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

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          <p>
            <s xml:id="echoid-s166" xml:space="preserve">
              <pb o="7" file="019" n="19" rhead=""/>
            laris F G, quæ vtrinque ad ſuperficiem ſphæ-
              <lb/>
              <figure xlink:label="fig-019-01" xlink:href="fig-019-01a" number="9">
                <image file="019-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/019-01"/>
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            ræ educta ad puncta A, C, ſecetur bifariam in
              <lb/>
            G. </s>
            <s xml:id="echoid-s167" xml:space="preserve">Dico G, centrum eſſe ſphæræ. </s>
            <s xml:id="echoid-s168" xml:space="preserve">Si enim nõ
              <lb/>
            eſt, ſit, ſi fieri poteſt, centrum H, ſecans diame
              <lb/>
            tros omnes bifariã, quod quidem in linea A C,
              <lb/>
            nõ exiſtet, cũ ea in puncto G, ſolũ bifariã diui
              <lb/>
            datur, ſed extra illã. </s>
            <s xml:id="echoid-s169" xml:space="preserve">Demittatur ex H, centro
              <lb/>
            ſphæræ ad planum circuli B D E, perpendicu
              <lb/>
            laris H I, quæ æquidiſtans erit lineæ F G; </s>
            <s xml:id="echoid-s170" xml:space="preserve">ac
              <lb/>
            proinde in punctum F, non cadet: </s>
            <s xml:id="echoid-s171" xml:space="preserve">coirent em̃
              <lb/>
            tunc duæ parallelæ H I, G F, in F, puncto,
              <lb/>
            quod fieri non poteſt. </s>
            <s xml:id="echoid-s172" xml:space="preserve">Quoniam verò perpen
              <lb/>
            dicularis ex centro ſphæræ in planũ circuli B D E, demiſſa cadit in eius cen-
              <lb/>
              <note position="right" xlink:label="note-019-01" xlink:href="note-019-01a" xml:space="preserve">Coroll. 1.
                <lb/>
              huius.</note>
            trum, erit I, centrum circuli B D E. </s>
            <s xml:id="echoid-s173" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s174" xml:space="preserve">F, ex conſtructione, centrum eſt
              <lb/>
            eiuſdem circuli. </s>
            <s xml:id="echoid-s175" xml:space="preserve">Quod abſurdum eſt. </s>
            <s xml:id="echoid-s176" xml:space="preserve">Idem enim circulus vnum tantum ha-
              <lb/>
            beat centrum neceſſe eſt. </s>
            <s xml:id="echoid-s177" xml:space="preserve">Non ergo aliud punctum præter G, centrum erit
              <lb/>
            ſphæræ. </s>
            <s xml:id="echoid-s178" xml:space="preserve">Quare datæ ſphæræ centrum inuenimus. </s>
            <s xml:id="echoid-s179" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s180" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div26" type="section" level="1" n="23">
          <head xml:id="echoid-head34" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s181" xml:space="preserve">HINC conſtat, ſi in ſphæra ſit circulus non per centrum ſphæræ traiectus, à cuius cen-
              <lb/>
            tro excitetur perpendicularis ad ipſius planum, in linea perpendiculari centrũ eſſe ſphærę.
              <lb/>
            </s>
            <s xml:id="echoid-s182" xml:space="preserve">Oſtenſum enim eſt, punctum G, quod perpendicularẽ A C, bifariã diuidit, eſſe ſphærę centrũ.</s>
            <s xml:id="echoid-s183" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div27" type="section" level="1" n="24">
          <head xml:id="echoid-head35" xml:space="preserve">THEOREMA 2. PROPOS. 3.</head>
          <p>
            <s xml:id="echoid-s184" xml:space="preserve">SPHAERA planum, à quo non ſecatur, non
              <lb/>
              <note position="left" xlink:label="note-019-02" xlink:href="note-019-02a" xml:space="preserve">3.</note>
            tangit in pluribus punctis vno.</s>
            <s xml:id="echoid-s185" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s186" xml:space="preserve">SI enim fieri poteſt, ſphæra planum, à quo non ſecatur, tangat in pluri-
              <lb/>
              <note position="right" xlink:label="note-019-03" xlink:href="note-019-03a" xml:space="preserve">2. huius.</note>
            bus punctis vno, vt in A, & </s>
            <s xml:id="echoid-s187" xml:space="preserve">B. </s>
            <s xml:id="echoid-s188" xml:space="preserve">Inuento igitur C, centro ſphæræ, ducantur re
              <lb/>
              <figure xlink:label="fig-019-02" xlink:href="fig-019-02a" number="10">
                <image file="019-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/019-02"/>
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            ctæ C A, C B: </s>
            <s xml:id="echoid-s189" xml:space="preserve">& </s>
            <s xml:id="echoid-s190" xml:space="preserve">per C A, C B, ducatur pla-
              <lb/>
            num faciens quidem in ſuperficie ſphæræ cir
              <lb/>
              <note position="right" xlink:label="note-019-04" xlink:href="note-019-04a" xml:space="preserve">1. huius.</note>
            cumferentiam circuli A B D, in plano autẽ
              <lb/>
            ſecante rectam lineam E A B F. </s>
            <s xml:id="echoid-s191" xml:space="preserve">Quia igitur
              <lb/>
              <note position="right" xlink:label="note-019-05" xlink:href="note-019-05a" xml:space="preserve">3. vndec.</note>
            planũ tangens, in quo eſt recta E A B F, ſphæ
              <lb/>
            ram non ſecat, atque adeò neque circulum
              <lb/>
            A B D, in ſphęrę ſuperſicie exiſtentem, fit vt
              <lb/>
            neq; </s>
            <s xml:id="echoid-s192" xml:space="preserve">recta E A B F, circulũ A B D, ſecet. </s>
            <s xml:id="echoid-s193" xml:space="preserve">Cadet
              <lb/>
            ergo recta A B, tota extra circulũ. </s>
            <s xml:id="echoid-s194" xml:space="preserve">Quoniã
              <lb/>
            vero duo puncta ſumpta ſunt A, B, in circũfe
              <lb/>
            rentia circuli A B D, cadet eadem recta A B, à
              <lb/>
            pũcto A, in punctũ B, ducta tota in tra circulũ
              <lb/>
              <note position="right" xlink:label="note-019-06" xlink:href="note-019-06a" xml:space="preserve">2. tertij.</note>
            A B D. </s>
            <s xml:id="echoid-s195" xml:space="preserve">Quod eſt abſurdũ. </s>
            <s xml:id="echoid-s196" xml:space="preserve">Sphęra igit̃ planũ,
              <lb/>
            à quo nõ ſecatur, nõ tangit in pluribus pũctis vno. </s>
            <s xml:id="echoid-s197" xml:space="preserve">Quod erat demonſtrandũ.</s>
            <s xml:id="echoid-s198" xml:space="preserve"/>
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        <div xml:id="echoid-div30" type="section" level="1" n="25">
          <head xml:id="echoid-head36" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s199" xml:space="preserve">HINC fit, ſi duo puncta ſignentur in ſuperficie ſphæræ, rectam, quæ illa connectit, intra
              <lb/>
            ſphæram cadere. </s>
            <s xml:id="echoid-s200" xml:space="preserve">quia videlicet cadit intra circulum, qui in ſphæræ ſuperficie circumferen
              <lb/>
              <note position="right" xlink:label="note-019-07" xlink:href="note-019-07a" xml:space="preserve">2. tertij.</note>
            tiam habet.</s>
            <s xml:id="echoid-s201" xml:space="preserve"/>
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