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

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            <s xml:id="echoid-s16883" xml:space="preserve">
              <pb o="471" file="483" n="483" rhead=""/>
            æquales erunt, vt in vltima figura præcedentis propoſ. </s>
            <s xml:id="echoid-s16884" xml:space="preserve">oſtendimus: </s>
            <s xml:id="echoid-s16885" xml:space="preserve">ac proin-
              <lb/>
            de vterque angulus ad A, datus erit, cum dimidium ſit an-
              <lb/>
              <figure xlink:label="fig-483-01" xlink:href="fig-483-01a" number="348">
                <image file="483-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/483-01"/>
              </figure>
            guli BAC, dati. </s>
            <s xml:id="echoid-s16886" xml:space="preserve">Quoniam ergo in triangulo ABD, an-
              <lb/>
            gulum habente rectum D, datus eſt arcus AB, recto angu-
              <lb/>
            lo oppoſitus, cum angulo BAD, nimirum cum dimidio
              <lb/>
              <note position="right" xlink:label="note-483-01" xlink:href="note-483-01a" xml:space="preserve">Schol. 41.
                <lb/>
              huius.</note>
            datianguli BAC; </s>
            <s xml:id="echoid-s16887" xml:space="preserve">cognitus erit arcus BD, dato angulo
              <lb/>
            BAD, oppoſitus: </s>
            <s xml:id="echoid-s16888" xml:space="preserve">qui duplicatus totum arcum BC, quæ-
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            ſitum reddet notum. </s>
            <s xml:id="echoid-s16889" xml:space="preserve">Rurſus quia in eodem triangulo ABD,
              <lb/>
              <note position="right" xlink:label="note-483-02" xlink:href="note-483-02a" xml:space="preserve">Schol. 51.
                <lb/>
              vel 45. huiꝰ.</note>
            rectum habente angulum D, datus eſt arcus AB, angulo
              <lb/>
            recto opppoſitus, cum arcu BD, circa angulum rectum:
              <lb/>
            </s>
            <s xml:id="echoid-s16890" xml:space="preserve">VEL, quia datus eſt arcus AB, recto angulo op-
              <lb/>
              <note position="right" xlink:label="note-483-03" xlink:href="note-483-03a" xml:space="preserve">Schol. 47.
                <lb/>
              huius.</note>
            poſitus, & </s>
            <s xml:id="echoid-s16891" xml:space="preserve">præterea angulus non rectus BAD:
              <lb/>
            </s>
            <s xml:id="echoid-s16892" xml:space="preserve">VEL denique, quia datus eſt arcus BD, circa re-
              <lb/>
              <note position="right" xlink:label="note-483-04" xlink:href="note-483-04a" xml:space="preserve">Schol. 56.
                <lb/>
              vel 42. huiꝰ.</note>
            ctum angulum, vnà cum angulo non recto BAD, qui
              <lb/>
            dato arcui BD, opponitur, conſtatq́; </s>
            <s xml:id="echoid-s16893" xml:space="preserve">pręterea ſpecies
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            reliqui anguli non recti B. </s>
            <s xml:id="echoid-s16894" xml:space="preserve">Nam ſi AB, fuerit quadran
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            te minor, erit angulus B, acutus, ſicut & </s>
            <s xml:id="echoid-s16895" xml:space="preserve">BAD, acutus
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            eſt: </s>
            <s xml:id="echoid-s16896" xml:space="preserve">Si vero AB, maior quadrante extiterit, erit angu-
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            lus B, obtuſus, quandoquidem BAD, acutus eſt;
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            </s>
            <s xml:id="echoid-s16897" xml:space="preserve">notus erit quoque, ex ſcholijs in margine adductis, angulus B; </s>
            <s xml:id="echoid-s16898" xml:space="preserve">ideoq́; </s>
            <s xml:id="echoid-s16899" xml:space="preserve">& </s>
            <s xml:id="echoid-s16900" xml:space="preserve">an-
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            gulus C, illi æqualis.</s>
            <s xml:id="echoid-s16901" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">38. huius.</note>
          <p style="it">
            <s xml:id="echoid-s16902" xml:space="preserve">PRAXIS petatur ex ſcholijs in margine adductis.</s>
            <s xml:id="echoid-s16903" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Praxis.</note>
          <p style="it">
