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

Table of figures

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            <s xml:id="echoid-s12783" xml:space="preserve">
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            & </s>
            <s xml:id="echoid-s12784" xml:space="preserve">duo Anguli A, C, duobus ãngulis D, F, æquales erunt, vterque vtrique. </s>
            <s xml:id="echoid-s12785" xml:space="preserve">Si
              <lb/>
              <note position="left" xlink:label="note-390-01" xlink:href="note-390-01a" xml:space="preserve">18. huius.</note>
            fuerint igitur duo triangula, &</s>
            <s xml:id="echoid-s12786" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12787" xml:space="preserve">Quod oſtendendum erat.</s>
            <s xml:id="echoid-s12788" xml:space="preserve"/>
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        <div xml:id="echoid-div1007" type="section" level="1" n="515">
          <head xml:id="echoid-head550" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s12789" xml:space="preserve">_DIXIMVS,_ vtrumque reliquorum angulorum debere eſſe vel maiorem, vel
              <lb/>
            minorem recto. </s>
            <s xml:id="echoid-s12790" xml:space="preserve">Nam alias falſa eſſet propoſitio. </s>
            <s xml:id="echoid-s12791" xml:space="preserve">Sit enim triangulum ſphæricum
              <lb/>
              <note position="left" xlink:label="note-390-02" xlink:href="note-390-02a" xml:space="preserve">20.1 Theod.</note>
            quodcunque _ABC,_ habens duo latera _AB, AC,_ æqualia: </s>
            <s xml:id="echoid-s12792" xml:space="preserve">Producto autem latere
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              <figure xlink:label="fig-390-01" xlink:href="fig-390-01a" number="228">
                <image file="390-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/390-01"/>
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            _CB,_ ad _D,_ ita vt _CD,_ ſit arcus ſemicirculo minor, duca-
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            tur per puncta _A, D,_ arcus circuli maximi _AD. </s>
            <s xml:id="echoid-s12793" xml:space="preserve">Itaque
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            triangula _ADB, ADC,_ angulum angulo æqualem habẽt,
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            nempe _D,_ communem, & </s>
            <s xml:id="echoid-s12794" xml:space="preserve">duo latera _AD, AB,_ æqualia
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            duobus lateribus _AD, AC,_ vtrumque vtrique; </s>
            <s xml:id="echoid-s12795" xml:space="preserve">& </s>
            <s xml:id="echoid-s12796" xml:space="preserve">tamen
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            reliqua latera _DB, DC,_ æqualia non ſunt, nec reliqui
              <lb/>
            anguli _DAB, DAC,_ immoneque anguli _ABD, ACD,_
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            niſi vterq; </s>
            <s xml:id="echoid-s12797" xml:space="preserve">rectus ſit, vt demonſtrabimus. </s>
            <s xml:id="echoid-s12798" xml:space="preserve">Hoc autemideò
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            euenit, quòd non vterque angulus _ABD, ACD,_ maior
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            eſt vel minor recto, ſed vel vterq; </s>
            <s xml:id="echoid-s12799" xml:space="preserve">rectus, vel vnus maior
              <lb/>
            recto, & </s>
            <s xml:id="echoid-s12800" xml:space="preserve">alter minor: </s>
            <s xml:id="echoid-s12801" xml:space="preserve">quodita oſtendemus. </s>
            <s xml:id="echoid-s12802" xml:space="preserve">Sit primum angulus _ABD,_ rectus.
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            </s>
            <s xml:id="echoid-s12803" xml:space="preserve">Dico & </s>
            <s xml:id="echoid-s12804" xml:space="preserve">_C,_ rectum eſſe. </s>
            <s xml:id="echoid-s12805" xml:space="preserve">Recto enim exiſtente angulo _ABD,_ erit & </s>
            <s xml:id="echoid-s12806" xml:space="preserve">_ABC,_ rectus; </s>
            <s xml:id="echoid-s12807" xml:space="preserve">
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            quòd ambo anguli ad _B,_ æquales ſint duobus rectis: </s>
            <s xml:id="echoid-s12808" xml:space="preserve">ſed hic æqualis eſt angulo _C,_ ob
              <lb/>
              <note position="left" xlink:label="note-390-03" xlink:href="note-390-03a" xml:space="preserve">5. huius.</note>
              <note position="left" xlink:label="note-390-04" xlink:href="note-390-04a" xml:space="preserve">8. huius.</note>
            æqualitatem laterum _AB, AC._ </s>
            <s xml:id="echoid-s12809" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s12810" xml:space="preserve">_C,_ rectus erit.</s>
            <s xml:id="echoid-s12811" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s12812" xml:space="preserve">_SIT_ deinde angulus _ABD,_ maior recto. </s>
            <s xml:id="echoid-s12813" xml:space="preserve">Dico _C,_ minorem eſſe recto. </s>
            <s xml:id="echoid-s12814" xml:space="preserve">Cum enim
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            _ABD,_ ſit recto maior, erit _ABC,_ minor recto, cum ambo duobus rectis ſint æquales.
