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

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        <div xml:id="echoid-div934" type="section" level="1" n="486">
          <p>
            <s xml:id="echoid-s11937" xml:space="preserve">
              <pb o="359" file="371" n="371" rhead=""/>
            tra A, & </s>
            <s xml:id="echoid-s11938" xml:space="preserve">C, erunt arcus BAD, BCD, ſemicirculi; </s>
            <s xml:id="echoid-s11939" xml:space="preserve">cum circuli maximi ſe mu-
              <lb/>
              <note position="right" xlink:label="note-371-01" xlink:href="note-371-01a" xml:space="preserve">11. 1 Theod.</note>
            tuo bifariam ſecent. </s>
            <s xml:id="echoid-s11940" xml:space="preserve">Quare tam arcus BA,
              <lb/>
              <figure xlink:label="fig-371-01" xlink:href="fig-371-01a" number="197">
                <image file="371-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/371-01"/>
              </figure>
            BC, ſemicirculo minor eſt. </s>
            <s xml:id="echoid-s11941" xml:space="preserve">Eodem modo,
              <lb/>
            productis arcubus AB, AC, oſtendemus ar
              <lb/>
            cum AC, ſemicirculo eſſe minorem. </s>
            <s xml:id="echoid-s11942" xml:space="preserve">Con-
              <lb/>
            uenient autem arcus BA, BC, producti vl-
              <lb/>
            tra puncta A, & </s>
            <s xml:id="echoid-s11943" xml:space="preserve">C, propterea quòd ſphæ-
              <lb/>
            ricos angulos faciunt cũ arcu AC, ſuntq̀;
              <lb/>
            </s>
            <s xml:id="echoid-s11944" xml:space="preserve">omnes tres arcus portiones circulorum ma
              <lb/>
            ximorum, qui ſe mutuo ſecant in punctis
              <lb/>
            A,B, C, non autem tangunt. </s>
            <s xml:id="echoid-s11945" xml:space="preserve">Hinc enim
              <lb/>
            fit, vt vterque arcus BA, BC, productus arcum AC, productum ſecet in pun-
              <lb/>
            ctis A, C, vt ex defin. </s>
            <s xml:id="echoid-s11946" xml:space="preserve">conſtat; </s>
            <s xml:id="echoid-s11947" xml:space="preserve">ac proinde inter ſe coeant vltra puncta A, C. </s>
            <s xml:id="echoid-s11948" xml:space="preserve">In
              <lb/>
            omniergo triangulo ſphærico, &</s>
            <s xml:id="echoid-s11949" xml:space="preserve">c. </s>
            <s xml:id="echoid-s11950" xml:space="preserve">Quod erat demon ſtrandum.</s>
            <s xml:id="echoid-s11951" xml:space="preserve"/>
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        <div xml:id="echoid-div936" type="section" level="1" n="487">
          <head xml:id="echoid-head521" xml:space="preserve">THEOR. 2. PROPOS. 3.</head>
          <head xml:id="echoid-head522" xml:space="preserve">IN omni triangulo ſphærico, duo latera reli-
            <lb/>
          quo ſunt maiora, quomodocunque aſſumpta.</head>
          <p>
            <s xml:id="echoid-s11952" xml:space="preserve">SIT triangulum ſphæricum ABC. </s>
            <s xml:id="echoid-s11953" xml:space="preserve">Dico duo quælibet latera, vt AB, AC,
              <lb/>
            maiora eſſe latere BC. </s>
            <s xml:id="echoid-s11954" xml:space="preserve">Si enim triangulum eſt æquilaterum, manifeſtum eſt
              <lb/>
            duo ſimul dupla eſſe reliqui, atque adeo maiora. </s>
            <s xml:id="echoid-s11955" xml:space="preserve">Quod ſi alterum laterũ AB,
              <lb/>
            AC, æquale ſit lateri BC, vel maius,
              <lb/>
              <figure xlink:label="fig-371-02" xlink:href="fig-371-02a" number="198">
                <image file="371-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/371-02"/>
              </figure>
