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

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        <div xml:id="echoid-div522" type="section" level="1" n="253">
          <p>
            <s xml:id="echoid-s6941" xml:space="preserve">
              <pb o="183" file="195" n="195" rhead=""/>
            arcus grad. </s>
            <s xml:id="echoid-s6942" xml:space="preserve">90. </s>
            <s xml:id="echoid-s6943" xml:space="preserve">& </s>
            <s xml:id="echoid-s6944" xml:space="preserve">ex chorda arcus grad. </s>
            <s xml:id="echoid-s6945" xml:space="preserve">60. </s>
            <s xml:id="echoid-s6946" xml:space="preserve">cognoſcemus chordam arcus grad.
              <lb/>
            </s>
            <s xml:id="echoid-s6947" xml:space="preserve">30. </s>
            <s xml:id="echoid-s6948" xml:space="preserve">quo duo illi inter ſe differunt. </s>
            <s xml:id="echoid-s6949" xml:space="preserve">Eodemq́; </s>
            <s xml:id="echoid-s6950" xml:space="preserve">modo plurimorum arcuum chor-
              <lb/>
            das inueſtigabimus.</s>
            <s xml:id="echoid-s6951" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6952" xml:space="preserve">RVRSVS perea, quæ propoſ. </s>
            <s xml:id="echoid-s6953" xml:space="preserve">14. </s>
            <s xml:id="echoid-s6954" xml:space="preserve">eiusq́; </s>
            <s xml:id="echoid-s6955" xml:space="preserve">corollario demonſtrauimus,
              <lb/>
            reperiemus chordam cuiuſq; </s>
            <s xml:id="echoid-s6956" xml:space="preserve">arcus compoſiti ex duobus, quorum chordæ no-
              <lb/>
            tæ ſint. </s>
            <s xml:id="echoid-s6957" xml:space="preserve">Vt ex chorda arcus grad. </s>
            <s xml:id="echoid-s6958" xml:space="preserve">60. </s>
            <s xml:id="echoid-s6959" xml:space="preserve">& </s>
            <s xml:id="echoid-s6960" xml:space="preserve">ex chorda arcus grad. </s>
            <s xml:id="echoid-s6961" xml:space="preserve">90. </s>
            <s xml:id="echoid-s6962" xml:space="preserve">nota red-
              <lb/>
            detur chorda arcus grad. </s>
            <s xml:id="echoid-s6963" xml:space="preserve">150. </s>
            <s xml:id="echoid-s6964" xml:space="preserve">ex illis duobus compoſiti. </s>
            <s xml:id="echoid-s6965" xml:space="preserve">Sic etiam ex chor-
              <lb/>
            da arcus grad. </s>
            <s xml:id="echoid-s6966" xml:space="preserve">90. </s>
            <s xml:id="echoid-s6967" xml:space="preserve">& </s>
            <s xml:id="echoid-s6968" xml:space="preserve">ex chorda arcus grad. </s>
            <s xml:id="echoid-s6969" xml:space="preserve">36. </s>
            <s xml:id="echoid-s6970" xml:space="preserve">cognoſcetur chorda arcus
              <lb/>
            grad. </s>
            <s xml:id="echoid-s6971" xml:space="preserve">126. </s>
            <s xml:id="echoid-s6972" xml:space="preserve">&</s>
            <s xml:id="echoid-s6973" xml:space="preserve">c.</s>
            <s xml:id="echoid-s6974" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6975" xml:space="preserve">PRAETEREA per doctrinam propoſ. </s>
            <s xml:id="echoid-s6976" xml:space="preserve">15. </s>
            <s xml:id="echoid-s6977" xml:space="preserve">eiusq́; </s>
            <s xml:id="echoid-s6978" xml:space="preserve">coroll. </s>
            <s xml:id="echoid-s6979" xml:space="preserve">cognita chor-
              <lb/>
            da cuiuſuis arcus, cognoſcemus & </s>
            <s xml:id="echoid-s6980" xml:space="preserve">chordam dimidiati arcus. </s>
            <s xml:id="echoid-s6981" xml:space="preserve">Vt ex chorda ar-
              <lb/>
            cus grad. </s>
            <s xml:id="echoid-s6982" xml:space="preserve">60. </s>
            <s xml:id="echoid-s6983" xml:space="preserve">notam efficiemus chordam arcus grad. </s>
            <s xml:id="echoid-s6984" xml:space="preserve">30. </s>
            <s xml:id="echoid-s6985" xml:space="preserve">Ex hac chordam ar-
              <lb/>
            cus grad. </s>
            <s xml:id="echoid-s6986" xml:space="preserve">15. </s>
            <s xml:id="echoid-s6987" xml:space="preserve">Ex hac vero chordam arcus grad. </s>
            <s xml:id="echoid-s6988" xml:space="preserve">7. </s>
            <s xml:id="echoid-s6989" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6990" xml:space="preserve">30. </s>
            <s xml:id="echoid-s6991" xml:space="preserve">& </s>
            <s xml:id="echoid-s6992" xml:space="preserve">ex hac chordam
              <lb/>
            arcus grad. </s>
            <s xml:id="echoid-s6993" xml:space="preserve">3. </s>
            <s xml:id="echoid-s6994" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6995" xml:space="preserve">45. </s>
            <s xml:id="echoid-s6996" xml:space="preserve">Item ex chorda arcus grad. </s>
            <s xml:id="echoid-s6997" xml:space="preserve">72. </s>
            <s xml:id="echoid-s6998" xml:space="preserve">explorabimus chordam
              <lb/>
            arcus grad. </s>
            <s xml:id="echoid-s6999" xml:space="preserve">36. </s>
            <s xml:id="echoid-s7000" xml:space="preserve">Et ex hac chordã arcus grad. </s>
            <s xml:id="echoid-s7001" xml:space="preserve">18. </s>
            <s xml:id="echoid-s7002" xml:space="preserve">Et ex hac chordã arcus grad. </s>
            <s xml:id="echoid-s7003" xml:space="preserve">9.
