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

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        <div xml:id="echoid-div476" type="section" level="1" n="240">
          <pb o="171" file="183" n="183" rhead=""/>
          <p style="it">
            <s xml:id="echoid-s6142" xml:space="preserve">_CAETERVM_ _Q_uadrantist tam ſinus rectus, quàm verſus eſt ſinus totus; </s>
            <s xml:id="echoid-s6143" xml:space="preserve">ſinus
              <lb/>
              <note position="right" xlink:label="note-183-01" xlink:href="note-183-01a" xml:space="preserve">Sinus tã re
                <lb/>
              ctus, q̃ ver-
                <lb/>
              ſus Quadiã
                <lb/>
              tis eſt ſinus
                <lb/>
              totus, ſinus
                <lb/>
              vero cõple-
                <lb/>
              menti ni-
                <lb/>
              hil eſt.</note>
            vero complementi nihil eſt, vt manifeſtum eſt ex prima figura in definitionibus poſita.</s>
            <s xml:id="echoid-s6144" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6145" xml:space="preserve">_IAM_ vero ex cognito ſinu recto ita arcum inuenies. </s>
            <s xml:id="echoid-s6146" xml:space="preserve">_Q_uære ſinum rectum propo-
              <lb/>
            ſitum inter ſinus tabulæ; </s>
            <s xml:id="echoid-s6147" xml:space="preserve">vel ſi eum non inueneris, ſume proxime maiorem, vel mino-
              <lb/>
            rem, qui nimirum paucioribus vnitatibus à propoſito ſinu diſtat. </s>
            <s xml:id="echoid-s6148" xml:space="preserve">_N_am in vertice ta-
              <lb/>
            bulæ reperies gradus, & </s>
            <s xml:id="echoid-s6149" xml:space="preserve">ad ſini ſtram è regione ſinus accepti, _M_inuta illius arcus, qui
              <lb/>
            propoſito ſinut reſpondet. </s>
            <s xml:id="echoid-s6150" xml:space="preserve">_V_t ſi cognitus ſit ſinus _7510767_. </s>
            <s xml:id="echoid-s6151" xml:space="preserve">_I_nuenio ſinum _7510722_.
              <lb/>
            </s>
            <s xml:id="echoid-s6152" xml:space="preserve">proxime minorem, qui paucioribus vmtatibus à ſinu cognito diſtat, quàm ſinus
              <lb/>
              <note position="right" xlink:label="note-183-02" xlink:href="note-183-02a" xml:space="preserve">Arcus qua-
                <lb/>
              drante mi-
                <lb/>
              not quo pà
                <lb/>
              cto ex ſinu
                <lb/>
              recto cogni
                <lb/>
              to eliciat̃.</note>
            _7512642_. </s>
            <s xml:id="echoid-s6153" xml:space="preserve">proxime maior: </s>
            <s xml:id="echoid-s6154" xml:space="preserve">_C_ui ſinui proxime minori reſpõdent in vertice tabulæ grad.
              <lb/>
            </s>
            <s xml:id="echoid-s6155" xml:space="preserve">_48_. </s>
            <s xml:id="echoid-s6156" xml:space="preserve">& </s>
            <s xml:id="echoid-s6157" xml:space="preserve">ad ſiniſtram _M_inuta _41_. </s>
            <s xml:id="echoid-s6158" xml:space="preserve">_A_rcum ergo grad. </s>
            <s xml:id="echoid-s6159" xml:space="preserve">_48_. </s>
            <s xml:id="echoid-s6160" xml:space="preserve">& </s>
            <s xml:id="echoid-s6161" xml:space="preserve">_M_in _41_ dico deberi ſinui pro-
              <lb/>
            poſito. </s>
            <s xml:id="echoid-s6162" xml:space="preserve">_N_am vnitates illæ, quibus ſinus propoſitus à ſinu dicti arcus differt, non indu-
              <lb/>
            cunt errorem notabilem. </s>
            <s xml:id="echoid-s6163" xml:space="preserve">_S_i tamen arcum cupis præciſiorem, inueſtiganda erit pars
              <lb/>
            proportionalis, hac arte. </s>
            <s xml:id="echoid-s6164" xml:space="preserve">_C_ape differentiam inter ſinum proxime minorem, & </s>
            <s xml:id="echoid-s6165" xml:space="preserve">ſinum
              <lb/>
            proxime maiorem: </s>
            <s xml:id="echoid-s6166" xml:space="preserve">_I_tem differentiam inter ſinum propoſitum, & </s>
            <s xml:id="echoid-s6167" xml:space="preserve">illum in tabula re-