            vel etiã vtrumq; </s>
            <s xml:id="echoid-s11956" xml:space="preserve">maius, perſpicuum
              <lb/>
            quoque eſt, duo latera AB, AC, ma-
              <lb/>
            iora eſſe reliquo BC. </s>
            <s xml:id="echoid-s11957" xml:space="preserve">Si vero vtrum-
              <lb/>
            que latus AB, AC, aſſumptum late-
              <lb/>
            re tertio BC, minus ſit, demonſtrabi-
              <lb/>
            mus, latera AB, AC, ſimul maiora eſ-
              <lb/>
            ſe latere BC, hac ratione. </s>
            <s xml:id="echoid-s11958" xml:space="preserve">Perficia tur
              <lb/>
            circulus arcus tertij BC. </s>
            <s xml:id="echoid-s11959" xml:space="preserve">Deinde ex
              <lb/>
            polo B, nempe ex altero extremo ma
              <lb/>
            ioris lateris BC, ad interuallũ vtriuſ-
              <lb/>
            uis arcuum minorum, nimirum ad in-
              <lb/>
            teruallũ arcus BA, in ſuperficie ſphæ
              <lb/>
            ræ circulus deſcribatun AD, ſecans ar
              <lb/>
            cum BC, qui maior ponitur arcu BA,
              <lb/>
            in D, puncto inter B, & </s>
            <s xml:id="echoid-s11960" xml:space="preserve">C. </s>
            <s xml:id="echoid-s11961" xml:space="preserve">Et quoniam
              <lb/>
            circulus BC, tranſit quoque per reliquum polum circuli AD; </s>
            <s xml:id="echoid-s11962" xml:space="preserve">ſit alter po-
              <lb/>
              <note position="right" xlink:label="note-371-02" xlink:href="note-371-02a" xml:space="preserve">ſchol. 10. 1.</note>
            lus E, qui per ſemicirculũ remotus erit à polo B; </s>
            <s xml:id="echoid-s11963" xml:space="preserve">ita vt ſemicirculus ſit BCE.
              <lb/>
            </s>
            <s xml:id="echoid-s11964" xml:space="preserve">
              <note position="right" xlink:label="note-371-03" xlink:href="note-371-03a" xml:space="preserve">Theod.</note>
            Cum ergo arcus BC, ſemicirculo minor ſit, exiſtet polus E, vltra punctum C:
              <lb/>
            </s>
            <s xml:id="echoid-s11965" xml:space="preserve">
              <note position="right" xlink:label="note-371-04" xlink:href="note-371-04a" xml:space="preserve">2. huius.</note>
            Eſt autem punctum D, inter B, & </s>
            <s xml:id="echoid-s11966" xml:space="preserve">C, vt dictum eſt. </s>
            <s xml:id="echoid-s11967" xml:space="preserve">Punctum igitur C, inter
              <lb/>
            puncta D, E, cadet. </s>
            <s xml:id="echoid-s11968" xml:space="preserve">Quare cum ex puncto C, quod extra peripheriam circuli
              <lb/>
            AD, eſt, & </s>
            <s xml:id="echoid-s11969" xml:space="preserve">præter eiuſdem polum E, ſignatur, ducantur duo arcus maximorum
              <lb/>
            circulorum CB, CA, ſemicirculo minores (quòd latera ſint trianguli ſphæ-
              <lb/>
              <note position="right" xlink:label="note-371-05" xlink:href="note-371-05a" xml:space="preserve">2. huius.</note>
            rici ABC.) </s>
            <s xml:id="echoid-s11970" xml:space="preserve">ad peripheriam AD, erit arcus CD, per polum B, tranſiens, mi-
              <lb/>
              <note position="right" xlink:label="note-371-06" xlink:href="note-371-06a" xml:space="preserve">ſchol. 21.</note>
            nor arcu CA. </s>
            <s xml:id="echoid-s11971" xml:space="preserve">Additis ergo æqualibus arcubus DB, AB; </s>
            <s xml:id="echoid-s11972" xml:space="preserve">(ſunt autem æqua-
              <lb/>
              <note position="right" xlink:label="note-371-07" xlink:href="note-371-07a" xml:space="preserve">2 Theod.</note>
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