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

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          <pb o="420" file="432" n="432" rhead=""/>
          <p style="it">
            <s xml:id="echoid-s14648" xml:space="preserve">IN triangulo ABC, cuius angulus C, rectus, dat@
              <lb/>
              <figure xlink:label="fig-432-01" xlink:href="fig-432-01a" number="286">
                <image file="432-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/432-01"/>
              </figure>
            ſint primum duo arcus AC, CB, circa angulum rectum
              <lb/>
            C. </s>
            <s xml:id="echoid-s14649" xml:space="preserve">Dico dari quoque tertium arcum AB, cum duobus an-
              <lb/>
            gulis A,
              <emph style="sc">B</emph>
            . </s>
            <s xml:id="echoid-s14650" xml:space="preserve">Quoniam enim eſt, vt ſinus complementi ar-
              <lb/>
              <note position="left" xlink:label="note-432-01" xlink:href="note-432-01a" xml:space="preserve">43. huius.</note>
            cus
              <emph style="sc">Ab</emph>
            , ad ſinum complementi arcus AC, ita ſinus com-
              <lb/>
            plementi arcus CB, ad ſinum totum; </s>
            <s xml:id="echoid-s14651" xml:space="preserve">erit conuertendo, vt
              <lb/>
            ſinus totus ad ſinum complementi arcus CB, ita ſinus com
              <lb/>
            plementi arcus AC, ad ſinum complementi arcus AB.</s>
            <s xml:id="echoid-s14652" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14653" xml:space="preserve">QV AMOBREM, datis duobus arcubus rectum angulum ambien
              <lb/>
              <note position="left" xlink:label="note-432-02" xlink:href="note-432-02a" xml:space="preserve">Praxis, quã
                <lb/>
              do dantut
                <lb/>
              duo arcus
                <lb/>
              circa angu
                <lb/>
              lũ rectum.</note>
            tibus, ſi fiat, vt ſinus totus ad ſinum complementi vtriuſlibet arcuum
              <lb/>
            datorum, ita ſinus complementi alterius arcus dati ad aliud, producetur
              <lb/>
            ſinus complementi arcus recto angulo oppoſiti, qui quæritur. </s>
            <s xml:id="echoid-s14654" xml:space="preserve">Ex dato au-
              <lb/>
            tem arcu, quirecto angulo opponitur, cum vtrouis arcu cir ca rectum an-
              <lb/>
            gulum, inuenietur angulus ci oppoſitus, vt in probtemate 1. </s>
            <s xml:id="echoid-s14655" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s14656" xml:space="preserve">41.
              <lb/>
            </s>
            <s xml:id="echoid-s14657" xml:space="preserve">tradidimus.</s>
            <s xml:id="echoid-s14658" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14659" xml:space="preserve">VTRVM vero quæſitus arcus AB, quadrante minor ſit, aut maior, docebunt
              <lb/>
              <note position="left" xlink:label="note-432-03" xlink:href="note-432-03a" xml:space="preserve">35. huius.</note>
            duo arcus dati, Si enim vter que fuerit minor, aut maior quadrante, erit arcus AB,
              <lb/>
            quadrante minor: </s>
            <s xml:id="echoid-s14660" xml:space="preserve">Si vero vnus ſit quadrante minor, & </s>
            <s xml:id="echoid-s14661" xml:space="preserve">alter maior, erit arcus AB,
              <lb/>
            quadrante maior.</s>
            <s xml:id="echoid-s14662" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14663" xml:space="preserve">DATVS deinde ſit arcus AB, recto angulo oppoſitus, cum alterutro arcuum
              <lb/>
            circa angulum rectum, vt cum AC. </s>
            <s xml:id="echoid-s14664" xml:space="preserve">Dico rurſum dari reliquum arcum CB, cum
              <lb/>
            duobus angulis A, B. </s>
            <s xml:id="echoid-s14665" xml:space="preserve">Nam cum ſit, vt ſinus complementi arcus
              <emph style="sc">Ab</emph>
            , ad ſinum com-
              <lb/>
              <note position="left" xlink:label="note-432-04" xlink:href="note-432-04a" xml:space="preserve">43. huius.</note>
            plementi arcus AC, ita ſinus complementi arcus
              <emph style="sc">Cb</emph>
            , ad ſinum totum; </s>
            <s xml:id="echoid-s14666" xml:space="preserve">erit conuer-
