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

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          <pb o="187" file="199" n="199" rhead=""/>
          <p style="it">
            <s xml:id="echoid-s7528" xml:space="preserve">NEC vero prætereundum eſt, ſi, poſita diametro par
              <lb/>
              <note position="right" xlink:label="note-199-01" xlink:href="note-199-01a" xml:space="preserve">
                <lb/>
              ## Arcus ### Chordæ
                <lb/>
              G # M # Par. # M # Sec.
                <lb/>
              0 # 30 # 0 # 31 # 25
                <lb/>
              10 # 0 # 10 # 27 # 32
                <lb/>
              20 # 0 # 20 # 50 # 16
                <lb/>
              45 # 0 # 45 # 55 # 19
                <lb/>
              50 # 0 # 50 # 42 # 51
                <lb/>
              60 # 0 # 60 # 0 # 0
                <lb/>
              66 # 30 # 65 # 47 # 43
                <lb/>
              80 # 30 # 77 # 32 # 6
                <lb/>
              90 # 0 # 84 # 51 # 10
                <lb/>
              120 # 0 # 103 # 55 # 23
                <lb/>
              170 # 0 # 119 # 32 # 37
                <lb/>
              </note>
            tium 120 chordas arcuum inquiramus in partibus, Mi-
              <lb/>
            nutis, & </s>
            <s xml:id="echoid-s7529" xml:space="preserve">Secundis, vt Ptolemæus fecit, chordas arcuum
              <lb/>
            minorum, quàm grad. </s>
            <s xml:id="echoid-s7530" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7531" xml:space="preserve">habere plures Partes, Minu@a,
              <lb/>
            ac Secunda: </s>
            <s xml:id="echoid-s7532" xml:space="preserve">quam arcus, quorum ſunt chordæ: </s>
            <s xml:id="echoid-s7533" xml:space="preserve">at ve-
              <lb/>
            ro chordas arcuum maiorum, quàm grad 60. </s>
            <s xml:id="echoid-s7534" xml:space="preserve">eſſe pau-
              <lb/>
            ciorum Partium, Minutorum, ac Secundorum, quàm ar-
              <lb/>
            cus illis reſpondentes. </s>
            <s xml:id="echoid-s7535" xml:space="preserve">Vt in tabula hic appoſita manife-
              <lb/>
            ſtum eſt, quam ex Ptolemæi tabula exerceptam huc tran-
              <lb/>
            ſtuli. </s>
            <s xml:id="echoid-s7536" xml:space="preserve">In qua cernis chordas arcuum minorum, quàm
              <lb/>
            grad. </s>
            <s xml:id="echoid-s7537" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7538" xml:space="preserve">maiores eſſe, quoad numerum partium, Mi-
              <lb/>
            nutorum, & </s>
            <s xml:id="echoid-s7539" xml:space="preserve">ſecundorum, quàm arcus reſpondentes,
              <lb/>
            quoad gradus, ac Minuta; </s>
            <s xml:id="echoid-s7540" xml:space="preserve">chordas vero arcuum ma-
              <lb/>
            iorum, quàm grad. </s>
            <s xml:id="echoid-s7541" xml:space="preserve">60. </s>
            <s xml:id="echoid-s7542" xml:space="preserve">eſſe minores arcubus reſponden-
              <lb/>
            tibus, quoad eoſdem numeros. </s>
            <s xml:id="echoid-s7543" xml:space="preserve">Cuius quidem rei hæc eſt
              <lb/>
            demonſtratio.</s>
            <s xml:id="echoid-s7544" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7545" xml:space="preserve">IN ſemicirculo ABCDE, ſit arcus AC, grad. </s>
            <s xml:id="echoid-s7546" xml:space="preserve">60.
              <lb/>
            </s>
            <s xml:id="echoid-s7547" xml:space="preserve">& </s>
            <s xml:id="echoid-s7548" xml:space="preserve">
              <emph style="sc">Ab</emph>
            , minor, nempe grad. </s>
            <s xml:id="echoid-s7549" xml:space="preserve">45. </s>
            <s xml:id="echoid-s7550" xml:space="preserve">at AD, maior, puta grad. </s>
            <s xml:id="echoid-s7551" xml:space="preserve">
              <lb/>
            80. </s>
            <s xml:id="echoid-s7552" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7553" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7554" xml:space="preserve">ducanturque chordæ AB,
              <emph style="sc">Ac</emph>
            , AD. </s>
            <s xml:id="echoid-s7555" xml:space="preserve">Dico chordam AB, maiorem eſſe,
              <lb/>
            quàm Par. </s>
            <s xml:id="echoid-s7556" xml:space="preserve">45. </s>
            <s xml:id="echoid-s7557" xml:space="preserve">at chordam AD, minorem, quàm Partiũ
              <lb/>
              <figure xlink:label="fig-199-01" xlink:href="fig-199-01a" number="148">
                <image file="199-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/199-01"/>
              </figure>
            80. </s>
            <s xml:id="echoid-s7558" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7559" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7560" xml:space="preserve">Cumenim maior ſit proportio arcus AC,
              <lb/>
              <note position="right" xlink:label="note-199-02" xlink:href="note-199-02a" xml:space="preserve">10. huius.</note>
            ad arcum AB, quam chordæ AC, ad chordam
              <emph style="sc">Ab</emph>
            : </s>
            <s xml:id="echoid-s7561" xml:space="preserve">ſit
              <lb/>
            autem proportio arcus AC, ad arcum AB, eadem, quæ
              <lb/>
            60. </s>
            <s xml:id="echoid-s7562" xml:space="preserve">ad 45. </s>
            <s xml:id="echoid-s7563" xml:space="preserve">erit proportio chordæ AC, ad chordam
              <emph style="sc">Ab</emph>
            ,
              <lb/>
            minor, quàm 60. </s>
