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

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          <p>
            <s xml:id="echoid-s17523" xml:space="preserve">
              <pb o="483" file="495" n="495" rhead=""/>
            dimus. </s>
            <s xml:id="echoid-s17524" xml:space="preserve">Cum ergo angulus B, datus ſit, erit quoque C, illi æqualis, datus. </s>
            <s xml:id="echoid-s17525" xml:space="preserve">Dein-
              <lb/>
            de quia in triangulo ABD, habente rectum angulum D, datus eſt arcus AB,
              <lb/>
            angulo recto oppoſitus, cum angulo B; </s>
            <s xml:id="echoid-s17526" xml:space="preserve">dabitur quoque angulus BAD: </s>
            <s xml:id="echoid-s17527" xml:space="preserve">qui
              <lb/>
              <note position="right" xlink:label="note-495-01" xlink:href="note-495-01a" xml:space="preserve">Schol. 47.
                <lb/>
              huius.</note>
            duplicatus totum angulum BAC, quæſitum offeret notum. </s>
            <s xml:id="echoid-s17528" xml:space="preserve">Hinc, quoniam in
              <lb/>
            eodem triangulo ABD, datus eſt arcus AB, recto angulo oppoſitus, cum an-
              <lb/>
              <note position="right" xlink:label="note-495-02" xlink:href="note-495-02a" xml:space="preserve">Schol. 41.
                <lb/>
              huius.</note>
            gulo BAD, inuento:</s>
            <s xml:id="echoid-s17529" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17530" xml:space="preserve">VEL, quia vterq; </s>
            <s xml:id="echoid-s17531" xml:space="preserve">angulus non rectus B, & </s>
            <s xml:id="echoid-s17532" xml:space="preserve">BAD,
              <lb/>
              <note position="right" xlink:label="note-495-03" xlink:href="note-495-03a" xml:space="preserve">Schol. 42.
                <lb/>
              vel52. huiꝰ.</note>
            datus eſt:</s>
            <s xml:id="echoid-s17533" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17534" xml:space="preserve">VEL denique, quia datus eſt arcus AB, angulo re-
              <lb/>
              <note position="right" xlink:label="note-495-04" xlink:href="note-495-04a" xml:space="preserve">Schol. 45.
                <lb/>
              huius.</note>
            cto oppoſitus, cum angulo B, non recto;</s>
            <s xml:id="echoid-s17535" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17536" xml:space="preserve">cognoſcetur quoque, per ſcholia in margine allata, arcus BD, circa angulum
              <lb/>
            rectum; </s>
            <s xml:id="echoid-s17537" xml:space="preserve">atque adeo & </s>
            <s xml:id="echoid-s17538" xml:space="preserve">eius duplus BC, qui in quirendus proponitur.</s>
            <s xml:id="echoid-s17539" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s17540" xml:space="preserve">PRAXIS facile colligi poteſt ex ſcholijs in margine appoſitis.</s>
            <s xml:id="echoid-s17541" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s17542" xml:space="preserve">SI vero ſolos ſinus adhibere malueris; </s>
            <s xml:id="echoid-s17543" xml:space="preserve">inueniendus primum erit ar-
              <lb/>
              <note position="right" xlink:label="note-495-05" xlink:href="note-495-05a" xml:space="preserve">Praxis, per
                <lb/>
              ſolos ſinus,
                <lb/>
              quãdo duo
                <lb/>
              arcus dati
                <lb/>
              ęquales sũt.</note>
            cus AD, per praxim problematis 2. </s>
            <s xml:id="echoid-s17544" xml:space="preserve">ſcholij propoſ. </s>
            <s xml:id="echoid-s17545" xml:space="preserve">41. </s>
            <s xml:id="echoid-s17546" xml:space="preserve">Atque hinc per
              <lb/>
            praxim problematis ſcholij propoſ. </s>
            <s xml:id="echoid-s17547" xml:space="preserve">43. </s>
            <s xml:id="echoid-s17548" xml:space="preserve">arcus BD: </s>
            <s xml:id="echoid-s17549" xml:space="preserve">qui duplicatus totum
              <lb/>
            quæſitum BC, dabit. </s>
            <s xml:id="echoid-s17550" xml:space="preserve">Deinde per praxim problematis 1. </s>
            <s xml:id="echoid-s17551" xml:space="preserve">ſcholij propoſ. </s>
            <s xml:id="echoid-s17552" xml:space="preserve">41.