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            </s>
            <s xml:id="echoid-s12815" xml:space="preserve">
              <note position="left" xlink:label="note-390-05" xlink:href="note-390-05a" xml:space="preserve">5. huius.</note>
            Igitur & </s>
            <s xml:id="echoid-s12816" xml:space="preserve">angulus _C,_ qui æqualis eſt angulo _ABC,_ recto minor erit.</s>
            <s xml:id="echoid-s12817" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">8. huius.</note>
          <p style="it">
            <s xml:id="echoid-s12818" xml:space="preserve">_SIT_ tandem angulus _ABD,_ minor recto. </s>
            <s xml:id="echoid-s12819" xml:space="preserve">Dico _C,_ eſſe recto maiorem. </s>
            <s xml:id="echoid-s12820" xml:space="preserve">cum enim
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            _ABD,_ ſit minor recto, erit _ABC,_ hoc eſt, ſibi æqualis _C,_ maior recto.</s>
            <s xml:id="echoid-s12821" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Error Ni-
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          colai Co-
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          pernici.</note>
          <p style="it">
            <s xml:id="echoid-s12822" xml:space="preserve">_HINC_ manifeſtum eſt, propoſitionem _8._ </s>
            <s xml:id="echoid-s12823" xml:space="preserve">Nicolai Copernici de ſphæricis triangu-
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            lis, lib. </s>
            <s xml:id="echoid-s12824" xml:space="preserve">_1._ </s>
            <s xml:id="echoid-s12825" xml:space="preserve">Reuolutionum falſam eſſe, quo ad eam partem, in qua dicit. </s>
            <s xml:id="echoid-s12826" xml:space="preserve">_Si bina trian
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            gula duo latera duobus lateribus æqualia habuerint, alterum alteri, & </s>
            <s xml:id="echoid-s12827" xml:space="preserve">angu-
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            lum angulo æqualem, quiad baſim fuerit; </s>
            <s xml:id="echoid-s12828" xml:space="preserve">baſim quoque baſi, ac reliquos an-
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            gulos reliquis angulis habebunt æquales. </s>
            <s xml:id="echoid-s12829" xml:space="preserve">Hoc enim verum non eſt, niſi ponatur
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            vter que reliquorum angulorum ad baſim vel maior recto, vel minor. </s>
            <s xml:id="echoid-s12830" xml:space="preserve">In triangulis
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            enim propoſitis _ADB, ADC,_ ſunt duo latera _AD, AB,_ duobus lateribus _AD, AC,_
              <lb/>
            æqualia, angulusq́; </s>
            <s xml:id="echoid-s12831" xml:space="preserve">_D,_ communis eſt ſuper baſes _DB, DC;_ </s>
            <s xml:id="echoid-s12832" xml:space="preserve">& </s>
            <s xml:id="echoid-s12833" xml:space="preserve">tamen baſes non ſunt
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            æquales, ob cauſam dictam.</s>
            <s xml:id="echoid-s12834" xml:space="preserve"/>
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            <s xml:id="echoid-s12835" xml:space="preserve">_VNDE_ errat idem Nicolaus in eodem libro propoſ. </s>
            <s xml:id="echoid-s12836" xml:space="preserve">II. </s>
            <s xml:id="echoid-s12837" xml:space="preserve">vbi ait. </s>
            <s xml:id="echoid-s12838" xml:space="preserve">_Omne trian-
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              <note position="left" xlink:label="note-390-08" xlink:href="note-390-08a" xml:space="preserve">Alius error
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              Nicolai Co
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              pernici.</note>
            gulum, cuius duo latera fuerint data cum aliquo angulo, datorum eſſicitur
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            angulorum, & </s>
            <s xml:id="echoid-s12839" xml:space="preserve">laterum. </s>
            <s xml:id="echoid-s12840" xml:space="preserve">Nam etiamſi latera _AD, AB,_ nota ſintcum angulo _D,_
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            non tamen inde in notitiam alterius lateris, & </s>
            <s xml:id="echoid-s12841" xml:space="preserve">aliorum angulorum perueniemus,
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            cum reliquum latus poſsit eſſe vel _DB,_ vel _DC,_ &</s>
            <s xml:id="echoid-s12842" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12843" xml:space="preserve">Neceſſe eſt ergo aliud quip-
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            piam præterea conſtare, antequam reliquum latus, cum reliquis angulis notum effi-
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            ciatur, vt in Scholio propoſ. </s>
            <s xml:id="echoid-s12844" xml:space="preserve">45. </s>
            <s xml:id="echoid-s12845" xml:space="preserve">perſpicuum faciemus.</s>
            <s xml:id="echoid-s12846" xml:space="preserve"/>
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        <div xml:id="echoid-div1011" type="section" level="1" n="516">
          <head xml:id="echoid-head551" xml:space="preserve">THEOR. 23. PROPOS. 25.</head>
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            <s xml:id="echoid-s12847" xml:space="preserve">IN omni triangulo ſphærico Iſoſcele, ſi </s>
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