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

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        <div xml:id="echoid-div1002" type="section" level="1" n="513">
          <p style="it">
            <s xml:id="echoid-s12730" xml:space="preserve">
              <pb o="377" file="389" n="389" rhead=""/>
            los _BAC, DAC,_ æqualia, vtrumque vtrique, & </s>
            <s xml:id="echoid-s12731" xml:space="preserve">tamen neque veliqua latera _BC,_
              <lb/>
            _DC,_ æqualia inter ſe ſunt, neque reliqui anguli _BAC, DAC,_ vt manifeſturn eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s12732" xml:space="preserve">Hoc autem ideo accidit, quòd _A,_ polus ſit arcuum _BC, DC._</s>
            <s xml:id="echoid-s12733" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12734" xml:space="preserve">_HINC_ perſpicuum quoque eſt, copernicũ hallucinari lib. </s>
            <s xml:id="echoid-s12735" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12736" xml:space="preserve">Reuolutionum pro-
              <lb/>
              <note position="right" xlink:label="note-389-01" xlink:href="note-389-01a" xml:space="preserve">Error Ni-
                <lb/>
              colai Co-
                <lb/>
              pernici.</note>
            poſ. </s>
            <s xml:id="echoid-s12737" xml:space="preserve">12. </s>
            <s xml:id="echoid-s12738" xml:space="preserve">cum aſſerit, omnetriangulum ſphæricum, cuius duo anguli vtcunque dati
              <lb/>
            fuerint, cum aliquo latere, datorum effici angulorum, & </s>
            <s xml:id="echoid-s12739" xml:space="preserve">laterum. </s>
            <s xml:id="echoid-s12740" xml:space="preserve">Nam in trian-
              <lb/>
            gulo _ABC,_ etiamſi dentur duo anguli _B, C,_ cum duobus lateribus _AB, AC,_ (& </s>
            <s xml:id="echoid-s12741" xml:space="preserve">non
              <lb/>
            cum vnotantum, vtipſe vult) non tamen ſtatim reliquum latus, & </s>
            <s xml:id="echoid-s12742" xml:space="preserve">reliquus angu-
              <lb/>
            lus cognoſcetur; </s>
            <s xml:id="echoid-s12743" xml:space="preserve">cum reliquum latus eſſe poſsit vel _BC,_ vel _DC,_ & </s>
            <s xml:id="echoid-s12744" xml:space="preserve">reliquus angu-
              <lb/>
            lus vel _BAC,_ vel _DAC,_ &</s>
            <s xml:id="echoid-s12745" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12746" xml:space="preserve">Aliquid ergo aliud præterea cõſtet, neceſſe eſt, vt relio
              <lb/>
            quus angulus, cum reliquis lateribus cognoſcatur, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s12747" xml:space="preserve">45. </s>
            <s xml:id="echoid-s12748" xml:space="preserve">oſtẽdemus.</s>
            <s xml:id="echoid-s12749" xml:space="preserve"/>
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        <div xml:id="echoid-div1005" type="section" level="1" n="514">
          <head xml:id="echoid-head549" xml:space="preserve">THEOR. 22. PROPOS. 24.</head>
          <p>
            <s xml:id="echoid-s12750" xml:space="preserve">SI fuerint duo triangula ſphærica, quæ vnum
              <lb/>
            angulum vni angulo æqualem habeant, & </s>
            <s xml:id="echoid-s12751" xml:space="preserve">duo la-
              <lb/>
            tera duobus lateribus circa alium angulum æqua-
              <lb/>
            lia vtrumque vtrique, atq; </s>
            <s xml:id="echoid-s12752" xml:space="preserve">vtrum que reliquorum
              <lb/>
            angulorum vel maiorem recto, vel minorem: </s>
            <s xml:id="echoid-s12753" xml:space="preserve">Erit
              <lb/>
            & </s>
            <s xml:id="echoid-s12754" xml:space="preserve">reliquum latus reliquo lateri æquale, & </s>
            <s xml:id="echoid-s12755" xml:space="preserve">reliqui
              <lb/>
            anguli reliquis angulis æquales, vterque vtrique.</s>
            <s xml:id="echoid-s12756" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12757" xml:space="preserve">IN duobus triangulis ſphæricis ABC, DEF, ſint anguli B, E, æquales,
              <lb/>
            & </s>
            <s xml:id="echoid-s12758" xml:space="preserve">duo latera BC, CA, ęqualia duobus lateribus EF, FD, vtrumque vtrique,
              <lb/>
              <figure xlink:label="fig-389-01" xlink:href="fig-389-01a" number="227">
                <image file="389-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/389-01"/>
              </figure>
            circa angulos C, F, & </s>
            <s xml:id="echoid-s12759" xml:space="preserve">vterq; </s>
            <s xml:id="echoid-s12760" xml:space="preserve">angulorũ reli-
              <lb/>
            quorum A, D, vel minor ſit, vel maior recto.