              <lb/>
            </s>
            <s xml:id="echoid-s17553" xml:space="preserve">vel per praxim problematis 2. </s>
            <s xml:id="echoid-s17554" xml:space="preserve">ſcholij propoſ. </s>
            <s xml:id="echoid-s17555" xml:space="preserve">42. </s>
            <s xml:id="echoid-s17556" xml:space="preserve">reperiendus angulus
              <lb/>
            BAD; </s>
            <s xml:id="echoid-s17557" xml:space="preserve">ex quo eius duplus BAC, quem quærimus, notus erit: </s>
            <s xml:id="echoid-s17558" xml:space="preserve">tertius au-
              <lb/>
            tem angulus C, iam datus eſt, cum æqualis ſit dato angulo B.</s>
            <s xml:id="echoid-s17559" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17560" xml:space="preserve">DATIS igitur duobus arcubus trianguli ſphærici non rectanguli, cuns
              <lb/>
            vno angulo, qui alteri eorum opponitur, &</s>
            <s xml:id="echoid-s17561" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17562" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s17563" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1393" type="section" level="1" n="616">
          <head xml:id="echoid-head651" xml:space="preserve">SCHOLIVM. I.</head>
          <p style="it">
            <s xml:id="echoid-s17564" xml:space="preserve">NECESSE eſt autem conſtare in hoc problemate, num angulus
              <emph style="sc">C</emph>
            , alteri da-
              <lb/>
            to arcui oppoſitus ſit acutus, obtuſus ve, vt ſciatur, num perpendicularis arcus AD,
              <lb/>
            intra triangulum cadat, nec ne. </s>
            <s xml:id="echoid-s17565" xml:space="preserve">Hoc enim ignorato, neſciremus, an angulus CAD,
              <lb/>
            addendus ſit angulo
              <emph style="sc">Ba</emph>
            D, an ab eo ſubtrahendus, vt inueniatur angulus
              <emph style="sc">Ba</emph>
            C, quæ-
              <lb/>
            ſitus: </s>
            <s xml:id="echoid-s17566" xml:space="preserve">Item an arcus CD, arcui BD, ſit adij ciendus, an ſubducendus ex eo, vt ar-
              <lb/>
            cus quæſitus
              <emph style="sc">B</emph>
            C, reperiatur. </s>
            <s xml:id="echoid-s17567" xml:space="preserve">Vel denique, num angulus inuentus ACD, ſit is, qui
              <lb/>
            quæritur, an vero reliquus duorum rectorũ, vt manife§tum eſt. </s>
            <s xml:id="echoid-s17568" xml:space="preserve">Non eſſe porro ſatis,
              <lb/>
            ſi duo arcus dentur, cum angulo vni eorum oppoſito, ad inquirendos reliquos angu-
              <lb/>
            los, cum reliquo arcu, iam dudum ſupra docuimus in ſcholio propoſ. </s>
            <s xml:id="echoid-s17569" xml:space="preserve">24. </s>
            <s xml:id="echoid-s17570" xml:space="preserve">Qua in re
              <lb/>
              <note position="right" xlink:label="note-495-06" xlink:href="note-495-06a" xml:space="preserve">Error Co-
                <lb/>
              pernici.</note>
            Nicolaum Copernicum erraſſe lib. </s>
            <s xml:id="echoid-s17571" xml:space="preserve">1. </s>
            <s xml:id="echoid-s17572" xml:space="preserve">Reuolutionum, pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s17573" xml:space="preserve">11. </s>
            <s xml:id="echoid-s17574" xml:space="preserve">triang. </s>
            <s xml:id="echoid-s17575" xml:space="preserve">ſphær. </s>
            <s xml:id="echoid-s17576" xml:space="preserve">ibidem monuimus. </s>
            <s xml:id="echoid-s17577" xml:space="preserve">Quod tamen bre
              <lb/>
              <figure xlink:label="fig-495-01" xlink:href="fig-495-01a" number="356">
                <image file="495-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/495-01"/>
              </figure>
              <note position="right" xlink:label="note-495-07" xlink:href="note-495-07a" xml:space="preserve">Nõ ſatis eſ-
                <lb/>
              ſe, dari duos
                <lb/>
              arcus, cum
                <lb/>
              angulo vni
                <lb/>
              eorũ oppo
                <lb/>
              ſito, in triã
                <lb/>
              gulo nõ re-
                <lb/>
              ctãgulo, vt
                <lb/>
              reliqua in-
                <lb/>
              ueniantur.</note>
            uiter ita hic rurſus oſtendemus. </s>
            <s xml:id="echoid-s17578" xml:space="preserve">Sint duo arcus æquales
              <lb/>
            AD, AC, angulum DAC, ambientes, & </s>
            <s xml:id="echoid-s17579" xml:space="preserve">vterque qua-
              <lb/>
            drante minor, aut maior. </s>
            <s xml:id="echoid-s17580" xml:space="preserve">Ducto autem per C, D, arcu
              <lb/>
            circuli maximi CD, ducatur ad eum productum alius ar
              <lb/>
            cus
              <emph style="sc">AB</emph>
            , ex A, neque per polos arcus CD, neque per po-
              <lb/>
            los arcus AD, ita vt anguli B, & </s>
            <s xml:id="echoid-s17581" xml:space="preserve">DAB, ſint non recti.
              <lb/>
            </s>
            <s xml:id="echoid-s17582" xml:space="preserve">Sed neque angulus ADB, rectus eſt. </s>
            <s xml:id="echoid-s17583" xml:space="preserve">Si namque vterque
              <lb/>
            arcus AD, AC, minor eſt quadrante, erunt duo anguli C, & </s>
            <s xml:id="echoid-s17584" xml:space="preserve">ADC, acuti; </s>
            <s xml:id="echoid-s17585" xml:space="preserve">ſi vero
              <lb/>
              <note position="right" xlink:label="note-495-08" xlink:href="note-495-08a" xml:space="preserve">25. huius.</note>
            vterq; </s>
            <s xml:id="echoid-s17586" xml:space="preserve">arcus AD,
              <emph style="sc">A</emph>
            C, quadrante maior eſt, erunt duo anguli C, & </s>
            <s xml:id="echoid-s17587" xml:space="preserve">ADC, obtuſi.</s>
            <s xml:id="echoid-s17588" xml:space="preserve"/>
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