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

Table of handwritten notes

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            <s xml:id="echoid-s1298" xml:space="preserve">IN eadem adhuc figura ſint duo circuli paralleli _A C, B F,_ quos circulus maxis
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            mus _A B,_ tangat in _A, B._ </s>
            <s xml:id="echoid-s1299" xml:space="preserve">Dico circulos _A C, B F,_ æquales inter ſe eſſe. </s>
            <s xml:id="echoid-s1300" xml:space="preserve">Quoniam
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            enim paralleli ponuntur circuli _A C, B F,_ ipſi circa eoſdem polos erunt, qui ſint _D,_
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              <note position="right" xlink:label="note-047-01" xlink:href="note-047-01a" xml:space="preserve">1. huius.</note>
            _E;_ </s>
            <s xml:id="echoid-s1301" xml:space="preserve">per quos, & </s>
            <s xml:id="echoid-s1302" xml:space="preserve">polos circuli _A B,_ circulus maximus deſcribatur _A F B,_ qui per con
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              <note position="right" xlink:label="note-047-02" xlink:href="note-047-02a" xml:space="preserve">20. 1. huius.</note>
            tactus _A, B,_ tranſibit. </s>
            <s xml:id="echoid-s1303" xml:space="preserve">Quoniam vero circuli maximi in ſphæra ſe mutuo ſecant bi
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              <note position="right" xlink:label="note-047-03" xlink:href="note-047-03a" xml:space="preserve">4. huius.</note>
            fariam, ſemicirculus erit _A D B,_ atque adeo ſemicirculo _D B E,_ æqualis. </s>
            <s xml:id="echoid-s1304" xml:space="preserve">Dempto
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            ergo arcu communi _D B,_ æquales remanebunt arcus _D A, E B;_ </s>
            <s xml:id="echoid-s1305" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s1306" xml:space="preserve">rectæ
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            _D A, E B,_ ex polis _D, E,_ ad circunferentias circulorum _A C, B F,_ ductæ æquales.
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            </s>
            <s xml:id="echoid-s1307" xml:space="preserve">
              <note position="right" xlink:label="note-047-04" xlink:href="note-047-04a" xml:space="preserve">29. tertij.
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              Schol. 21. 1.
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              huius.</note>
            Quare circuli _A C, B F,_ æquales erunt. </s>
            <s xml:id="echoid-s1308" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s1309" xml:space="preserve"/>
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        <div xml:id="echoid-div148" type="section" level="1" n="81">
          <head xml:id="echoid-head93" xml:space="preserve">THEOR. 8. PROP. 8.</head>
          <note position="right" xml:space="preserve">10.</note>
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            <s xml:id="echoid-s1310" xml:space="preserve">SI in ſphæra maximus circulus ad aliquẽ ſphæ
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            ræ circulum obliquus ſit, tanget is duos circulos
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            æqualcs quidem inter ſe, parallelos autem prædi-
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            cto circulo, ad quem obliquus eſt.</s>
            <s xml:id="echoid-s1311" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s1312" xml:space="preserve">IN ſphæra maximus circulus A B, ad circulum quemcunque C D, obli-
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            quus ſit. </s>
            <s xml:id="echoid-s1313" xml:space="preserve">Dico circulum A B, tangere duos circulos inter ſe quidem æquales,
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            parallelos autem ipſi C D. </s>
            <s xml:id="echoid-s1314" xml:space="preserve">Sint E,F, poli circuli C D, per quos, & </s>
            <s xml:id="echoid-s1315" xml:space="preserve">polos cir
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              <figure xlink:label="fig-047-01" xlink:href="fig-047-01a" number="53">
                <image file="047-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/047-01"/>
              </figure>
              <note position="right" xlink:label="note-047-06" xlink:href="note-047-06a" xml:space="preserve">21. 1. huius.</note>
            culi A B, circulus maximus deſcribatur
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              <note position="right" xlink:label="note-047-07" xlink:href="note-047-07a" xml:space="preserve">20. 2. huius.</note>
            E A B, ſecans A B, in A, & </s>
            <s xml:id="echoid-s1316" xml:space="preserve">B. </s>
            <s xml:id="echoid-s1317" xml:space="preserve">Ex polo dein
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            de E, & </s>
            <s xml:id="echoid-s1318" xml:space="preserve">interuallo E A, circulus deſcriba-
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            tur A G. </s>
            <s xml:id="echoid-s1319" xml:space="preserve">Et quoniam circuli A B, A G, in
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            eodem puncto A, ſecant maximum circulũ
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              <note position="right" xlink:label="note-047-08" xlink:href="note-047-08a" xml:space="preserve">3. huius.</note>
            E A B, in quo polos habent, ipſi ſe mutuo
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            tangent in A. </s>
            <s xml:id="echoid-s1320" xml:space="preserve">Circulus igitur maximus A B,
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            tangens circulum A G, tanget alterum il-
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              <note position="right" xlink:label="note-047-09" xlink:href="note-047-09a" xml:space="preserve">6. huius.</note>
            li æqualem, & </s>
            <s xml:id="echoid-s1321" xml:space="preserve">parallelum, qui ſit B H. </s>
            <s xml:id="echoid-s1322" xml:space="preserve">Quia
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            vero circuli paralleli A G, B H, circa eoſdẽ
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              <note position="right" xlink:label="note-047-10" xlink:href="note-047-10a" xml:space="preserve">1. huius.</note>
            polos ſunt E, F: </s>
            <s xml:id="echoid-s1323" xml:space="preserve">Sunt autem E, F, poli etiã
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            circuli C D; </s>
            <s xml:id="echoid-s1324" xml:space="preserve">erunt tres circuli A G, C D,
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              <note position="right" xlink:label="note-047-11" xlink:href="note-047-11a" xml:space="preserve">2. huius.</note>
            B H, circa eoſdem polos; </s>
            <s xml:id="echoid-s1325" xml:space="preserve">atque adeo paralle
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            li inter ſe erũt. </s>
            <s xml:id="echoid-s1326" xml:space="preserve">Tangit igitur maximus circu
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            lus A B, duos A G, B H, æquales quidem inter ſe, parallelos autem ipſi C D,
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            ad quem obliquus eſt. </s>
            <s xml:id="echoid-s1327" xml:space="preserve">Quocirca, ſi in ſphæra maximus circulus ad aliquem,
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            &</s>
            <s xml:id="echoid-s1328" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1329" xml:space="preserve">Quod oſtendendum erat.</s>
            <s xml:id="echoid-s1330" xml:space="preserve"/>
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        <div xml:id="echoid-div150" type="section" level="1" n="82">
          <head xml:id="echoid-head94" xml:space="preserve">SCHOLIVM.</head>
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            <s xml:id="echoid-s1331" xml:space="preserve">_ALIVD_ theorema hoc loco adijcitur in alia verſione, videlicet.</s>
            <s xml:id="echoid-s1332" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1333" xml:space="preserve">SI in ſphæra maximus circulus aliquem circulorum in ſphæri-
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              <note position="right" xlink:label="note-047-12" xlink:href="note-047-12a" xml:space="preserve">11.</note>
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