ſinu
                <lb/>
              complemẽ
                <lb/>
              ti cruatur.</note>
            dus in parte inferiori tabulæ, & </s>
            <s xml:id="echoid-s6275" xml:space="preserve">_M_inuta ad dextram. </s>
            <s xml:id="echoid-s6276" xml:space="preserve">_I_ta enim habebitur arcus quæ-
              <lb/>
            situs. </s>
            <s xml:id="echoid-s6277" xml:space="preserve">_V_elcerte inueniendus erit arcus, vt prius diximus, ſinui dato, tanquam recto,
              <lb/>
            reſpondens, is que ex quadrante demendus, vt arcus quæsitus relinquatur. </s>
            <s xml:id="echoid-s6278" xml:space="preserve">_V_t si co-
              <lb/>
            gnitus sit _7510767_. </s>
            <s xml:id="echoid-s6279" xml:space="preserve">sinus complementi alicuius arcus. </s>
            <s xml:id="echoid-s6280" xml:space="preserve">_I_nuenio sinum _7510722_. </s>
            <s xml:id="echoid-s6281" xml:space="preserve">pro-
              <lb/>
            xime minorem; </s>
            <s xml:id="echoid-s6282" xml:space="preserve">quoniam paucioribus hic vnitatibus à sinu cognito diſtat, quàm sinus
              <lb/>
            _7512642_. </s>
            <s xml:id="echoid-s6283" xml:space="preserve">proxime maior in tabula sinuum: </s>
            <s xml:id="echoid-s6284" xml:space="preserve">_C_ui sinui proxime minori reſpondent in
              <lb/>
            ima ſede tabulæ grad. </s>
            <s xml:id="echoid-s6285" xml:space="preserve">_41_. </s>
            <s xml:id="echoid-s6286" xml:space="preserve">& </s>
            <s xml:id="echoid-s6287" xml:space="preserve">ad dexteram _M_inuta _19_. </s>
            <s xml:id="echoid-s6288" xml:space="preserve">_A_rcus igitur grad. </s>
            <s xml:id="echoid-s6289" xml:space="preserve">_41_. </s>
            <s xml:id="echoid-s6290" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6291" xml:space="preserve">_19_.
              <lb/>
            </s>
            <s xml:id="echoid-s6292" xml:space="preserve">eſt is, qui quæritur. </s>
            <s xml:id="echoid-s6293" xml:space="preserve">_H_uius enim complementum eſt arcus grad. </s>
            <s xml:id="echoid-s6294" xml:space="preserve">_48_. </s>
            <s xml:id="echoid-s6295" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6296" xml:space="preserve">_41_. </s>
            <s xml:id="echoid-s6297" xml:space="preserve">cui sinus
              <lb/>
            datus debetur _I_dem arcus grad. </s>
            <s xml:id="echoid-s6298" xml:space="preserve">_41_. </s>
            <s xml:id="echoid-s6299" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6300" xml:space="preserve">_19_. </s>
            <s xml:id="echoid-s6301" xml:space="preserve">reperietur, si arcus grad. </s>
            <s xml:id="echoid-s6302" xml:space="preserve">_48_. </s>
            <s xml:id="echoid-s6303" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6304" xml:space="preserve">_41_. </s>
            <s xml:id="echoid-s6305" xml:space="preserve">
              <lb/>
            sinui dato in vertice tabulæ, & </s>
            <s xml:id="echoid-s6306" xml:space="preserve">ad siniſtram reſpondens ex quadrante ſubducatur. </s>
            <s xml:id="echoid-s6307" xml:space="preserve">
              <lb/>
            _Q_uòd si partem proportionalem ſupra inuentam, nimirum _S_ec. </s>
            <s xml:id="echoid-s6308" xml:space="preserve">_1._ </s>
            <s xml:id="echoid-s6309" xml:space="preserve">detrahas ex arcure
              <lb/>
              <note position="left" xlink:label="note-184-02" xlink:href="note-184-02a" xml:space="preserve">Arcus qua-
                <lb/>
              drante mi-
                <lb/>
              nor magis
                <lb/>
              pręcisꝰ, qua
                <lb/>
              via ex ſinu
                <lb/>
              cõplementi
                <lb/>
              @ognoſcat̃.</note>
            perto grad. </s>
            <s xml:id="echoid-s6310" xml:space="preserve">_41_. </s>
            <s xml:id="echoid-s6311" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6312" xml:space="preserve">_19_. </s>
            <s xml:id="echoid-s6313" xml:space="preserve">(quia maiorem arcum, quàm par eſt, dato sinui _7510767_. </s>
            <s xml:id="echoid-s6314" xml:space="preserve">tri-
              <lb/>
            buimus.) </s>
