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

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          <p style="it">
            <s xml:id="echoid-s14817" xml:space="preserve">
              <pb o="424" file="436" n="436" rhead=""/>
            ſit arcus
              <emph style="sc">Ab</emph>
            , recto angulo oppoſitus, ſpeciem quoque arcus BC, cognoſceremus. </s>
            <s xml:id="echoid-s14818" xml:space="preserve">Nam
              <lb/>
            ſi AB, ſit quadrante minor, erit vterque AC, BC, vet
              <lb/>
              <figure xlink:label="fig-436-01" xlink:href="fig-436-01a" number="290">
                <image file="436-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/436-01"/>
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            minor quadrante, vel maior: </s>
            <s xml:id="echoid-s14819" xml:space="preserve">qualis ergo eſt datus arcus
              <lb/>
              <note position="left" xlink:label="note-436-01" xlink:href="note-436-01a" xml:space="preserve">36. huius.</note>
            AC, talis quoque erit arcus BC. </s>
            <s xml:id="echoid-s14820" xml:space="preserve">Si vero AB, fuerit
              <lb/>
            maior quadrante, & </s>
            <s xml:id="echoid-s14821" xml:space="preserve">datus arcus AC, minor quidem
              <lb/>
            quadrante, erit BC, quadrante maior; </s>
            <s xml:id="echoid-s14822" xml:space="preserve">ſi vero datus ar-
              <lb/>
            cus AC, ſit quadrante maior, erit
              <emph style="sc">BC</emph>
            , quadrante mi-
              <lb/>
            nor. </s>
            <s xml:id="echoid-s14823" xml:space="preserve">Itaque non ſatis eſt, dari arcum, cum angulo oppo-
              <lb/>
            ſito, vt vult Copernicus propoſ 4. </s>
            <s xml:id="echoid-s14824" xml:space="preserve">de triangulis ſphæri-
              <lb/>
            cis. </s>
            <s xml:id="echoid-s14825" xml:space="preserve">Id quod ſupra in ſcholio propoſ. </s>
            <s xml:id="echoid-s14826" xml:space="preserve">21. </s>
            <s xml:id="echoid-s14827" xml:space="preserve">monuimus.</s>
            <s xml:id="echoid-s14828" xml:space="preserve"/>
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        </div>
        <div xml:id="echoid-div1183" type="section" level="1" n="565">
          <head xml:id="echoid-head600" xml:space="preserve">II.</head>
          <p style="it">
            <s xml:id="echoid-s14829" xml:space="preserve">IN triangulo ſphærico rectangulo, datis duobus arcubus circa
              <lb/>
            rectum angulum, vtrumlibetangulorum non rectorum, vnà cum ar-
              <lb/>
            cu reliquo, qui angulo recto opponitur, explorare.</s>
            <s xml:id="echoid-s14830" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14831" xml:space="preserve">IN eodem triangulo dati ſint duo arcus AC,
              <emph style="sc">BC</emph>
            . </s>
            <s xml:id="echoid-s14832" xml:space="preserve">Dico dari quoque vtrum vis
              <lb/>
            angulorum A,
              <emph style="sc">B</emph>
            , & </s>
            <s xml:id="echoid-s14833" xml:space="preserve">arcum
              <emph style="sc">AB</emph>
            . </s>
            <s xml:id="echoid-s14834" xml:space="preserve">Cum enim ſit, vt ſinus totus ad ſinum arcus AC,
              <lb/>
              <note position="left" xlink:label="note-436-02" xlink:href="note-436-02a" xml:space="preserve">44. huius.</note>
            ita tangens anguli A, ad tangentem arcus
              <emph style="sc">BC</emph>
            : </s>
            <s xml:id="echoid-s14835" xml:space="preserve">Et conuertendo, vt ſinus arcus AC,
              <lb/>
            ad ſinum totum, ita tangens arcus
              <emph style="sc">BC</emph>
            , ad tangentem anguli A; </s>
            <s xml:id="echoid-s14836" xml:space="preserve">Eademq́; </s>
            <s xml:id="echoid-s14837" xml:space="preserve">ratione,
              <lb/>
            vt ſinus arcus
              <emph style="sc">BC</emph>
            , ad ſinum totum, ita tangens arcus
              <emph style="sc">AC</emph>
            , ad tangentem anguli
              <emph style="sc">B</emph>
            .</s>
            <s xml:id="echoid-s14838" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14839" xml:space="preserve">SI fiat, vt ſinus vtriuſuis ar cuum circa angulum rectum ad ſinurn
              <lb/>
              <note position="left" xlink:label="note-436-03" xlink:href="note-436-03a" xml:space="preserve">Praxis.</note>
            totum, ita tangens alterius arcus ad aliud, inuenietur tangens anguli huic
              <lb/>
            poſteriori arcui oppoſiti. </s>
            <s xml:id="echoid-s14840" xml:space="preserve">Ex datis quoque duobus ar cubus circa angulum
              <lb/>
            rectum cognoſcetur & </s>
            <s xml:id="echoid-s14841" xml:space="preserve">tertius arcus recto angulo oppoſitus, vt in proble-
              <lb/>
            mate propoſ. </s>
            <s xml:id="echoid-s14842" xml:space="preserve">43. </s>
            <s xml:id="echoid-s14843" xml:space="preserve">traditum eſt. </s>
            <s xml:id="echoid-s14844" xml:space="preserve">Vel certe ex dato vno arcu, & </s>
            <s xml:id="echoid-s14845" xml:space="preserve">alterutro
              <lb/>
            angulor um inuento, vt in problemate 2. </s>
            <s xml:id="echoid-s14846" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s14847" xml:space="preserve">42. </s>
            <s xml:id="echoid-s14848" xml:space="preserve">oſtenſum eſt.</s>
            <s xml:id="echoid-s14849" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14850" xml:space="preserve">NVM autem angulus quæſitus ſit acutus, obtuſuſve, docebit arcus ei oppoſitus.
