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

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        <div xml:id="echoid-div292" type="section" level="1" n="134">
          <p>
            <s xml:id="echoid-s3603" xml:space="preserve">
              <pb o="94" file="106" n="106" rhead=""/>
            tio autem arcus HM, ad arcum EI, maior eſt, quàm arcus MN, ad arcum
              <lb/>
              <note position="left" xlink:label="note-106-01" xlink:href="note-106-01a" xml:space="preserve">coroll. 10.
                <lb/>
              huius.</note>
            IK; </s>
            <s xml:id="echoid-s3604" xml:space="preserve">erit quoq; </s>
            <s xml:id="echoid-s3605" xml:space="preserve">maior ratio diametri ſphæræ ad diametrum circuli EG, quàm
              <lb/>
            arcus MN, ad arcum IK. </s>
            <s xml:id="echoid-s3606" xml:space="preserve">Et quia arcus PK, ſimilis eſt arcui BD, ex hy-
              <lb/>
            potheſi, & </s>
            <s xml:id="echoid-s3607" xml:space="preserve">arcus OK, ſimilis arcui MN; </s>
            <s xml:id="echoid-s3608" xml:space="preserve">eſtq́ue arcus PK, minor arcu OK; </s>
            <s xml:id="echoid-s3609" xml:space="preserve">erit
              <lb/>
              <note position="left" xlink:label="note-106-02" xlink:href="note-106-02a" xml:space="preserve">10. 2. huius.</note>
            quoque arcus BD, minor arcu MN; </s>
            <s xml:id="echoid-s3610" xml:space="preserve">ac proinde minor erit ratio arcus BD,
              <lb/>
            ad arcum IK, quàm arcus MN, ad eundẽ arcum IK. </s>
            <s xml:id="echoid-s3611" xml:space="preserve">Cum ergo oſtenſum ſit, ra
              <lb/>
              <note position="left" xlink:label="note-106-03" xlink:href="note-106-03a" xml:space="preserve">8. quinti.</note>
            tionem diametri ſphæræ ad diametrum circuli EG, maiorem eſſe, quàm arcus
              <lb/>
            MN, ad arcum IK; </s>
            <s xml:id="echoid-s3612" xml:space="preserve">Multo maior erit ratio diametri ſphæræ ad diametrum
              <lb/>
            cireuli EG, quàm arcus BD, ad arcum IK. </s>
            <s xml:id="echoid-s3613" xml:space="preserve">Si igitur in ſphæra maximi cir-
              <lb/>
            culi tangant vnum, &</s>
            <s xml:id="echoid-s3614" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3615" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s3616" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div294" type="section" level="1" n="135">
          <head xml:id="echoid-head149" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s3617" xml:space="preserve">_IN_ exemplari græco habetur, maiorem eſſe rationem duplæ diametri ſphæræ ad
              <lb/>
            diametrum circuli _
              <emph style="sc">Eg</emph>
            ,_ quàm arcus _
              <emph style="sc">B</emph>
            D,_ ad arcum _IK_ Quod quidem ex noſtra de-
              <lb/>
            monſtratione liquidò conſtat. </s>
            <s xml:id="echoid-s3618" xml:space="preserve">Cum enim diameter ſphæræ maiorem habeat rationem
              <lb/>
            ad diametrum circuli _EG,_ quàm arcus _BD,_ ad arcum _IK;_ </s>
            <s xml:id="echoid-s3619" xml:space="preserve">multo maiorem rationem
              <lb/>
            habebit dupla diametri ſphæræ ad diametrum circuli _
              <emph style="sc">Eg</emph>
            ,_ quàm arcus _
              <emph style="sc">B</emph>
            D,_ ad ar-
              <lb/>
            cum _IK;_ </s>
            <s xml:id="echoid-s3620" xml:space="preserve">propterea quòd dupla diametri ſphæræ ad diametrum circuli _
              <emph style="sc">Eg</emph>
            ,_ maiorem
              <lb/>
              <note position="left" xlink:label="note-106-04" xlink:href="note-106-04a" xml:space="preserve">8.quinti.</note>
            rationem habet, quàm diameter ſphæræ ad eandem diametrum circuli EG.</s>
            <s xml:id="echoid-s3621" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div296" type="section" level="1" n="136">
          <head xml:id="echoid-head150" xml:space="preserve">THEOR. 13. PROPOS. 13.</head>
          <note position="left" xml:space="preserve">15.</note>
          <p>
            <s xml:id="echoid-s3622" xml:space="preserve">SI in ſphæra paralleli circuli intercipiant cir-
              <lb/>
            cunferentias maximi alicuius circuli vtrinq; </s>
            <s xml:id="echoid-s3623" xml:space="preserve">æqua
              <lb/>
            les ab illo puncto, in quo ipſe maximus circulus
              <lb/>
            ſecat maximum parallelorum; </s>
            <s xml:id="echoid-s3624" xml:space="preserve">per puncta autem
              <lb/>
            terminantia æquales circunferentias, & </s>
            <s xml:id="echoid-s3625" xml:space="preserve">per paral-
              <lb/>
            lelorum polos deſcribantur maximi circuli, aut ſi
              <lb/>
            deſcribantur maximi circuli, qui vnum eundem-
              <lb/>
            que parallelorum tangant: </s>
            <s xml:id="echoid-s3626" xml:space="preserve">æquales intercipient cir
              <lb/>
            cunferentias de maximo parallelorum.</s>
            <s xml:id="echoid-s3627" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3628" xml:space="preserve">IN ſphæra AB, paralleli circuli CD, EF, auferant de maximo circulo
              <lb/>
              <figure xlink:label="fig-106-01" xlink:href="fig-106-01a" number="110">
                <image file="106-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/106-01"/>
              </figure>
            AF, duas circunferentias
              <lb/>
            æquales GC, GF, vtrin-
              <lb/>
            que à puncto G, in quo
              <lb/>
            circulus AF, ſecat maxi-
              <lb/>
            mum parallelorum BG;
              <lb/>
            </s>
            <s xml:id="echoid-s3629" xml:space="preserve">& </s>
            <s xml:id="echoid-s3630" xml:space="preserve">per puncta C, G, F, du
              <lb/>
            cãtur maximi circuli ſi-
              <lb/>
            ue per polos parallelo-
              <lb/>
            rum, vt in priori figura,
              <lb/>
            ſiue tangẽtes vnum eun-
              <lb/>
            demque parallelũ, vt in figura poſteriori, ſecantes maximum parallelorum </s>
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