            <s xml:id="echoid-s16904" xml:space="preserve">SOLIS ſinubus ita vtemur. </s>
            <s xml:id="echoid-s16905" xml:space="preserve">Per praxim problematis 2. </s>
            <s xml:id="echoid-s16906" xml:space="preserve">ſcholij pro
              <lb/>
              <note position="right" xlink:label="note-483-07" xlink:href="note-483-07a" xml:space="preserve">Praxis per
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              ſolos ſinus,
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              quádo dati
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              duo arcus
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              ſunt æqua-
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              les.</note>
            poſ. </s>
            <s xml:id="echoid-s16907" xml:space="preserve">41. </s>
            <s xml:id="echoid-s16908" xml:space="preserve">exquiremus arum BD; </s>
            <s xml:id="echoid-s16909" xml:space="preserve">qui duplicatus totum BC, qui quæritur,
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            dabit. </s>
            <s xml:id="echoid-s16910" xml:space="preserve">Deinde ex praxi problemat is 2. </s>
            <s xml:id="echoid-s16911" xml:space="preserve">ſcholij propoſ. </s>
            <s xml:id="echoid-s16912" xml:space="preserve">42. </s>
            <s xml:id="echoid-s16913" xml:space="preserve">quæremus an-
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            gulum B; </s>
            <s xml:id="echoid-s16914" xml:space="preserve">cui æqualis eſt alter angulus C.</s>
            <s xml:id="echoid-s16915" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16916" xml:space="preserve">DATIS igitur duobus arcubus trianguli ſphærici non rectanguli, cum
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            angulo ab ipſis comprehenſo; </s>
            <s xml:id="echoid-s16917" xml:space="preserve">reliquum arcum, cum reliquis angulis reperi-
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            mus. </s>
            <s xml:id="echoid-s16918" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s16919" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1338" type="section" level="1" n="610">
          <head xml:id="echoid-head645" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s16920" xml:space="preserve">HIC quoque potius vti voluimus theoremate ſcholij 2. </s>
            <s xml:id="echoid-s16921" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s16922" xml:space="preserve">58 in demonſtra-
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            tione ſecunda huius problemat is, quam theoremate eiuſdem propoſ. </s>
            <s xml:id="echoid-s16923" xml:space="preserve">58. </s>
            <s xml:id="echoid-s16924" xml:space="preserve">vt praxis mi-
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            nus fieret laborioſa. </s>
            <s xml:id="echoid-s16925" xml:space="preserve">Nam cum ſit, vt quadratum ſinus totius ad rectangulum ſub ſi-
              <lb/>
              <note position="right" xlink:label="note-483-08" xlink:href="note-483-08a" xml:space="preserve">58. huius.</note>
            nubus datorum arcuum inæqualium contentum, ita ſinus verſus anguli dati à dictis
              <lb/>
            arcubus comprehenſi ad differentiam inter ſinum verſum arcus dato angulo oppoſiti,
              <lb/>
            & </s>
            <s xml:id="echoid-s16926" xml:space="preserve">ſinum verſum differentiæ duorum arcuum datorum inæqualium: </s>
            <s xml:id="echoid-s16927" xml:space="preserve">ſi vellemus vti
              <lb/>
            hoc theoremate propoſ. </s>
            <s xml:id="echoid-s16928" xml:space="preserve">58. </s>
            <s xml:id="echoid-s16929" xml:space="preserve">moleſta redderetur multiplicatio in aurea regula, cum
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            ſinus verſus dati anguli multiplicandus eſſet per dictum rectangulum. </s>
            <s xml:id="echoid-s16930" xml:space="preserve">At in noſtra
              <lb/>
            praxi multo breuior fit muliiplicatio, vt patet, quamuis bis regulam auream adhi-
              <lb/>
            beamus.</s>
            <s xml:id="echoid-s16931" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1340" type="section" level="1" n="611">
          <head xml:id="echoid-head646" xml:space="preserve">PROBL. 6. PROP. 65.</head>
          <p>
            <s xml:id="echoid-s16932" xml:space="preserve">DATIS duobus angulis triáguli ſphærici </s>
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