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

Table of Notes

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        <div xml:id="echoid-div495" type="section" level="1" n="242">
          <head xml:id="echoid-head269" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s6612" xml:space="preserve">_QVAMVIS_ autem Theorema hoc proponatur ſolum de arcubus illis inæqualin
              <lb/>
            bus, quorũ maiori maior chorda ſubtenditur, quam minori: </s>
            <s xml:id="echoid-s6613" xml:space="preserve">_I_dem tamen locum etiam
              <lb/>
            habet in illis arcubus inæqualibus, quorum maioris chorda minor eſt, quam chordæ
              <lb/>
            minoris. </s>
            <s xml:id="echoid-s6614" xml:space="preserve">_N_am quia tunc arcus maior ad minorem habet proportionẽ maioris inæqua-
              <lb/>
            litatis, chorda vero maioris arcus ad chordam minoris arcus proportionem habet mi-
              <lb/>
            noris inæqualitatis, maior erit proportio maioris arcus ad minorem, quam chordæ
              <lb/>
            arcus maioris ad chordam minoris arcus.</s>
            <s xml:id="echoid-s6615" xml:space="preserve"/>
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        <div xml:id="echoid-div496" type="section" level="1" n="243">
          <head xml:id="echoid-head270" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s6616" xml:space="preserve">SEQVITVR ex hac propoſitione, minorem eſſe proportionem minoris arcus ad ma-
              <lb/>
            iorem, quam chordæ minoris arcus ad chordam maioris. </s>
            <s xml:id="echoid-s6617" xml:space="preserve">Cum enim maior arcus ad mi-
              <lb/>
            norem habeat maiorem proportionem, quam chorda maioris arcus ad chordam minoris,
              <lb/>
            vt demonſtratum eſt; </s>
            <s xml:id="echoid-s6618" xml:space="preserve">habebit conuertendo minor arcus ad maiorem, minorem propor-
              <lb/>
              <note position="right" xlink:label="note-189-01" xlink:href="note-189-01a" xml:space="preserve">26. quinti.</note>
            tionem, quam chorda arcus minoris ad chordam maioris.</s>
            <s xml:id="echoid-s6619" xml:space="preserve"/>
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        <div xml:id="echoid-div498" type="section" level="1" n="244">
          <head xml:id="echoid-head271" xml:space="preserve">THEOR. 8. PROPOS. II.</head>
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            <s xml:id="echoid-s6620" xml:space="preserve">SI in circulo quadrilaterum deſcribatur cum
              <lb/>
              <note position="right" xlink:label="note-189-02" xlink:href="note-189-02a" xml:space="preserve">Rectangu-
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              lũ ſub dia-
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              metris qua
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              drilateri in
                <lb/>
              circulo de-
                <lb/>
              ſcripti con
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              tentũ æqua
                <lb/>
              le eſt duo-
                <lb/>
              bus rectan-
                <lb/>
              gulis ſub
                <lb/>
              oppoſitis la
                <lb/>
              teribus con
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              tentis.</note>
            ſuis diametris; </s>
            <s xml:id="echoid-s6621" xml:space="preserve">eritrectãgulum ſub diametris com-
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            prehenſum æquale duobus rectãgulis ſimul, quæ
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            ſub lateribus oppoſitis continentur.</s>
            <s xml:id="echoid-s6622" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6623" xml:space="preserve">IN circulo ABCD, ſit quadrilaterum ABCD, cuius diametri AC, BD.
              <lb/>
            </s>
            <s xml:id="echoid-s6624" xml:space="preserve">Dico rectangulum ſub AC, BD, comprehenſum æquale eſſe rectangulis ſi-
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            mul ſub AD, BC, & </s>
            <s xml:id="echoid-s6625" xml:space="preserve">ſub AB, DC, contentis. </s>
            <s xml:id="echoid-s6626" xml:space="preserve">Fiat angulo DAC, æqualis
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            angulus BAE; </s>
            <s xml:id="echoid-s6627" xml:space="preserve">cadetq́ recta AE, vel in ipſam rectam AC; </s>
            <s xml:id="echoid-s6628" xml:space="preserve">vel inter AC,
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            rectam, & </s>
            <s xml:id="echoid-s6629" xml:space="preserve">punctum B; </s>
            <s xml:id="echoid-s6630" xml:space="preserve">vel deniq; </s>
            <s xml:id="echoid-s6631" xml:space="preserve">inter rectam AC, & </s>
            <s xml:id="echoid-s6632" xml:space="preserve">punctum D: </s>
            <s xml:id="echoid-s6633" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s6634" xml:space="preserve">erit
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            in primo caſu angulus BAC, angulo DAE; </s>
            <s xml:id="echoid-s6635" xml:space="preserve">& </s>
            <s xml:id="echoid-s6636" xml:space="preserve">in ſecundo caſu totus angu-
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            lus BAC,
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              <figure xlink:label="fig-189-01" xlink:href="fig-189-01a" number="139">
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            toti angulo
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            DAE, pro-
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            pter cõ mu-
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            nem angu-
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            lum EAC,
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            additum; </s>
            <s xml:id="echoid-s6637" xml:space="preserve">& </s>
            <s xml:id="echoid-s6638" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s6639" xml:space="preserve">in tertio
              <lb/>
            caſu reli-
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            quus angu-
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            lus BAC, reliquo angulo DAE, ob communem angulum EAC, ablatum
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            æqualis. </s>
            <s xml:id="echoid-s6640" xml:space="preserve">Et quoniam angulus quoq; </s>
            <s xml:id="echoid-s6641" xml:space="preserve">ACB, angulo ADB, æqualis eſt; </s>
            <s xml:id="echoid-s6642" xml:space="preserve">erit
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              <note position="right" xlink:label="note-189-03" xlink:href="note-189-03a" xml:space="preserve">21. tertij.</note>
            reliquus etiam angulus ABC, in triangulo ABC, reliquo angulo AED, in
              <lb/>
              <note position="right" xlink:label="note-189-04" xlink:href="note-189-04a" xml:space="preserve">32. primi.</note>
            triangulo AED, æqualis. </s>
            <s xml:id="echoid-s6643" xml:space="preserve">Erit igitur vt AC, ad CB, ita AD, ad DE. </s>
            <s xml:id="echoid-s6644" xml:space="preserve">Qua-
              <lb/>
              <note position="right" xlink:label="note-189-05" xlink:href="note-189-05a" xml:space="preserve">4. ſexti.</note>
            re rectangulum ſub AC, DE, æquale eſt rectangulo ſub CB, AD. </s>
            <s xml:id="echoid-s6645" xml:space="preserve">Rurſus
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              <note position="right" xlink:label="note-189-06" xlink:href="note-189-06a" xml:space="preserve">16. ſexti.</note>
            quia angulus BAE, angulo DAC, ex conſtructione æqualis eſt; </s>
            <s xml:id="echoid-s6646" xml:space="preserve">& </s>
            <s xml:id="echoid-s6647" xml:space="preserve">angulus
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            ABD, angulo ACD: </s>
            <s xml:id="echoid-s6648" xml:space="preserve">erit & </s>
            <s xml:id="echoid-s6649" xml:space="preserve">reliquus angulus AEB, in triangulo AEB, re-
              <lb/>
              <note position="right" xlink:label="note-189-07" xlink:href="note-189-07a" xml:space="preserve">21. tertij.</note>
            </s>
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