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

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          <pb o="8" file="020" n="20" rhead=""/>
          <note position="left" xml:space="preserve">4.</note>
        </div>
        <div xml:id="echoid-div32" type="section" level="1" n="26">
          <head xml:id="echoid-head37" xml:space="preserve">THEOREMA 3. PROPOS. 4.</head>
          <p>
            <s xml:id="echoid-s202" xml:space="preserve">SI Sphæra planum tangat, quod eam non ſe-
              <lb/>
            cet, recta linea ducta à centro ſphæræ ad conta-
              <lb/>
            ctum, perpendicularis erit ad planum.</s>
            <s xml:id="echoid-s203" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s204" xml:space="preserve">TANGAT Sphæra planum, quod ip
              <lb/>
              <note position="left" xlink:label="note-020-02" xlink:href="note-020-02a" xml:space="preserve">2. huius.</note>
              <figure xlink:label="fig-020-01" xlink:href="fig-020-01a" number="11">
                <image file="020-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/020-01"/>
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            ſam non ſecet, in puncto A: </s>
            <s xml:id="echoid-s205" xml:space="preserve">Et inuento B,
              <lb/>
            centro ſphæræ, ducatur ab eo recta B A, ad
              <lb/>
            punctum contactus A. </s>
            <s xml:id="echoid-s206" xml:space="preserve">Dico rectam B A, ad
              <lb/>
            dictum planum perpendicularem eſſe. </s>
            <s xml:id="echoid-s207" xml:space="preserve">Nam
              <lb/>
            per rectam A B, ducantur duo plana vtcun
              <lb/>
            que ſe mutuo ſecãtia, quæ in ſuperficie qui-
              <lb/>
              <note position="left" xlink:label="note-020-03" xlink:href="note-020-03a" xml:space="preserve">1. huius.</note>
            dem ſphæræ faciant circulorum circumfe-
              <lb/>
            rentias A C D E, A F D G, in plano autẽ
              <lb/>
              <note position="left" xlink:label="note-020-04" xlink:href="note-020-04a" xml:space="preserve">3. vndec.</note>
            tangente rectas H A I, K A L. </s>
            <s xml:id="echoid-s208" xml:space="preserve">Quoniara
              <lb/>
            igitur vterque circulus A C D E, A F D G,
              <lb/>
            per centrum B, ſphæræ traijcitur, erit quo-
              <lb/>
              <note position="left" xlink:label="note-020-05" xlink:href="note-020-05a" xml:space="preserve">Coroll. 1.
                <lb/>
              huius.</note>
            que B, vtriuſque centrum. </s>
            <s xml:id="echoid-s209" xml:space="preserve">Rurſus quia planum tangens ſphęram non ſecat,
              <lb/>
            fit, vt neque rectæ H A I, K A L, in eo exiſtentes eandem ſecent; </s>
            <s xml:id="echoid-s210" xml:space="preserve">ac proinde
              <lb/>
            neque circulos A C D E, A F D G, in ſphæræ ſuperficie exiſtentes. </s>
            <s xml:id="echoid-s211" xml:space="preserve">Tanget
              <lb/>
            igitur recta H A I, circulum A C D E, in puncto A, & </s>
            <s xml:id="echoid-s212" xml:space="preserve">recta K A L, circulum
              <lb/>
              <note position="left" xlink:label="note-020-06" xlink:href="note-020-06a" xml:space="preserve">18. tertij.</note>
            A F D G, in eodem puncto A. </s>
            <s xml:id="echoid-s213" xml:space="preserve">Igitur recta B A, & </s>
            <s xml:id="echoid-s214" xml:space="preserve">ad rectam H A I, & </s>
            <s xml:id="echoid-s215" xml:space="preserve">ad re-
              <lb/>
            ctam K A L, perpendicularis eſt. </s>
            <s xml:id="echoid-s216" xml:space="preserve">Quare eadem recta B A, & </s>
            <s xml:id="echoid-s217" xml:space="preserve">ad planum tan-
              <lb/>
              <note position="left" xlink:label="note-020-07" xlink:href="note-020-07a" xml:space="preserve">4. vndec.</note>
            gens, quod per rectas H A I, K A L, ducitur, perpendicularis erit. </s>
            <s xml:id="echoid-s218" xml:space="preserve">Si ſphæra
              <lb/>
            ergo planum tangat, quod eam non ſecet, &</s>
            <s xml:id="echoid-s219" xml:space="preserve">c. </s>
            <s xml:id="echoid-s220" xml:space="preserve">Quod oſtendendum erat.</s>
            <s xml:id="echoid-s221" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div34" type="section" level="1" n="27">
          <head xml:id="echoid-head38" xml:space="preserve">THEOREMA 4. PROPOS. 5.</head>
          <note position="left" xml:space="preserve">5.</note>
          <p>
            <s xml:id="echoid-s222" xml:space="preserve">SI Sphæra planum tangat, quod ipſam non ſe-
              <lb/>
            cet, à contactu autem excitetur recta linea ad an-
              <lb/>
            gulos rectos ipſi plano, in linea excitata erit cen-
              <lb/>
            trum ſphæræ.</s>
            <s xml:id="echoid-s223" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s224" xml:space="preserve">SPHAERA A B C D, tãgat in C, pun
              <lb/>
              <figure xlink:label="fig-020-02" xlink:href="fig-020-02a" number="12">
                <image file="020-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/020-02"/>
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            cto planum E F, quod eam non ſecet, à pun
              <lb/>
            cto autem C, excitetur ad planum E F, per-
              <lb/>
              <note position="left" xlink:label="note-020-09" xlink:href="note-020-09a" xml:space="preserve">12. vndec.</note>
            pendicularis C A. </s>
            <s xml:id="echoid-s225" xml:space="preserve">Dico in A C, centrum eſ
              <lb/>
            ſe ſphæræ. </s>
            <s xml:id="echoid-s226" xml:space="preserve">Si enim non eſt, ſit G, centrum
              <lb/>
            ſphæræ extra rectam A C, ſi fieri poteſt, & </s>
            <s xml:id="echoid-s227" xml:space="preserve">à
              <lb/>
            G, ad C, recta ducatur G C, quę ad planum
              <lb/>
              <note position="left" xlink:label="note-020-10" xlink:href="note-020-10a" xml:space="preserve">4. huius.</note>
            E F, perpendicularis erit: </s>
            <s xml:id="echoid-s228" xml:space="preserve">Erat autẽ & </s>
            <s xml:id="echoid-s229" xml:space="preserve">A C,
              <lb/>
            ad idem planum perpendicularis. </s>
            <s xml:id="echoid-s230" xml:space="preserve">Igitur ex
              <lb/>
            eodem puncto C, ad idem planum E F, duæ
              <lb/>
            perpendiculares ducuntur. </s>
            <s xml:id="echoid-s231" xml:space="preserve">Quod eſt </s>
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