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

Table of handwritten notes

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            <s xml:id="echoid-s530" xml:space="preserve">
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            recta _E F,_ in vtramque partem. </s>
            <s xml:id="echoid-s531" xml:space="preserve">_D_ico _E F,_ cadere in vtrumque polum circulè
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            _BGDH;_ </s>
            <s xml:id="echoid-s532" xml:space="preserve">Quoniam enim recta _E F,_ centrum ſphæræ, & </s>
            <s xml:id="echoid-s533" xml:space="preserve">centrum circuli _B G D H,_
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            connectens perpendicularis eſt ad planum eiuſdem circuli, cadet eadem _E F,_ vtrin
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              <note position="left" xlink:label="note-028-01" xlink:href="note-028-01a" xml:space="preserve">7. huius.</note>
            que protracta in polum vtrumque eiuſdem circuli. </s>
            <s xml:id="echoid-s534" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s535" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">8. huius.</note>
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        <div xml:id="echoid-div65" type="section" level="1" n="40">
          <head xml:id="echoid-head51" xml:space="preserve">COROLLARIVM.</head>
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            <s xml:id="echoid-s536" xml:space="preserve">EX his omnibus conſtat, in ſphæra quatuor hæc puncta, nempe duos polos cuiuſq; </s>
            <s xml:id="echoid-s537" xml:space="preserve">cir-
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            culi, eiuſdem centrum, & </s>
            <s xml:id="echoid-s538" xml:space="preserve">centrum ſphæræ, perpetuo in vna ſinea recta, nempe diametro
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            ſphæræ, exiſtere, & </s>
            <s xml:id="echoid-s539" xml:space="preserve">ipſam quidem diametrum ad planum eiuſdem circuli eſſe perpendi-
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            cularem: </s>
            <s xml:id="echoid-s540" xml:space="preserve">Adeo vt recta pet quælibet duo puncta ex his ducta tranſeat per reliqua duo, ſitq́;
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            </s>
            <s xml:id="echoid-s541" xml:space="preserve">ad planum circuli perpendicularis: </s>
            <s xml:id="echoid-s542" xml:space="preserve">Et recta pet vnum eorum ducta perpendicularis ad pla-
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            num circuli, tranſeat quoq; </s>
            <s xml:id="echoid-s543" xml:space="preserve">per tria puncta reliqua.</s>
            <s xml:id="echoid-s544" xml:space="preserve"/>
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        <div xml:id="echoid-div66" type="section" level="1" n="41">
          <head xml:id="echoid-head52" xml:space="preserve">THEOR. 10. PROP. 11.</head>
          <note position="left" xml:space="preserve">16.</note>
          <p>
            <s xml:id="echoid-s545" xml:space="preserve">IN ſphęra maximi circuli ſe mutuo ſecant bi-
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            fariam.</s>
            <s xml:id="echoid-s546" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s547" xml:space="preserve">IN ſphæra A B C D, ſecent ſe mutuo duo circuli maximi A C, B D, in
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            punctis E, F. </s>
            <s xml:id="echoid-s548" xml:space="preserve">Dico ſe mutuo ſecare bifariam. </s>
            <s xml:id="echoid-s549" xml:space="preserve">Quoniam enim circuli maximi
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            in ſphæra per centrum ſphæræ tranſeunt, tranſibunt circuli A C, B D, per
              <lb/>
              <note position="left" xlink:label="note-028-04" xlink:href="note-028-04a" xml:space="preserve">6. huius.</note>
            ſphæræ centrum, quod ſit G. </s>
            <s xml:id="echoid-s550" xml:space="preserve">Et quoniam idem eſt ſphæræ centrum, & </s>
            <s xml:id="echoid-s551" xml:space="preserve">circu-
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            li per ſphæræ centrum traiecti, erit punctum G, quod ſphæræ centrum poni-
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              <note position="left" xlink:label="note-028-05" xlink:href="note-028-05a" xml:space="preserve">Coroll. 1.
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              huius.</note>
            tur, centrum quoq; </s>
            <s xml:id="echoid-s552" xml:space="preserve">vtriuſq; </s>
            <s xml:id="echoid-s553" xml:space="preserve">circuli A C, B D, ita vt in vtroq; </s>
            <s xml:id="echoid-s554" xml:space="preserve">plano circu-
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            lorum A C, B D, exiſtat. </s>
            <s xml:id="echoid-s555" xml:space="preserve">Sunt autem & </s>
            <s xml:id="echoid-s556" xml:space="preserve">puncta E, F, in vtroq; </s>
            <s xml:id="echoid-s557" xml:space="preserve">eodem plano.
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            </s>
            <s xml:id="echoid-s558" xml:space="preserve">
              <figure xlink:label="fig-028-01" xlink:href="fig-028-01a" number="21">
                <image file="028-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/028-01"/>
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            Tria igitur pũcta E, G, F, in vtroq; </s>
            <s xml:id="echoid-s559" xml:space="preserve">plano circulo
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            rũ A C, B D, exiſtunt; </s>
            <s xml:id="echoid-s560" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s561" xml:space="preserve">adeo in cõmuni eorũ
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            ſectione erunt, cum ſolũ cõmunis eorum ſectio
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            ſit in vtroq; </s>
            <s xml:id="echoid-s562" xml:space="preserve">plano: </s>
            <s xml:id="echoid-s563" xml:space="preserve">Eſt autem communis eo-
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              <note position="left" xlink:label="note-028-06" xlink:href="note-028-06a" xml:space="preserve">3. vndec.</note>
            rum ſectio linea recta. </s>
            <s xml:id="echoid-s564" xml:space="preserve">Igitur tria puncta E, G, F,
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            in linea recta ex E, per G, ad F, ducta exiſtunt.
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            </s>
            <s xml:id="echoid-s565" xml:space="preserve">quæ cum tranſeat per G, centrum vtriuſq; </s>
            <s xml:id="echoid-s566" xml:space="preserve">cir-
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            culi, & </s>
            <s xml:id="echoid-s567" xml:space="preserve">ſphæræ, vt oſtenſum eſt, diameter erit
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            & </s>
            <s xml:id="echoid-s568" xml:space="preserve">ſphæræ, & </s>
            <s xml:id="echoid-s569" xml:space="preserve">vtriuſq; </s>
            <s xml:id="echoid-s570" xml:space="preserve">circuli; </s>
            <s xml:id="echoid-s571" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s572" xml:space="preserve">adeo vtrum-
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            que eorum bifariam ſecabit, ita vtſemicirculi
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            ſint E A F, F C E, E B F, F D E: </s>
            <s xml:id="echoid-s573" xml:space="preserve">In ſphæra er-
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            go maximi circuli ſe mutuo ſecant bifariam. </s>
            <s xml:id="echoid-s574" xml:space="preserve">
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            Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s575" xml:space="preserve"/>
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        <div xml:id="echoid-div68" type="section" level="1" n="42">
          <head xml:id="echoid-head53" xml:space="preserve">THEOR. 11. PROP. 12.</head>
          <note position="left" xml:space="preserve">17.</note>
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            <s xml:id="echoid-s576" xml:space="preserve">IN ſphæra circuli, qui ſe mutuo bifariam ſe-
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            cant, ſunt maximi.</s>
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