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

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        <div xml:id="echoid-div536" type="section" level="1" n="255">
          <head xml:id="echoid-head282" xml:space="preserve">LINAE TANGENTES,
            <lb/>
          atque Secantes.</head>
          <p style="it">
            <s xml:id="echoid-s7624" xml:space="preserve">QVANQVAM Aſtronomi omnia
              <lb/>
            ſua problemata, atque theoremata per ſolos ſi-
              <lb/>
            nus explicare poßint, vt communiter ab omni-
              <lb/>
            bus fieri ſolet, quia tamen multa facilius, ac bre-
              <lb/>
            uius expediuntur, ſi vnà cum ſinubus lineætan-
              <lb/>
            gentes, ſecantesque adhibeantur, vt ex doctri-
              <lb/>
            na triangulorum erit manifestum; </s>
            <s xml:id="echoid-s7625" xml:space="preserve">quas qui-
              <lb/>
            demlineas vtili ſane conſilio Recentiores exco-
              <lb/>
            gitarunt, atque in tabulas redegerunt: </s>
            <s xml:id="echoid-s7626" xml:space="preserve">viſum
              <lb/>
            est has etiam lineas paucis exponere, vt doctri-
              <lb/>
            na noſtrorum triangulorum perfectior euadat.
              <lb/>
            </s>
            <s xml:id="echoid-s7627" xml:space="preserve">Vniuerſa ſiquidem triangulorum doctrina in
              <lb/>
              <note position="left" xlink:label="note-200-01" xlink:href="note-200-01a" xml:space="preserve">Doctrina
                <lb/>
              triangulo -
                <lb/>
              rũ in quo
                <lb/>
              conſiſtat.</note>
            tribus hiſce line arum generibus, nempe in ſinu-
              <lb/>
            bus, lineis tangentibus, & </s>
            <s xml:id="echoid-s7628" xml:space="preserve">ſecantibus, potißi-
              <lb/>
            mum conſiſtere videtur. </s>
            <s xml:id="echoid-s7629" xml:space="preserve">Primum autem expli-
              <lb/>
            candum eſt, quid ſit linea tangens, & </s>
            <s xml:id="echoid-s7630" xml:space="preserve">quid ſe-
              <lb/>
            cans propoſiti cuiuſuis arcus.</s>
            <s xml:id="echoid-s7631" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s7632" xml:space="preserve">
              <emph style="sc">CVm</emph>
            ergoab altero extremo cuius libet arcus, qui quadrante minor ſit, ſemi-
              <lb/>
              <note position="left" xlink:label="note-200-02" xlink:href="note-200-02a" xml:space="preserve">Linea tan-
                <lb/>
              gens, & ſe-
                <lb/>
              cans quid.</note>
            diameter ducta fuerit, in cuius extremitate recta linea circulum tangat, & </s>
            <s xml:id="echoid-s7633" xml:space="preserve">per
              <lb/>
            alierum extremum eiuſdem arcus extendatur alia recta linea ex centro ad tangen-
              <lb/>
            tem lineam vſque: </s>
            <s xml:id="echoid-s7634" xml:space="preserve">appellatur portio lineæ tangentis inter duas rectas è centro egre-
              <lb/>
            dientes, Linea tangens illius arcus, quem eædẽ duæ rectæ e centro eductæ includunt:
              <lb/>
            </s>
            <s xml:id="echoid-s7635" xml:space="preserve">Recta vero altera puncto contactus oppoſita inter centrum, & </s>
            <s xml:id="echoid-s7636" xml:space="preserve">lineam tangentem, di-
              <lb/>
            citur Linea ſecans eiuſdem arcus. </s>
            <s xml:id="echoid-s7637" xml:space="preserve">Vt ſi in circulo AB, cuius centrum C, ſumatur ar-
              <lb/>
            cus AB, quadrante minor, & </s>
            <s xml:id="echoid-s7638" xml:space="preserve">in extremitate ſemidiametri
              <emph style="sc">Ac</emph>
            , ab extremitate </s>
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