              <lb/>
            pertũ, à quo minus differt; </s>
            <s xml:id="echoid-s6168" xml:space="preserve">& </s>
            <s xml:id="echoid-s6169" xml:space="preserve">dic. </s>
            <s xml:id="echoid-s6170" xml:space="preserve">_S_i differentia inter duos ſinus in tabula repertos dat
              <lb/>
              <note position="right" xlink:label="note-183-03" xlink:href="note-183-03a" xml:space="preserve">Arcus qua-
                <lb/>
              drante mi-
                <lb/>
              nor magis
                <lb/>
              p̃ciſus, quo
                <lb/>
              pacto p par
                <lb/>
              tẽ propor-
                <lb/>
              tionalẽ ex
                <lb/>
              dato ſinu
                <lb/>
              eliciatur.</note>
            _60_. </s>
            <s xml:id="echoid-s6171" xml:space="preserve">_S_ecunda addenda arcui ſinus proxime minoris, vel auferenda ab arcu ſinus proxi-
              <lb/>
            me maioris, (prout videlicet ſumpta fuerit differentia inter ſinum propoſitum, & </s>
            <s xml:id="echoid-s6172" xml:space="preserve">
              <lb/>
            ſinum proxime minorem, vel proxime maiorem) vt habeatur arcus ſinus proxime ma-
              <lb/>
            ioris, vel proxime minoris; </s>
            <s xml:id="echoid-s6173" xml:space="preserve">quot _S_ecunda poſtulat differentia inter ſinum propoſitum
              <lb/>
            & </s>
            <s xml:id="echoid-s6174" xml:space="preserve">ſinum proxime minorem, vel proxime maiorem, addenda arcui ſinus proxime mi-
              <lb/>
            noris, vel auferenda ab arcu ſinus proxime maioris, vt habeatur arcus propoſiti ſinus?
              <lb/>
            </s>
            <s xml:id="echoid-s6175" xml:space="preserve">_N_am hæc ſecunda inuenta addita arcui ſinus proxime minoris, vel ablata ab arcu
              <lb/>
            ſinus proxime maioris, dabunt arcum ſinus propoſiti. </s>
            <s xml:id="echoid-s6176" xml:space="preserve">_V_t in dato exemplo, ſi dicas. </s>
            <s xml:id="echoid-s6177" xml:space="preserve">
              <lb/>
            _D_ifferẽtia _1920_. </s>
            <s xml:id="echoid-s6178" xml:space="preserve">inter ſinum _7510722_. </s>
            <s xml:id="echoid-s6179" xml:space="preserve">proxime minorem, & </s>
            <s xml:id="echoid-s6180" xml:space="preserve">ſinum _17512642_. </s>
            <s xml:id="echoid-s6181" xml:space="preserve">pro-
              <lb/>
            xime maiorẽ, dat _60_. </s>
            <s xml:id="echoid-s6182" xml:space="preserve">_S_ecunda addenda arcui grad. </s>
            <s xml:id="echoid-s6183" xml:space="preserve">_48_. </s>
            <s xml:id="echoid-s6184" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6185" xml:space="preserve">_41_. </s>
            <s xml:id="echoid-s6186" xml:space="preserve">qui ſinui proxime mi-
              <lb/>
            nori reſpõdet, (quoniã propoſitus ſinus minus differt à ſinu proxime minori quàm à si
              <lb/>
            nu proxime maiori) vt habeatur arcus grad. </s>
            <s xml:id="echoid-s6187" xml:space="preserve">_48_. </s>
            <s xml:id="echoid-s6188" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6189" xml:space="preserve">_41_. </s>
            <s xml:id="echoid-s6190" xml:space="preserve">_S_ec. </s>
            <s xml:id="echoid-s6191" xml:space="preserve">_60_. </s>
            <s xml:id="echoid-s6192" xml:space="preserve">hoc eſt, grad. </s>
            <s xml:id="echoid-s6193" xml:space="preserve">_48_. </s>
            <s xml:id="echoid-s6194" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6195" xml:space="preserve">
              <lb/>
            _42_. </s>
            <s xml:id="echoid-s6196" xml:space="preserve">reſpõdens ſinui proxime maiori. </s>
            <s xml:id="echoid-s6197" xml:space="preserve">_Q_uot ergo Secũda poſtulat differẽtia _45_. </s>
            <s xml:id="echoid-s6198" xml:space="preserve">inter ſinũ
              <lb/>
            propoſitũ, & </s>
            <s xml:id="echoid-s6199" xml:space="preserve">ſinũ proxime minorẽ, addenda eidẽ arcui ſinus proxime minoris, vt fiat
