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

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        <div xml:id="echoid-div296" type="section" level="1" n="136">
          <p>
            <s xml:id="echoid-s3630" xml:space="preserve">
              <pb o="95" file="107" n="107" rhead=""/>
            H,I. </s>
            <s xml:id="echoid-s3631" xml:space="preserve">Dico arcus GH, GI, æquales eſſe. </s>
            <s xml:id="echoid-s3632" xml:space="preserve">Quoniam enim arcus GC, GF, æqua-
              <lb/>
            les ponuntur, erunt paralleli CD, EF, æquales. </s>
            <s xml:id="echoid-s3633" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s3634" xml:space="preserve">arcus GK, GL,
              <lb/>
              <note position="right" xlink:label="note-107-01" xlink:href="note-107-01a" xml:space="preserve">17. 2. huius</note>
            æquales erunt. </s>
            <s xml:id="echoid-s3635" xml:space="preserve">Quare rectæ ductæ CK, FL, æquales erunt; </s>
            <s xml:id="echoid-s3636" xml:space="preserve">ac proinde in cir-
              <lb/>
              <note position="right" xlink:label="note-107-02" xlink:href="note-107-02a" xml:space="preserve">18. 2. huius</note>
            culis æqualibus CD, EF, arcus æquales auferent CK, FL; </s>
            <s xml:id="echoid-s3637" xml:space="preserve">& </s>
            <s xml:id="echoid-s3638" xml:space="preserve">idcirco inter
              <lb/>
              <note position="right" xlink:label="note-107-03" xlink:href="note-107-03a" xml:space="preserve">3. huius.</note>
            ſe ſimiles erunt arcus Ck, FL: </s>
            <s xml:id="echoid-s3639" xml:space="preserve">Eſt autem arcus GH, arcui CK, & </s>
            <s xml:id="echoid-s3640" xml:space="preserve">arcus
              <lb/>
              <note position="right" xlink:label="note-107-04" xlink:href="note-107-04a" xml:space="preserve">28 tertij.</note>
            GI, arcui FL, ſimilis. </s>
            <s xml:id="echoid-s3641" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s3642" xml:space="preserve">arcus GH, GI, ſimiles inter ſe erunt, ac
              <lb/>
              <note position="right" xlink:label="note-107-05" xlink:href="note-107-05a" xml:space="preserve">10. vel. 13.</note>
            proinde, cum ſint eiuſdem circuli, æquales interſe. </s>
            <s xml:id="echoid-s3643" xml:space="preserve">Siigitur in ſphæra ma-
              <lb/>
              <note position="right" xlink:label="note-107-06" xlink:href="note-107-06a" xml:space="preserve">2. huius.</note>
            ximus circulus, &</s>
            <s xml:id="echoid-s3644" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3645" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s3646" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div298" type="section" level="1" n="137">
          <head xml:id="echoid-head151" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s3647" xml:space="preserve">_HINC_ etiam conſtat, ijsdem poſitis, omnes arcus maximorum circuloruminter
              <lb/>
            parallelos interceptos inter ſe æquales eſſe, quales ſunt _CH, HE, KG, GL, DI,_
              <lb/>
            _IF._ </s>
            <s xml:id="echoid-s3648" xml:space="preserve">Cum enim arcus _
              <emph style="sc">G</emph>
            C, GH,_ arcubus _
              <emph style="sc">G</emph>
            F,
              <emph style="sc">GI</emph>
            ,_ æquales ſint, erunt & </s>
            <s xml:id="echoid-s3649" xml:space="preserve">rectæ _CH_,
              <lb/>
              <note position="right" xlink:label="note-107-07" xlink:href="note-107-07a" xml:space="preserve">3. huius.</note>
            _FI,_ æquales; </s>
            <s xml:id="echoid-s3650" xml:space="preserve">ac propterea & </s>
            <s xml:id="echoid-s3651" xml:space="preserve">arcus _CH, FI,_ æquales erunt: </s>
            <s xml:id="echoid-s3652" xml:space="preserve">Sunt autem arcui _CH_,
              <lb/>
              <note position="right" xlink:label="note-107-08" xlink:href="note-107-08a" xml:space="preserve">28. tertij.</note>
