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

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        <div xml:id="echoid-div1311" type="section" level="1" n="607">
          <p style="it">
            <s xml:id="echoid-s16663" xml:space="preserve">
              <pb o="467" file="479" n="479" rhead=""/>
            lij propoſ. </s>
            <s xml:id="echoid-s16664" xml:space="preserve">42. </s>
            <s xml:id="echoid-s16665" xml:space="preserve">vel propoſ. </s>
            <s xml:id="echoid-s16666" xml:space="preserve">56. </s>
            <s xml:id="echoid-s16667" xml:space="preserve">aut certe praxis ſcholij propoſ. </s>
            <s xml:id="echoid-s16668" xml:space="preserve">47.</s>
            <s xml:id="echoid-s16669" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Praxis pet
            <lb/>
          ſolos ſinus,
            <lb/>
          quãdo duo
            <lb/>
          arcus da@ũ
            <lb/>
          quæſitũ an
            <lb/>
          gulũ conti-
            <lb/>
          nentes ſunt
            <lb/>
          æquales.</note>
          <p style="it">
            <s xml:id="echoid-s16670" xml:space="preserve">PER ſolos ſinus ita rem peragemus. </s>
            <s xml:id="echoid-s16671" xml:space="preserve">Ex praxi problematis 1. </s>
            <s xml:id="echoid-s16672" xml:space="preserve">propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s16673" xml:space="preserve">41. </s>
            <s xml:id="echoid-s16674" xml:space="preserve">inueniemus angulum BAD; </s>
            <s xml:id="echoid-s16675" xml:space="preserve">qui duplicatus totum BAC, dabit. </s>
            <s xml:id="echoid-s16676" xml:space="preserve">De-
              <lb/>
            inde per praxim problematis 2. </s>
            <s xml:id="echoid-s16677" xml:space="preserve">ſcholij propoſ. </s>
            <s xml:id="echoid-s16678" xml:space="preserve">42. </s>
            <s xml:id="echoid-s16679" xml:space="preserve">reperiemus angulum
              <lb/>
            B, qui ipſi C, æqualis est.</s>
            <s xml:id="echoid-s16680" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1324" type="section" level="1" n="608">
          <head xml:id="echoid-head643" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s16681" xml:space="preserve">IOANNES Regiom. </s>
            <s xml:id="echoid-s16682" xml:space="preserve">& </s>
            <s xml:id="echoid-s16683" xml:space="preserve">Nicolaus Copernicus alio etiam modo, datis omnibus
              <lb/>
            arcubus trianguli ſphærici, omnes tres angulos inquirunt, inueſtigantes nimirum
              <lb/>
            angulum quendam rectilineum in centro ſphæræ, cuius arcus angulum ſphæricum
              <lb/>
            quæſitum exhibet notum. </s>
            <s xml:id="echoid-s16684" xml:space="preserve">Sed eam rationem, quamuis acutam, & </s>
            <s xml:id="echoid-s16685" xml:space="preserve">ſubtilem, quoniam
              <lb/>
            obſcurior eſt, & </s>
            <s xml:id="echoid-s16686" xml:space="preserve">longior, dedita opera hic omiſimus: </s>
            <s xml:id="echoid-s16687" xml:space="preserve">præſertim, cum eam quilibev
              <lb/>
            apud Regiom. </s>
            <s xml:id="echoid-s16688" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s16689" xml:space="preserve">34. </s>
            <s xml:id="echoid-s16690" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s16691" xml:space="preserve">4. </s>
            <s xml:id="echoid-s16692" xml:space="preserve">triangulorum, & </s>
            <s xml:id="echoid-s16693" xml:space="preserve">apud Copernicum lib. </s>
            <s xml:id="echoid-s16694" xml:space="preserve">1. </s>
            <s xml:id="echoid-s16695" xml:space="preserve">Reuo-
              <lb/>
            lutionum propoſ 13. </s>
            <s xml:id="echoid-s16696" xml:space="preserve">de triangulis ſphæricis, legere poſsit.</s>
            <s xml:id="echoid-s16697" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s16698" xml:space="preserve">MALVIMVS in ſecund@ demonſtratione huius problematis vſurpare theoremæ
              <lb/>
            ſcholij 2. </s>
            <s xml:id="echoid-s16699" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s16700" xml:space="preserve">58. </s>
            <s xml:id="echoid-s16701" xml:space="preserve">quam cum Ioan. </s>
            <s xml:id="echoid-s16702" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s16703" xml:space="preserve">theorema eiuſdem propoſ. </s>
            <s xml:id="echoid-s16704" xml:space="preserve">58. </s>
            <s xml:id="echoid-s16705" xml:space="preserve">vt labo-
              <lb/>
            ris difficultatem effugeremus. </s>
            <s xml:id="echoid-s16706" xml:space="preserve">Nam cum ſit, vt rectangulum ſub ſinubus arcuum in-
              <lb/>
              <note position="right" xlink:label="note-479-02" xlink:href="note-479-02a" xml:space="preserve">58. huius.