              <lb/>
            arcus dati ſinus? </s>
            <s xml:id="echoid-s6200" xml:space="preserve">_I_nuenies enim _S_ecundũ _1._ </s>
            <s xml:id="echoid-s6201" xml:space="preserve">& </s>
            <s xml:id="echoid-s6202" xml:space="preserve">paulo amplius addendũ arcui grad. </s>
            <s xml:id="echoid-s6203" xml:space="preserve">_48_. </s>
            <s xml:id="echoid-s6204" xml:space="preserve">
              <lb/>
            _M_in. </s>
            <s xml:id="echoid-s6205" xml:space="preserve">_41_. </s>
            <s xml:id="echoid-s6206" xml:space="preserve">ita vt ſinui propoſito _7510767_. </s>
            <s xml:id="echoid-s6207" xml:space="preserve">reſpondeat arcus grad. </s>
            <s xml:id="echoid-s6208" xml:space="preserve">_48_. </s>
            <s xml:id="echoid-s6209" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6210" xml:space="preserve">_41_. </s>
            <s xml:id="echoid-s6211" xml:space="preserve">_S_ec. </s>
            <s xml:id="echoid-s6212" xml:space="preserve">_1._ </s>
            <s xml:id="echoid-s6213" xml:space="preserve">& </s>
            <s xml:id="echoid-s6214" xml:space="preserve">
              <lb/>
            paulo amplius. </s>
            <s xml:id="echoid-s6215" xml:space="preserve">_R_u-ſus ſit datus ſinus _455630_. </s>
            <s xml:id="echoid-s6216" xml:space="preserve">quem in tabula quæſitum non inuenio. </s>
            <s xml:id="echoid-s6217" xml:space="preserve">
              <lb/>
            _A_ccipio ergo proxime maiorem _456536_. </s>
            <s xml:id="echoid-s6218" xml:space="preserve">(_A_b hoc enim minus diſtat, quàm à proxime
              <lb/>
            minori _453630_.) </s>
            <s xml:id="echoid-s6219" xml:space="preserve">cui reſpondet arcus grad. </s>
            <s xml:id="echoid-s6220" xml:space="preserve">_2_. </s>
            <s xml:id="echoid-s6221" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6222" xml:space="preserve">_37_. </s>
            <s xml:id="echoid-s6223" xml:space="preserve">_Q_uòd ſi magis præciſum arcum
              <lb/>
            deſiderem, inquiram partem proportionalem, hoc modo. </s>
            <s xml:id="echoid-s6224" xml:space="preserve">_D_ifferentia _2906_. </s>
            <s xml:id="echoid-s6225" xml:space="preserve">inter ſinũ
              <lb/>
            _456536_. </s>
            <s xml:id="echoid-s6226" xml:space="preserve">proxime maiorem, & </s>
            <s xml:id="echoid-s6227" xml:space="preserve">ſinum _453630_. </s>
            <s xml:id="echoid-s6228" xml:space="preserve">proxime minorem, dat _60_. </s>
            <s xml:id="echoid-s6229" xml:space="preserve">_S_ecũda au-
              <lb/>
            ferenda ab arcu grad. </s>
            <s xml:id="echoid-s6230" xml:space="preserve">_2_. </s>
            <s xml:id="echoid-s6231" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6232" xml:space="preserve">_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="preserve">_2_. </s>
            <s xml:id="echoid-s6235" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6236" xml:space="preserve">_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="preserve">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="preserve">
              <lb/>
            fere, quæ ablata ex arcu grad. </s>
            <s xml:id="echoid-s6243" xml:space="preserve">_2_. </s>
            <s xml:id="echoid-s6244" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6245" xml:space="preserve">_37_. </s>
            <s xml:id="echoid-s6246" xml:space="preserve">relinquunt arcum grad. </s>
            <s xml:id="echoid-s6247" xml:space="preserve">_2_. </s>
            <s xml:id="echoid-s6248" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s6249" xml:space="preserve">_36_. </s>
            <s xml:id="echoid-s6250" xml:space="preserve">_S_ec. </s>
            <s xml:id="echoid-s6251" xml:space="preserve">
              <lb/>
            _41_. </s>
            <s xml:id="echoid-s6252" xml:space="preserve">sinui dato _455630_. </s>
            <s xml:id="echoid-s6253" xml:space="preserve">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>
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