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

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          <pb o="17" file="029" n="29" rhead=""/>
          <p>
            <s xml:id="echoid-s578" xml:space="preserve">IN ſphæra A B C D, circuli A E, B D, ſe mutuo ſecent bifariam in pun-
              <lb/>
            ctis E, F. </s>
            <s xml:id="echoid-s579" xml:space="preserve">Dico circulos A C, B D, eſſe maximos. </s>
            <s xml:id="echoid-s580" xml:space="preserve">Cum enim ſe mutuo fecent
              <lb/>
            bifariam in E, F, erit ducta recta E F, vtriuſq; </s>
            <s xml:id="echoid-s581" xml:space="preserve">diameter, cum ſola diameter
              <lb/>
              <figure xlink:label="fig-029-01" xlink:href="fig-029-01a" number="22">
                <image file="029-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/029-01"/>
              </figure>
            circulũ quemcunq; </s>
            <s xml:id="echoid-s582" xml:space="preserve">bifariam diuidat; </s>
            <s xml:id="echoid-s583" xml:space="preserve">ac proin-
              <lb/>
            de diuiſa recta E F, bifariã in G, erit G, vtriuſq;
              <lb/>
            </s>
            <s xml:id="echoid-s584" xml:space="preserve">circuli centrum: </s>
            <s xml:id="echoid-s585" xml:space="preserve">quod dico etiam eſſe ſphæræ
              <lb/>
            centrum, atq; </s>
            <s xml:id="echoid-s586" xml:space="preserve">adeo vtrumq; </s>
            <s xml:id="echoid-s587" xml:space="preserve">circulum per ſphę
              <lb/>
            ræ centrum duci. </s>
            <s xml:id="echoid-s588" xml:space="preserve">Sinamq; </s>
            <s xml:id="echoid-s589" xml:space="preserve">G, dicatur non eſſe
              <lb/>
            centrum ſphæræ, ac proinde circulos A C, B D,
              <lb/>
            non eſſe per ſphæræ centrum ductos; </s>
            <s xml:id="echoid-s590" xml:space="preserve">hoc ipſo
              <lb/>
            oſtendemus, G, eſſe centrum ſphæræ, atq; </s>
            <s xml:id="echoid-s591" xml:space="preserve">idcir
              <lb/>
            co vtrumq; </s>
            <s xml:id="echoid-s592" xml:space="preserve">circulum per ſphæræ centrum du-
              <lb/>
            ci. </s>
            <s xml:id="echoid-s593" xml:space="preserve">Erigatur enim ex G, ad planum circuli A C,
              <lb/>
              <note position="right" xlink:label="note-029-01" xlink:href="note-029-01a" xml:space="preserve">12. vndec.</note>
            perpendicularis G H: </s>
            <s xml:id="echoid-s594" xml:space="preserve">Item G I, perpendicula-
              <lb/>
            ris ad planum circuli B D. </s>
            <s xml:id="echoid-s595" xml:space="preserve">Quoniam igitur cir
              <lb/>
            culi A C, B D, ponuntur non tranſire per centrum ſphæræ, tranſibit vtraq;
              <lb/>
            </s>
            <s xml:id="echoid-s596" xml:space="preserve">perpendicularis G H, G I, per centrum ſphæræ. </s>
            <s xml:id="echoid-s597" xml:space="preserve">Quare punctum G, in quo
              <lb/>
              <note position="right" xlink:label="note-029-02" xlink:href="note-029-02a" xml:space="preserve">Coroll. 2.
