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

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            <s xml:id="echoid-s346" xml:space="preserve">
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            trum circuli B G D H, atque adeo F, centrum erit circuli. </s>
            <s xml:id="echoid-s347" xml:space="preserve">Quòd ſi circu-
              <lb/>
              <note position="left" xlink:label="note-024-01" xlink:href="note-024-01a" xml:space="preserve">Coroll. 1.
                <lb/>
              huius.</note>
            lus B G D H, per centrum ſphæræ ducatur, erit ipſum centrum ſphæræ E,
              <lb/>
            idem quod F, centrum circuli; </s>
            <s xml:id="echoid-s348" xml:space="preserve">ex quo ad planum circuli excitata ſit perpen-
              <lb/>
              <note position="left" xlink:label="note-024-02" xlink:href="note-024-02a" xml:space="preserve">12. vndec.</note>
            dicularis A C. </s>
            <s xml:id="echoid-s349" xml:space="preserve">Ductis igitur diametris B D, G H, vtcunque, ducantur ab ea
              <lb/>
            rum extremis rectæ ad puncta A, C. </s>
            <s xml:id="echoid-s350" xml:space="preserve">Et quia A F, perpendicularis eſt ad planũ
              <lb/>
              <figure xlink:label="fig-024-01" xlink:href="fig-024-01a" number="17">
                <image file="024-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/024-01"/>
              </figure>
            circuli B G D H, erunt
              <lb/>
            anguli omnes, quos ad F,
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            facit, recti, ex defin. </s>
            <s xml:id="echoid-s351" xml:space="preserve">3. </s>
            <s xml:id="echoid-s352" xml:space="preserve">lib.
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            </s>
            <s xml:id="echoid-s353" xml:space="preserve">11. </s>
            <s xml:id="echoid-s354" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s355" xml:space="preserve">quare duo
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            triangula A F B, A F H,
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            duo latera A F, F B, duo
              <lb/>
            bus lateribus A F, F H,
              <lb/>
            æqualia habent, quę qui
              <lb/>
            dem angulos comprehen
              <lb/>
            dunt æquales, nempe re-
              <lb/>
            ctos. </s>
            <s xml:id="echoid-s356" xml:space="preserve">Igitur baſes A B,
              <lb/>
            A H, æquales erunt. </s>
            <s xml:id="echoid-s357" xml:space="preserve">Eo-
              <lb/>
              <note position="left" xlink:label="note-024-03" xlink:href="note-024-03a" xml:space="preserve">4. primi.</note>
            dem modo oſtẽ demus & </s>
            <s xml:id="echoid-s358" xml:space="preserve">
              <lb/>
            rectas A D, A G, & </s>
            <s xml:id="echoid-s359" xml:space="preserve">alias
              <lb/>
            quaſcunque ex A, ad circumferentiam circuli B G D H, ductas tam inter ſe,
              <lb/>
            quàm rectis A B, A H, æquales eſſe. </s>
            <s xml:id="echoid-s360" xml:space="preserve">Punctũ ergo A, polus eſt circuli B G D H,
              <lb/>
            ex defin. </s>
            <s xml:id="echoid-s361" xml:space="preserve">5. </s>
            <s xml:id="echoid-s362" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s363" xml:space="preserve">Non aliter demonſtrabimus, & </s>
            <s xml:id="echoid-s364" xml:space="preserve">C, punctum eiuſdem cir
              <lb/>
            culi polum eſſe. </s>
            <s xml:id="echoid-s365" xml:space="preserve">Si igitur ſit in ſphæra circulus, & </s>
            <s xml:id="echoid-s366" xml:space="preserve">à centro, &</s>
            <s xml:id="echoid-s367" xml:space="preserve">c. </s>
            <s xml:id="echoid-s368" xml:space="preserve">Quod erat
              <lb/>
            oſtendendum.</s>
            <s xml:id="echoid-s369" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div45" type="section" level="1" n="31">
          <head xml:id="echoid-head42" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s370" xml:space="preserve">_IN_ verſione Maurolyci adduntur ſequentia duo theoremata, quæ Arabes adie-
              <lb/>
            cerunt.</s>
            <s xml:id="echoid-s371" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div46" type="section" level="1" n="32">
          <head xml:id="echoid-head43" xml:space="preserve">I.</head>
          <p>
            <s xml:id="echoid-s372" xml:space="preserve">SI ſit in ſphæra circulus, a cuius centro educatur perpendicu-
              <lb/>
              <note position="left" xlink:label="note-024-04" xlink:href="note-024-04a" xml:space="preserve">10.</note>
            laris ad circuli planum, quæ in vtramque partem producatur, cadet
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            hæc in vtrumque polum circuli.</s>
            <s xml:id="echoid-s373" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s374" xml:space="preserve">_IN_ eadem figura ex _F,_ centro circuli _B G D H,_ erigatur recta _F A,_ perpendi-
              <lb/>
              <note position="left" xlink:label="note-024-05" xlink:href="note-024-05a" xml:space="preserve">12. vndec.</note>
            cularis ad circuli planum, quæ occurr at ſuperficiei ſphæræ in punctis _A, C._ </s>
            <s xml:id="echoid-s375" xml:space="preserve">Dico
              <lb/>
            _A, C,_ eſſe polos circuli _B G D H._ </s>
            <s xml:id="echoid-s376" xml:space="preserve">Erunt enim rurſus ex definit. </s>
            <s xml:id="echoid-s377" xml:space="preserve">3. </s>
            <s xml:id="echoid-s378" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s379" xml:space="preserve">11. </s>
            <s xml:id="echoid-s380" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s381" xml:space="preserve">om
              <lb/>
            nes anguli, quos ad _F,_ facit recta _A F,_ recti. </s>
            <s xml:id="echoid-s382" xml:space="preserve">Quare, vt prius, lineæ _A B, A D, A G,_
              <lb/>
            _A H,_ &</s>
            <s xml:id="echoid-s383" xml:space="preserve">c. </s>
            <s xml:id="echoid-s384" xml:space="preserve">æquales inter ſe erunt, &</s>
            <s xml:id="echoid-s385" xml:space="preserve">c.</s>
            <s xml:id="echoid-s386" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">4. primi.
            <lb/>
          Coroll. 2.
            <lb/>
          huius.</note>
          <p style="it">
            <s xml:id="echoid-s387" xml:space="preserve">_ALITER._ </s>
            <s xml:id="echoid-s388" xml:space="preserve">Quoniam perpendicularis _F A,_ tranſit per centrum ſphæræ _E;_ </s>
            <s xml:id="echoid-s389" xml:space="preserve">du
              <lb/>
            cta erit recta _E F,_ ex _E,_ centro ſphæræ ad planum circuli _B G D H,_ perpendicu-
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            laris. </s>
            <s xml:id="echoid-s390" xml:space="preserve">Quare vt demonſtratum eſt, cadet in polos eiuſdem circuli. </s>
            <s xml:id="echoid-s391" xml:space="preserve">Quod eſt pro-
              <lb/>
              <note position="left" xlink:label="note-024-07" xlink:href="note-024-07a" xml:space="preserve">3. huius.</note>
            poſitum.</s>
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