                <lb/>
              & permu-
                <lb/>
              tando.</note>
            æqualium angulum quæſitum ambientium ad quadratum ſinus totius, ita differen-
              <lb/>
            tiainter ſinum verſum arcus eidem angulo oppoſiti, & </s>
            <s xml:id="echoid-s16707" xml:space="preserve">ſinum verſum differentiæ ar-
              <lb/>
            cuum illorum inæqualium, ad ſinum verſum anguli quæſiti: </s>
            <s xml:id="echoid-s16708" xml:space="preserve">ſi vellemus hoc theore-
              <lb/>
            mate propoſ. </s>
            <s xml:id="echoid-s16709" xml:space="preserve">58. </s>
            <s xml:id="echoid-s16710" xml:space="preserve">vti, obtineret rectangulum illud primum aureæ regulæ locum. </s>
            <s xml:id="echoid-s16711" xml:space="preserve">Qua-
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            re laborioſa redderetur diuiſio, vt patet. </s>
            <s xml:id="echoid-s16712" xml:space="preserve">Facilior autem fit diuiſio ſecundum theore-
              <lb/>
            ma ſcholij 2. </s>
            <s xml:id="echoid-s16713" xml:space="preserve">eiuſdem propoſ. </s>
            <s xml:id="echoid-s16714" xml:space="preserve">58. </s>
            <s xml:id="echoid-s16715" xml:space="preserve">cum primum locum aureæ regulæ quantitas quartæ
              <lb/>
            proportionalis occupet, quæ multo minor eſt illo rectangulo, facileq́; </s>
            <s xml:id="echoid-s16716" xml:space="preserve">inuenitur per
              <lb/>
            abiectionem ſolam tot figurarum ad dexteram ex eo rectangulo, quot cifræ in ſinu to
              <lb/>
            to cominentur; </s>
            <s xml:id="echoid-s16717" xml:space="preserve">propterea quod dictum rectangulum per ſinum totum ſit diuidendum,
              <lb/>
            vt illa quantitas quarta proportionalis producatur.</s>
            <s xml:id="echoid-s16718" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1326" type="section" level="1" n="609">
          <head xml:id="echoid-head644" xml:space="preserve">PROBL. 5. PROPOS. 64.</head>
          <p>
            <s xml:id="echoid-s16719" xml:space="preserve">DATIS duobus arcubus trianguli ſphærici
              <lb/>
            non rectanguli, cum angulo ab ipſis comprehen-
              <lb/>
            ſo; </s>
            <s xml:id="echoid-s16720" xml:space="preserve">reliquum arcum, cum reliquis angulis reperire.</s>
            <s xml:id="echoid-s16721" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16722" xml:space="preserve">IN ſphærico triangulo ABC, non rectãgulo dati ſint duo arcus AB, BC,
              <lb/>
              <note position="right" xlink:label="note-479-03" xlink:href="note-479-03a" xml:space="preserve">Quãdo duo
                <lb/>
              arcus dati
                <lb/>
              inæquales
                <lb/>
              ſunr, & neu
                <lb/>
              t@r quadrãs</note>
            cum angulo B. </s>
            <s xml:id="echoid-s16723" xml:space="preserve">Oportet ex his & </s>
            <s xml:id="echoid-s16724" xml:space="preserve">reliquum arcum AC, & </s>
            <s xml:id="echoid-s16725" xml:space="preserve">reliquos angulos
              <lb/>
            BAC, & </s>
            <s xml:id="echoid-s16726" xml:space="preserve">ACB, exquirere. </s>
            <s xml:id="echoid-s16727" xml:space="preserve">Sint primum dati arcus inæquales, & </s>
            <s xml:id="echoid-s16728" xml:space="preserve">ex termino
              <lb/>
            vnius eorum, nempe ex termino A, arcus AB, ad alterum arcum BC, demit-
              <lb/>
            tatur arcus per pendicularis AD: </s>
            <s xml:id="echoid-s16729" xml:space="preserve">qu@an intra triangulum, an vero extra ca-
              <lb/>
            dat, calculus, & </s>
            <s xml:id="echoid-s16730" xml:space="preserve">operatio docebit. </s>
            <s xml:id="echoid-s16731" xml:space="preserve">Quoniam enim in triangulo ABD, cu-
              <lb/>
            ius angulus D, rectus, datus eſt arcus AB, recto angulo oppoſitus, cum an-
              <lb/>
            gulo B; </s>
            <s xml:id="echoid-s16732" xml:space="preserve">dabitur quoque arcus perpendicularis AD, dato angulo B, oppoſi-
              <lb/>
              <note position="right" xlink:label="note-479-04" xlink:href="note-479-04a" xml:space="preserve">Schol. 41.
                <lb/>
              huius.</note>
            tus. </s>
            <s xml:id="echoid-s16733" xml:space="preserve">Rurſus, quia in eodem triangulo datus eſt arcus AB, recto angulo oppo-
              <lb/>
              <note position="right" xlink:label="note-479-05" xlink:href="note-479-05a" xml:space="preserve">Schol. 45.
                <lb/>
              huius.</note>
            ſitus, cum augulo B:</s>
            <s xml:id="echoid-s16734" xml:space="preserve"/>
          </p>
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