                <lb/>
              huius.</note>
            conueniunt, centrum erit ſphæræ, aliàs centrum non exiſteret in vtraque:
              <lb/>
            </s>
            <s xml:id="echoid-s598" xml:space="preserve">ac proinde vterq; </s>
            <s xml:id="echoid-s599" xml:space="preserve">circulus per centrum ſphæræ traijcietur. </s>
            <s xml:id="echoid-s600" xml:space="preserve">Sunt ergo circu
              <lb/>
              <note position="right" xlink:label="note-029-03" xlink:href="note-029-03a" xml:space="preserve">6. huius.</note>
            li A C, B D, per centrum ſphæræ traiecti, maximi. </s>
            <s xml:id="echoid-s601" xml:space="preserve">In ſphæra ergo circuli, qui
              <lb/>
            ſe mutuo bifariam ſecant, ſunt maximi. </s>
            <s xml:id="echoid-s602" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s603" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div70" type="section" level="1" n="43">
          <head xml:id="echoid-head54" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s604" xml:space="preserve">_HIC_ vides mirabilem ſane argumentandi modum. </s>
            <s xml:id="echoid-s605" xml:space="preserve">_N_am ex eo, quòd _G,_ dici-
              <lb/>
            tur non eſſe centrum ſphæræ, demonſtratum eſt demonſtratione affirmatiua, _G,_ eſ-
              <lb/>
            ſe centrum ſphæræ. </s>
            <s xml:id="echoid-s606" xml:space="preserve">quo modo argumentandi etiam vſus eſt _E_uclides lib. </s>
            <s xml:id="echoid-s607" xml:space="preserve">9. </s>
            <s xml:id="echoid-s608" xml:space="preserve">propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s609" xml:space="preserve">12. </s>
            <s xml:id="echoid-s610" xml:space="preserve">& </s>
            <s xml:id="echoid-s611" xml:space="preserve">_C_ardanus lib. </s>
            <s xml:id="echoid-s612" xml:space="preserve">5. </s>
            <s xml:id="echoid-s613" xml:space="preserve">de _P_roport. </s>
            <s xml:id="echoid-s614" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s615" xml:space="preserve">201. </s>
            <s xml:id="echoid-s616" xml:space="preserve">vt in ſcholio eiuſdẽ propoſ. </s>
            <s xml:id="echoid-s617" xml:space="preserve">monuimus.</s>
            <s xml:id="echoid-s618" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div71" type="section" level="1" n="44">
          <head xml:id="echoid-head55" xml:space="preserve">THEOREMA 12. PROPOS. 13.</head>
          <note position="right" xml:space="preserve">18.</note>
          <p>
            <s xml:id="echoid-s619" xml:space="preserve">SI in ſphæra maximus circulus circulum quẽ-
              <lb/>
            piam ad rectos angulos ſecet; </s>
            <s xml:id="echoid-s620" xml:space="preserve">& </s>
            <s xml:id="echoid-s621" xml:space="preserve">bifariam eum ſe-
              <lb/>
            cat, & </s>
            <s xml:id="echoid-s622" xml:space="preserve">per polos.</s>
            <s xml:id="echoid-s623" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s624" xml:space="preserve">IN ſphæra maximus circulus A B C D,
              <lb/>
              <figure xlink:label="fig-029-02" xlink:href="fig-029-02a" number="23">
                <image file="029-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/029-02"/>
              </figure>
            ſecet circulũ B E D, in punctis B, D, ad an-
              <lb/>
            gulos rectos, hoc eſt, planũ circuli A B C D,
              <lb/>
            rectum ſit ad planum circuli B E D; </s>
            <s xml:id="echoid-s625" xml:space="preserve">ſitq́; </s>
            <s xml:id="echoid-s626" xml:space="preserve">cõ-
              <lb/>
            munis eorum ſectio recta B D. </s>
            <s xml:id="echoid-s627" xml:space="preserve">Dico circu-
              <lb/>
            lum A B C D, bifariam, & </s>
            <s xml:id="echoid-s628" xml:space="preserve">per polos ſecare
              <lb/>
            circulum B E D. </s>
            <s xml:id="echoid-s629" xml:space="preserve">Sumpto enim F, centro cir
              <lb/>
              <note position="right" xlink:label="note-029-05" xlink:href="note-029-05a" xml:space="preserve">1. tertij.</note>
            culi maximi A B C D, quod & </s>
            <s xml:id="echoid-s630" xml:space="preserve">centrũ ſphę-
              <lb/>
            ræ erit, (Nam cum circulus maximus duca-
              <lb/>
              <note position="right" xlink:label="note-029-06" xlink:href="note-029-06a" xml:space="preserve">6. huius.</note>
            tur per centrum ſphæræ, erit eius centrum
              <lb/>
              <note position="right" xlink:label="note-029-07" xlink:href="note-029-07a" xml:space="preserve">Coroll. 1.
                <lb/>
              huius.</note>
            idem, quod ſphæræ.) </s>
            <s xml:id="echoid-s631" xml:space="preserve">ducatur ex F, ad planũ
              <lb/>
            circuli B E D, perpendicularis F G, quæ in
              <lb/>
              <note position="right" xlink:label="note-029-08" xlink:href="note-029-08a" xml:space="preserve">11. vndec.</note>
            </s>
          </p>
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