              <lb/>
            </s>
            <s xml:id="echoid-s12761" xml:space="preserve">Dico reliqua latera AB, DE, æqualia quo-
              <lb/>
            que eſſe, & </s>
            <s xml:id="echoid-s12762" xml:space="preserve">reliquos duos angulos A, C, re-
              <lb/>
            liquis duobus angulis D, F, vtrũq; </s>
            <s xml:id="echoid-s12763" xml:space="preserve">vtrique. </s>
            <s xml:id="echoid-s12764" xml:space="preserve">
              <lb/>
            Si enim latera AB, DE, æqualia non ſunt,
              <lb/>
            ſit AB, maius, & </s>
            <s xml:id="echoid-s12765" xml:space="preserve">abſcindatur arcus BG,
              <lb/>
              <note position="right" xlink:label="note-389-02" xlink:href="note-389-02a" xml:space="preserve">1. huius.</note>
            æqualis arcui DE, & </s>
            <s xml:id="echoid-s12766" xml:space="preserve">per puncta C, G, ar-
              <lb/>
            cus circuli maximi ducatur CH. </s>
            <s xml:id="echoid-s12767" xml:space="preserve">Quia igi-
              <lb/>
              <note position="right" xlink:label="note-389-03" xlink:href="note-389-03a" xml:space="preserve">20.1 Theod.</note>
            tur latera BG, BC, æqualia ſunt lateribus
              <lb/>
            ED, EF, angulosque comprehendunt æquales B, E; </s>
            <s xml:id="echoid-s12768" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s12769" xml:space="preserve">arcus GC, DF,
              <lb/>
              <note position="right" xlink:label="note-389-04" xlink:href="note-389-04a" xml:space="preserve">7. huius.</note>
            & </s>
            <s xml:id="echoid-s12770" xml:space="preserve">anguli G, D, æquales: </s>
            <s xml:id="echoid-s12771" xml:space="preserve">Ponitur autem arcus DF, arcui AC, æqualis. </s>
            <s xml:id="echoid-s12772" xml:space="preserve">Ae-
              <lb/>
            qualis igitur erit quoque arcus GC, eidem arcui AC; </s>
            <s xml:id="echoid-s12773" xml:space="preserve">atque adeo anguli A,
              <lb/>
              <note position="right" xlink:label="note-389-05" xlink:href="note-389-05a" xml:space="preserve">8. huius.</note>
            & </s>
            <s xml:id="echoid-s12774" xml:space="preserve">CGA, æquales. </s>
            <s xml:id="echoid-s12775" xml:space="preserve">Et quoniam anguli duo ad G, ſunt æquales duobus re-
              <lb/>
              <note position="right" xlink:label="note-389-06" xlink:href="note-389-06a" xml:space="preserve">5. huius.</note>
            ctis, erunt queque duo anguli BGC, & </s>
            <s xml:id="echoid-s12776" xml:space="preserve">A, duobus rectis æquales; </s>
            <s xml:id="echoid-s12777" xml:space="preserve">ac proin-
              <lb/>
            de, cum angulus BGC, oſtenſus ſit æqualis angulo D, erunt & </s>
            <s xml:id="echoid-s12778" xml:space="preserve">duo anguli
              <lb/>
            D, & </s>
            <s xml:id="echoid-s12779" xml:space="preserve">A, duobus rectis æquales. </s>
            <s xml:id="echoid-s12780" xml:space="preserve">Quod fieri non poteſt. </s>
            <s xml:id="echoid-s12781" xml:space="preserve">Cum enim vterque
              <lb/>
            minor recto ponatur, vel maior, erunt ambo ſimul vel duobus rectis minores,
              <lb/>
            vel maiores. </s>
            <s xml:id="echoid-s12782" xml:space="preserve">Non ergo inæqualia ſunt latera AB, DE, ſed æqualia. </s>
            <s xml:id="echoid-s12783" xml:space="preserve"/>
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