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

Table of figures

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            <s xml:id="echoid-s12897" xml:space="preserve">
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            bus rectis ſint, & </s>
            <s xml:id="echoid-s12898" xml:space="preserve">ACB, ponatur recto minor; </s>
            <s xml:id="echoid-s12899" xml:space="preserve">erit ACD, recto maior; </s>
            <s xml:id="echoid-s12900" xml:space="preserve">ae
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              <figure xlink:label="fig-392-01" xlink:href="fig-392-01a" number="230">
                <image file="392-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/392-01"/>
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            propterea maior, quam B, qui recto etiam minor
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            ponitur. </s>
            <s xml:id="echoid-s12901" xml:space="preserve">Sunt ergo arcus AB, AC, ſimul ſemi-
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              <note position="left" xlink:label="note-392-01" xlink:href="note-392-01a" xml:space="preserve">15. huius.</note>
            circulo minores; </s>
            <s xml:id="echoid-s12902" xml:space="preserve">atque idcirco, cum ipſi ſint ę qua-
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            les, vterque quadrante minor erit. </s>
            <s xml:id="echoid-s12903" xml:space="preserve">Quod eſt pro-
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            poſitum.</s>
            <s xml:id="echoid-s12904" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s12905" xml:space="preserve">POSTREMO ſit vterque angulorum B, C,
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            obtuſus. </s>
            <s xml:id="echoid-s12906" xml:space="preserve">Dico utrumque arcum AB, AC, maio-
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            rem eſſe quadrante. </s>
            <s xml:id="echoid-s12907" xml:space="preserve">Cum enim duo anguli ad C,
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            ſint æquales duobus rectis, & </s>
            <s xml:id="echoid-s12908" xml:space="preserve">ACB, ponatur maior
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              <note position="left" xlink:label="note-392-02" xlink:href="note-392-02a" xml:space="preserve">5. huius.</note>
            recto, erit ACD, recto minor, atque idcirco mi-
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            nor angulo B, qui recto quoque maior ponitur.
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            </s>
            <s xml:id="echoid-s12909" xml:space="preserve">
              <note position="left" xlink:label="note-392-03" xlink:href="note-392-03a" xml:space="preserve">25. huius.</note>
            Arcus ergo AB, AC, ſimul maiores ſunt ſemicir-
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            culo; </s>
            <s xml:id="echoid-s12910" xml:space="preserve">atque adeò, cum ipſi æquales ſint, erit uterq;
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            </s>
            <s xml:id="echoid-s12911" xml:space="preserve">quadrante maior. </s>
            <s xml:id="echoid-s12912" xml:space="preserve">Quod eſt propoſitum. </s>
            <s xml:id="echoid-s12913" xml:space="preserve">In omni
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            ergo triangulo ſphærico Iſoſcele, &</s>
            <s xml:id="echoid-s12914" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12915" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s12916" xml:space="preserve"/>
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        <div xml:id="echoid-div1018" type="section" level="1" n="517">
          <head xml:id="echoid-head552" xml:space="preserve">COROLLARIVM.</head>
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            <s xml:id="echoid-s12917" xml:space="preserve">EX his ſequitur, omne triangulum ſphæricum æquilaterum, ſeu æquiangulum, ſi ſin-
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            gula latera ſint quadrantes, habere ſingulos angulos rectos: </s>
            <s xml:id="echoid-s12918" xml:space="preserve">ſi verò quadrante minora, acu-
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            tos. </s>
            <s xml:id="echoid-s12919" xml:space="preserve">Si denique quadrante maiora, obtuſos. </s>
            <s xml:id="echoid-s12920" xml:space="preserve">Et omne triangulum ſphæricum æquiangu-
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            lum, ſeu æquilaterum, ſi ſinguli anguli ſint recti, habere ſingula latera quadrantes: </s>
            <s xml:id="echoid-s12921" xml:space="preserve">Si verò
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            acuti, quadrante minora: </s>