              <lb/>
            </s>
            <s xml:id="echoid-s14851" xml:space="preserve">Hic enim ſi minor quadrante ſuerit, erit angulus ei oppoſitus, acutus, ſi vero ma-
              <lb/>
              <note position="left" xlink:label="note-436-04" xlink:href="note-436-04a" xml:space="preserve">54. huius.</note>
            ior, obtuſus.</s>
            <s xml:id="echoid-s14852" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14853" xml:space="preserve">QVONIAM verò in ſcholio 2. </s>
            <s xml:id="echoid-s14854" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s14855" xml:space="preserve">præcedentis diximus, per lineas tangen-
              <lb/>
            tes, ac ſecantes breuius nonnulla expediri, quam per ſinus, intelligendum id eſt de ijs,
              <lb/>
            quæ primo loco in problematibus quæruntur, non autem, quæ ſecundo loco inueſti-
              <lb/>
            gantur. </s>
            <s xml:id="echoid-s14856" xml:space="preserve">Quod vt planius fiat, exponemus, quo paõto vtrumque problema hic pro-
              <lb/>
            poſitum abſoluendum ſit per ſinus. </s>
            <s xml:id="echoid-s14857" xml:space="preserve">Itaque, vt ex arcu circa angulum rectum dato,
              <lb/>
            cum alterutro angulorum acutorum, inueniatur alter arcus circa angulum rectums
              <lb/>
            qui primo loco in primo problemate inueſtigandus proponitur: </s>
            <s xml:id="echoid-s14858" xml:space="preserve">ita progrediendum
              <lb/>
            erit. </s>
            <s xml:id="echoid-s14859" xml:space="preserve">Si arcus circa rectum angulum detur cum angulo oppoſito, inquirendus pri-
              <lb/>
            mum erit arcus recto angulo oppoſitus, ex problemate 3. </s>
            <s xml:id="echoid-s14860" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s14861" xml:space="preserve">41. </s>
            <s xml:id="echoid-s14862" xml:space="preserve">Deinde ex hoc
              <lb/>
            arcu inuento, & </s>
            <s xml:id="echoid-s14863" xml:space="preserve">dato arcu, eliciendus erit, per problema propoſ. </s>
            <s xml:id="echoid-s14864" xml:space="preserve">43. </s>
            <s xml:id="echoid-s14865" xml:space="preserve">alter arcus cir
              <lb/>
            ca angulum rectum, qui quæritur. </s>
            <s xml:id="echoid-s14866" xml:space="preserve">Si vero detur arcus circa angulum rectum cum
              <lb/>
            angulo adiacente, quærendus eſt primum per problema 2. </s>
            <s xml:id="echoid-s14867" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s14868" xml:space="preserve">42. </s>
            <s xml:id="echoid-s14869" xml:space="preserve">alter angulus
              <lb/>
            acutus. </s>
            <s xml:id="echoid-s14870" xml:space="preserve">Deinde per problema 1. </s>
            <s xml:id="echoid-s14871" xml:space="preserve">eiuſdem propoſ. </s>
            <s xml:id="echoid-s14872" xml:space="preserve">42. </s>
            <s xml:id="echoid-s14873" xml:space="preserve">ex hoc angulo inuento, & </s>
            <s xml:id="echoid-s14874" xml:space="preserve">angulo
              <lb/>
            dato, arcus dato angulo oppoſitus eliciendus. </s>
            <s xml:id="echoid-s14875" xml:space="preserve">At, vt ex duobus arcubus circa angu-
              <lb/>
            lum rectum datis, vteruis angulorum acutorum eruatur; </s>
            <s xml:id="echoid-s14876" xml:space="preserve">qui primo loco in ſecun-
              <lb/>
            do problemate inquiritur: </s>
            <s xml:id="echoid-s14877" xml:space="preserve">reperiendus erit primum arcus recto angulo oppoſitus </s>
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