              <lb/>
            tendo, vt ſinus complementi arcus AC, ad ſinum complementi arcus
              <emph style="sc">Ab</emph>
            , ita ſinus
              <lb/>
            totus ad ſinum complementi arcus
              <emph style="sc">Cb</emph>
            .</s>
            <s xml:id="echoid-s14667" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14668" xml:space="preserve">QV APROPTER, dato arcu, qui recto angulo opponitur, cum
              <lb/>
              <note position="left" xlink:label="note-432-05" xlink:href="note-432-05a" xml:space="preserve">Praxis, quã
                <lb/>
              do datur
                <lb/>
              arcus recto
                <lb/>
              angulo op-
                <lb/>
              poſitus, cũ
                <lb/>
              alterutro
                <lb/>
              circa angu
                <lb/>
              lũ rectum.</note>
            alterutro arcuum circa angulum rectum, ſi ſiat, vt ſinus complementi ar-
              <lb/>
            cus dati circa angulum rectum ad ſinum complementi arcus angulo recto
              <lb/>
            oppoſiti, ita ſinus totus ad aliud, inuenietur ſinus complementi alterius
              <lb/>
            arcus circa angulum rectum, qui quæritur. </s>
            <s xml:id="echoid-s14669" xml:space="preserve">Ex quouis autem arcu dato
              <lb/>
            cir ca rectum angulum, cum arcu, quirecto angulo opponitur, reperietur
              <lb/>
            angulus illi arcui oppoſitus, vt in problemate 1. </s>
            <s xml:id="echoid-s14670" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s14671" xml:space="preserve">41. </s>
            <s xml:id="echoid-s14672" xml:space="preserve">demonſtra-
              <lb/>
            tum est.</s>
            <s xml:id="echoid-s14673" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14674" xml:space="preserve">AN vero tertius arcus CB, quæſitus ſit quadrante minor, aut maior, intellige-
              <lb/>
            mus ex duobus arcubus datis. </s>
            <s xml:id="echoid-s14675" xml:space="preserve">Si namque arcus
              <emph style="sc">AB</emph>
            , angulo recto oppoſitus fuerit
              <lb/>
            quadrante minor, ſi quidem & </s>
            <s xml:id="echoid-s14676" xml:space="preserve">alter datus AC, ſit quadrante minor, erit & </s>
            <s xml:id="echoid-s14677" xml:space="preserve">arcus
              <lb/>
            CB, quadrante minor; </s>
            <s xml:id="echoid-s14678" xml:space="preserve">ſi vero AC, ſit quadrante maior, erit & </s>
            <s xml:id="echoid-s14679" xml:space="preserve">CB, maior qua-
              <lb/>
              <note position="left" xlink:label="note-432-06" xlink:href="note-432-06a" xml:space="preserve">36. huius.</note>
            drante. </s>
            <s xml:id="echoid-s14680" xml:space="preserve">Si autem
              <emph style="sc">AB</emph>
            , fuerit quadrante maior, ſi quidem & </s>
            <s xml:id="echoid-s14681" xml:space="preserve">
              <emph style="sc">A</emph>
            C, ſit quadrante
              <lb/>
            maior, erit CB, quadrante minor; </s>
            <s xml:id="echoid-s14682" xml:space="preserve">ſi vero AC, ſit minor quadrante, erit CB,
              <lb/>
            quadrante maior.</s>
            <s xml:id="echoid-s14683" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1170" type="section" level="1" n="561">
          <head xml:id="echoid-head596" xml:space="preserve">SCHOLIVM. II.</head>
          <p style="it">
            <s xml:id="echoid-s14684" xml:space="preserve">QVAMVIS & </s>
            <s xml:id="echoid-s14685" xml:space="preserve">hanc propoſ. </s>
            <s xml:id="echoid-s14686" xml:space="preserve">43. </s>
            <s xml:id="echoid-s14687" xml:space="preserve">& </s>
            <s xml:id="echoid-s14688" xml:space="preserve">antecedentem 42. </s>
            <s xml:id="echoid-s14689" xml:space="preserve">quadrimembrem feco-
              <lb/>
              <note position="left" xlink:label="note-432-07" xlink:href="note-432-07a" xml:space="preserve">Quicquid
                <lb/>
              demonſtra
                <lb/>
              tur de triã-
                <lb/>
              gulo ſphæ.</note>
            </s>
          </p>
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