            arcus _
              <emph style="sc">Kg</emph>
            , DI,_ & </s>
            <s xml:id="echoid-s3653" xml:space="preserve">arcui _FI_, arcus _LG, EH,_ æquales. </s>
            <s xml:id="echoid-s3654" xml:space="preserve">Igitur omnes illi ſex ars
              <lb/>
              <note position="right" xlink:label="note-107-09" xlink:href="note-107-09a" xml:space="preserve">10. vel 13.</note>
            cus æquales erunt.</s>
            <s xml:id="echoid-s3655" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">2. huius.</note>
        </div>
        <div xml:id="echoid-div300" type="section" level="1" n="138">
          <head xml:id="echoid-head152" xml:space="preserve">THEOREMA 14. PROPOS. 14.</head>
          <note position="right" xml:space="preserve">16.</note>
          <p>
            <s xml:id="echoid-s3656" xml:space="preserve">SI in ſphæra maximus circulus aliquem circu-
              <lb/>
            lumtangat, alius autem maximus circulus obli-
              <lb/>
            quus ad parallelos tangat circulos maiores illis,
              <lb/>
            quos tangebat maximus circulus primo poſitus:
              <lb/>
            </s>
            <s xml:id="echoid-s3657" xml:space="preserve">inæquales intercipient circunferẽtias parallelorũ
              <lb/>
            circulorum, quarum propiores vtriuis polorum
              <lb/>
            maiores erunt, quàm vt ſimiles ſint remotioribus.</s>
            <s xml:id="echoid-s3658" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3659" xml:space="preserve">IN ſphæra maximus circulus AB, tangat circulum AC; </s>
            <s xml:id="echoid-s3660" xml:space="preserve">& </s>
            <s xml:id="echoid-s3661" xml:space="preserve">alius maximus
              <lb/>
            DE, tãgat alium maiorẽ DF, ſecet-
              <lb/>
              <figure xlink:label="fig-107-01" xlink:href="fig-107-01a" number="111">
                <image file="107-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/107-01"/>
              </figure>
            q́ue duos parallelos quoſcũq; </s>
            <s xml:id="echoid-s3662" xml:space="preserve">GH,
              <lb/>
            BI, in k, E. </s>
            <s xml:id="echoid-s3663" xml:space="preserve">Dico arcus k H, EI, in-
              <lb/>
            æquales eſſe, maioremque eſſe k H,
              <lb/>
            polo conſpicuo propiorem, quàm
              <lb/>
            vt ſimilis ſit arcui EI, remotiori:
              <lb/>
            </s>
            <s xml:id="echoid-s3664" xml:space="preserve">vel ipſum EB, polo occulto pro-
              <lb/>
            piorẽ eſſe maiorem, quam vt arcui
              <lb/>
            KG, remotiori ſimilis ſit. </s>
            <s xml:id="echoid-s3665" xml:space="preserve">Per pun-
              <lb/>
            cta enim E, K, deſcribantur maximi
              <lb/>
              <note position="right" xlink:label="note-107-12" xlink:href="note-107-12a" xml:space="preserve">15. 2. huius.</note>
            circuli LE, CN, tangentes circu-
              <lb/>
            lum AC, ita vt ſemicirculià C, per
              <lb/>
            N, & </s>
            <s xml:id="echoid-s3666" xml:space="preserve">ab A, per B, procedentes non
              <lb/>
            conueniant: </s>
            <s xml:id="echoid-s3667" xml:space="preserve">item ſemicirculi ab L,
              <lb/>
            per E, & </s>
            <s xml:id="echoid-s3668" xml:space="preserve">ab A, per I, tendentes non
              <lb/>
            coeant. </s>
            <s xml:id="echoid-s3669" xml:space="preserve">Erunt igitur arcus MH,
              <lb/>
              <note position="right" xlink:label="note-107-13" xlink:href="note-107-13a" xml:space="preserve">13. 2. huius.</note>
            EI, ſimiles. </s>
            <s xml:id="echoid-s3670" xml:space="preserve">Quare k H, maior eſt, quàm vt arcui EI, ſimilis ſit. </s>
            <s xml:id="echoid-s3671" xml:space="preserve"/>
          </p>
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