            <s xml:id="echoid-s7564" xml:space="preserve">ad 45. </s>
            <s xml:id="echoid-s7565" xml:space="preserve">Quare cum chorda
              <emph style="sc">A</emph>
            C, ſit
              <lb/>
            Partium 60. </s>
            <s xml:id="echoid-s7566" xml:space="preserve">vtpote quæ ſemidiametro æqualis eſt, per
              <lb/>
            coroll. </s>
            <s xml:id="echoid-s7567" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s7568" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7569" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s7570" xml:space="preserve">4. </s>
            <s xml:id="echoid-s7571" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s7572" xml:space="preserve">erit chorda
              <emph style="sc">Ab</emph>
            , maior,
              <lb/>
            quàm Partium 45. </s>
            <s xml:id="echoid-s7573" xml:space="preserve">propterea quòd 60. </s>
            <s xml:id="echoid-s7574" xml:space="preserve">ad numerum, quimaior ſit, quàm 45. </s>
            <s xml:id="echoid-s7575" xml:space="preserve">mi-
              <lb/>
            norem proportionem habet, quàm ad 45. </s>
            <s xml:id="echoid-s7576" xml:space="preserve">Atq; </s>
            <s xml:id="echoid-s7577" xml:space="preserve">ita in tabella ſuperiori vides chordam
              <lb/>
              <note position="right" xlink:label="note-199-03" xlink:href="note-199-03a" xml:space="preserve">8. quinti.</note>
            arcus grad. </s>
            <s xml:id="echoid-s7578" xml:space="preserve">45. </s>
            <s xml:id="echoid-s7579" xml:space="preserve">eſſe Partium 45. </s>
            <s xml:id="echoid-s7580" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7581" xml:space="preserve">55. </s>
            <s xml:id="echoid-s7582" xml:space="preserve">Sec. </s>
            <s xml:id="echoid-s7583" xml:space="preserve">19. </s>
            <s xml:id="echoid-s7584" xml:space="preserve">Rurſus quia maior eſt proportio
              <lb/>
            arcus
              <emph style="sc">A</emph>
            D, ad arcum AC, quàm chordæ AD, ad chordam AC: </s>
            <s xml:id="echoid-s7585" xml:space="preserve">Eſt autem proportio
              <lb/>
              <note position="right" xlink:label="note-199-04" xlink:href="note-199-04a" xml:space="preserve">10. huius.</note>
            arcus AD, ad arcum
              <emph style="sc">A</emph>
            C, eadem, quæ grad. </s>
            <s xml:id="echoid-s7586" xml:space="preserve">80. </s>
            <s xml:id="echoid-s7587" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7588" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7589" xml:space="preserve">ad 60. </s>
            <s xml:id="echoid-s7590" xml:space="preserve">erit chordæ AD,
              <lb/>
            ad chordam AC, minor proportio, quàm Par. </s>
            <s xml:id="echoid-s7591" xml:space="preserve">80. </s>
            <s xml:id="echoid-s7592" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7593" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7594" xml:space="preserve">ad 60. </s>
            <s xml:id="echoid-s7595" xml:space="preserve">Cum ergo chorda
              <lb/>
            AC, ſit Partium 60. </s>
            <s xml:id="echoid-s7596" xml:space="preserve">erit chorda AD, minor, quàm Par. </s>
            <s xml:id="echoid-s7597" xml:space="preserve">80. </s>
            <s xml:id="echoid-s7598" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7599" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7600" xml:space="preserve">propterea quòd
              <lb/>
            numerus, qui minor ſit, quàm Par. </s>
            <s xml:id="echoid-s7601" xml:space="preserve">80. </s>
            <s xml:id="echoid-s7602" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7603" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7604" xml:space="preserve">ad 60. </s>
            <s xml:id="echoid-s7605" xml:space="preserve">minorem proportionẽ habet,
              <lb/>
              <note position="right" xlink:label="note-199-05" xlink:href="note-199-05a" xml:space="preserve">8. quinti.</note>
            quàm Par. </s>
            <s xml:id="echoid-s7606" xml:space="preserve">80. </s>
            <s xml:id="echoid-s7607" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7608" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7609" xml:space="preserve">ad eundem numerum 60. </s>
            <s xml:id="echoid-s7610" xml:space="preserve">Atqueita cernis in ſuperiori tabella
              <lb/>
            chordã arcus grad. </s>
            <s xml:id="echoid-s7611" xml:space="preserve">80. </s>
            <s xml:id="echoid-s7612" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7613" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7614" xml:space="preserve">cõtinere partes duntaxat 77. </s>
            <s xml:id="echoid-s7615" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7616" xml:space="preserve">32. </s>
            <s xml:id="echoid-s7617" xml:space="preserve">Sec. </s>
            <s xml:id="echoid-s7618" xml:space="preserve">6. </s>
            <s xml:id="echoid-s7619" xml:space="preserve">Eademq́;
              <lb/>
            </s>
            <s xml:id="echoid-s7620" xml:space="preserve">ratio eſt dealij schordis minoribus, & </s>
            <s xml:id="echoid-s7621" xml:space="preserve">maioribus, quàm
              <emph style="sc">A</emph>
            C, hoc eſt, quàm chorda ar-
              <lb/>
            cus grad. </s>
            <s xml:id="echoid-s7622" xml:space="preserve">60.</s>
            <s xml:id="echoid-s7623" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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