            <s xml:id="echoid-s12922" xml:space="preserve">ſi denique obtuſi, quadrante maiora.</s>
            <s xml:id="echoid-s12923" xml:space="preserve"/>
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        <div xml:id="echoid-div1019" type="section" level="1" n="518">
          <head xml:id="echoid-head553" xml:space="preserve">SCHOLIVM.</head>
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            <s xml:id="echoid-s12924" xml:space="preserve">_CAETERVM,_ quando duo latera trianguli ſpliarici ſunt quadrätes, vtrum-
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            que angulum ad baſim eſſe rectum: </s>
            <s xml:id="echoid-s12925" xml:space="preserve">Et ſi vterque angulus ad baſim rectus eſt, vtrum-
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            que latus eſſe quadrantem, demonſtrari etiam poterit bac ratione.</s>
            <s xml:id="echoid-s12926" xml:space="preserve"/>
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            <s xml:id="echoid-s12927" xml:space="preserve">_SINT_ in triangulo _ABC,_ quadrantes _AB, AC._ </s>
            <s xml:id="echoid-s12928" xml:space="preserve">Dico
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              <figure xlink:label="fig-392-02" xlink:href="fig-392-02a" number="231">
                <image file="392-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/392-02"/>
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            angulos _B, C,_ eſſe rectos. </s>
            <s xml:id="echoid-s12929" xml:space="preserve">Productis enim arcubus _AB, AC,_
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            donec coëantin _D,_ vt ſint ABD, ACD, ſemicirculi; </s>
            <s xml:id="echoid-s12930" xml:space="preserve">erunt
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              <note position="left" xlink:label="note-392-04" xlink:href="note-392-04a" xml:space="preserve">11. 1. Theod.</note>
            quoque arcus _DB, DC,_ quadrantes; </s>
            <s xml:id="echoid-s12931" xml:space="preserve">atque adeo vterque
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            arcus _ABD, ACD,_ bifariam diuidetur ab arcu _B C,_ in
              <lb/>
              <note position="left" xlink:label="note-392-05" xlink:href="note-392-05a" xml:space="preserve">Schol. 9.
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              2. Theod.</note>
            punctis _B,_ & </s>
            <s xml:id="echoid-s12932" xml:space="preserve">_C._ </s>
            <s xml:id="echoid-s12933" xml:space="preserve">Igitur arcus _BC,_ per polos arcuum _AB,_
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            _AC,_ tranſibit; </s>
            <s xml:id="echoid-s12934" xml:space="preserve">atqueidcirco rectos angulos ad _B,_ & </s>
            <s xml:id="echoid-s12935" xml:space="preserve">_C,_
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              <note position="right" xlink:label="note-392-06" xlink:href="note-392-06a" xml:space="preserve">15. 1 Theod.</note>
            efficiet.</s>
            <s xml:id="echoid-s12936" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s12937" xml:space="preserve">_VERVM_ iam anguli _B, C,_ recti ſint. </s>
            <s xml:id="echoid-s12938" xml:space="preserve">Dico latera _AB,_
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            _AC,_ quadrantes eſſe. </s>
            <s xml:id="echoid-s12939" xml:space="preserve">cum enim anguli _B, C,_ ſint recti,
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              <note position="left" xlink:label="note-392-07" xlink:href="note-392-07a" xml:space="preserve">13. 1. Theod.</note>
            tranſibit arcus _BC,_ per polos arcuum _ABD, ACD,_ qui
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              <note position="left" xlink:label="note-392-08" xlink:href="note-392-08a" xml:space="preserve">11. 1. Theod.</note>
            quidem ſemicirculi ſunt; </s>
            <s xml:id="echoid-s12940" xml:space="preserve">atque adeò vtrumque bifariam ſe-
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              <note position="left" xlink:label="note-392-09" xlink:href="note-392-09a" xml:space="preserve">9. 2. Theod.</note>
            cabit in _B, C._ </s>
            <s xml:id="echoid-s12941" xml:space="preserve">Sunt ergo arcus _AB, AC, DB, DC,_ qua-
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            drantes. </s>
            <s xml:id="echoid-s12942" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s12943" xml:space="preserve"/>
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          <head xml:id="echoid-head554" xml:space="preserve">THEOR. 24. PROPOS. 26.</head>
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            <s xml:id="echoid-s12944" xml:space="preserve">IN omni triangulo Iſoſcele ſphærico, </s>
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