            <s xml:id="echoid-s6315" xml:space="preserve">inuenietur arcus magis præciſus grad. </s>
            <s xml:id="echoid-s6316" xml:space="preserve">_41_. </s>
            <s xml:id="echoid-s6317" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6318" xml:space="preserve">_18_. </s>
            <s xml:id="echoid-s6319" xml:space="preserve">_S_ec. </s>
            <s xml:id="echoid-s6320" xml:space="preserve">_59_. </s>
            <s xml:id="echoid-s6321" xml:space="preserve">_Q_ui etiam repe-
              <lb/>
            rietur, si arcum grad. </s>
            <s xml:id="echoid-s6322" xml:space="preserve">_48_. </s>
            <s xml:id="echoid-s6323" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6324" xml:space="preserve">_41_. </s>
            <s xml:id="echoid-s6325" xml:space="preserve">_S_ec. </s>
            <s xml:id="echoid-s6326" xml:space="preserve">_1._ </s>
            <s xml:id="echoid-s6327" xml:space="preserve">eidem ſinui, tanquam recto, debitum, & </s>
            <s xml:id="echoid-s6328" xml:space="preserve">ſe-
              <lb/>
            cundum partem propertionalem inuentum, detrahas ex quadrante. </s>
            <s xml:id="echoid-s6329" xml:space="preserve">_R_urſus detur
              <lb/>
            _455630_. </s>
            <s xml:id="echoid-s6330" xml:space="preserve">sinus complementi alicuius arcus, quem in tabula quæsitum non inuenio.
              <lb/>
            </s>
            <s xml:id="echoid-s6331" xml:space="preserve">_A_ccipio ergo proxime maiorem _456536_. </s>
            <s xml:id="echoid-s6332" xml:space="preserve">(quoniam ab hoc minus diſtat, quàm à pro-
              <lb/>
            xime minore _453630_.) </s>
            <s xml:id="echoid-s6333" xml:space="preserve">cui in parte inferiori tabulæ reſpondet arcus grad. </s>
            <s xml:id="echoid-s6334" xml:space="preserve">_87_. </s>
            <s xml:id="echoid-s6335" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6336" xml:space="preserve">
              <lb/>
            _23_. </s>
            <s xml:id="echoid-s6337" xml:space="preserve">quæſitus; </s>
            <s xml:id="echoid-s6338" xml:space="preserve">cum huius complementum ſit arcus grad. </s>
            <s xml:id="echoid-s6339" xml:space="preserve">_2_. </s>
            <s xml:id="echoid-s6340" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6341" xml:space="preserve">_37_. </s>
            <s xml:id="echoid-s6342" xml:space="preserve">sinui dato, tanquã
              <lb/>
            recto, debitus. </s>
            <s xml:id="echoid-s6343" xml:space="preserve">_Q_uòd si partem proportionalem ſupra inuentam, nimirum _S_ec. </s>
            <s xml:id="echoid-s6344" xml:space="preserve">_19_. </s>
            <s xml:id="echoid-s6345" xml:space="preserve">ad-
              <lb/>
            das arcui inuento grad. </s>
            <s xml:id="echoid-s6346" xml:space="preserve">_87_. </s>
            <s xml:id="echoid-s6347" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6348" xml:space="preserve">_23_. </s>
            <s xml:id="echoid-s6349" xml:space="preserve">(quia minorem arcum, quàm par eſt, dato sinui
              <lb/>
            _455630_. </s>
            <s xml:id="echoid-s6350" xml:space="preserve">tribuimus.) </s>
            <s xml:id="echoid-s6351" xml:space="preserve">inuenietur arcus magis præciſus grad. </s>
            <s xml:id="echoid-s6352" xml:space="preserve">_87_. </s>
            <s xml:id="echoid-s6353" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6354" xml:space="preserve">_23_. </s>
            <s xml:id="echoid-s6355" xml:space="preserve">_S_ec. </s>
            <s xml:id="echoid-s6356" xml:space="preserve">_19_. </s>
            <s xml:id="echoid-s6357" xml:space="preserve">_Q_uẽ
              <lb/>
            etiam reperies, si arcum grad. </s>
            <s xml:id="echoid-s6358" xml:space="preserve">_2_. </s>
            <s xml:id="echoid-s6359" xml:space="preserve">_M_in _36_. </s>
            <s xml:id="echoid-s6360" xml:space="preserve">_S_ec. </s>
            <s xml:id="echoid-s6361" xml:space="preserve">_41_. </s>
            <s xml:id="echoid-s6362" xml:space="preserve">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"/>
          </p>
          <p style="it">
            <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>
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