              <lb/>
            </s>
            <s xml:id="echoid-s7004" xml:space="preserve">Et ex hac chordã arcus grad. </s>
            <s xml:id="echoid-s7005" xml:space="preserve">4. </s>
            <s xml:id="echoid-s7006" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7007" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7008" xml:space="preserve">Et ex hac chordam arcus grad. </s>
            <s xml:id="echoid-s7009" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7010" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7011" xml:space="preserve">
              <lb/>
            15. </s>
            <s xml:id="echoid-s7012" xml:space="preserve">Sic etiam, quoniam per propoſ. </s>
            <s xml:id="echoid-s7013" xml:space="preserve">13. </s>
            <s xml:id="echoid-s7014" xml:space="preserve">eiusq́; </s>
            <s xml:id="echoid-s7015" xml:space="preserve">coroll. </s>
            <s xml:id="echoid-s7016" xml:space="preserve">ex chordis arcuum
              <lb/>
            grad. </s>
            <s xml:id="echoid-s7017" xml:space="preserve">36. </s>
            <s xml:id="echoid-s7018" xml:space="preserve">& </s>
            <s xml:id="echoid-s7019" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s7020" xml:space="preserve">48. </s>
            <s xml:id="echoid-s7021" xml:space="preserve">cognoſcitur chorda arcus grad. </s>
            <s xml:id="echoid-s7022" xml:space="preserve">12. </s>
            <s xml:id="echoid-s7023" xml:space="preserve">quo illi duo inter ſe
              <lb/>
            differunt, cognoſcemus ex chorda arcus grad. </s>
            <s xml:id="echoid-s7024" xml:space="preserve">12. </s>
            <s xml:id="echoid-s7025" xml:space="preserve">chordam arcus grad. </s>
            <s xml:id="echoid-s7026" xml:space="preserve">6. </s>
            <s xml:id="echoid-s7027" xml:space="preserve">Et ex
              <lb/>
            hac chordam arcus grad. </s>
            <s xml:id="echoid-s7028" xml:space="preserve">3. </s>
            <s xml:id="echoid-s7029" xml:space="preserve">Ex hac chordam arcus grad. </s>
            <s xml:id="echoid-s7030" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7031" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7032" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7033" xml:space="preserve">Et ex hac
              <lb/>
            chordam arcus grad. </s>
            <s xml:id="echoid-s7034" xml:space="preserve">0. </s>
            <s xml:id="echoid-s7035" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7036" xml:space="preserve">45. </s>
            <s xml:id="echoid-s7037" xml:space="preserve">Deinde ſi per ea, quæ demonſtrata ſunt, ar-
              <lb/>
              <note position="right" xlink:label="note-195-01" xlink:href="note-195-01a" xml:space="preserve">Supputa-
                <lb/>
              tio chorda-
                <lb/>
              rũ arcuum
                <lb/>
              Min. 45. ſe-
                <lb/>
              ſe ſnperan-
                <lb/>
              tium.</note>
            cuum cæterorum chordas diligẽter ex inuentis inquiramus, inueniemus chor
              <lb/>
            das omnium arcuum, qui ſe ordine continuo ſuperant Minutis 45. </s>
            <s xml:id="echoid-s7038" xml:space="preserve">ita vt pri-
              <lb/>
            mus arcus contineat grad. </s>
            <s xml:id="echoid-s7039" xml:space="preserve">0. </s>
            <s xml:id="echoid-s7040" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7041" xml:space="preserve">45. </s>
            <s xml:id="echoid-s7042" xml:space="preserve">ſecundus grad. </s>
            <s xml:id="echoid-s7043" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7044" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7045" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7046" xml:space="preserve">tertius grad. </s>
            <s xml:id="echoid-s7047" xml:space="preserve">2.
              <lb/>
            </s>
            <s xml:id="echoid-s7048" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7049" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7050" xml:space="preserve">vltimus deniq; </s>
            <s xml:id="echoid-s7051" xml:space="preserve">ſit totus ſemicirculus grad. </s>
            <s xml:id="echoid-s7052" xml:space="preserve">180. </s>
            <s xml:id="echoid-s7053" xml:space="preserve">Immo vero, ſi, vt
              <lb/>
            proxime docuimus, inuenta fuerit chorda arcus grad. </s>
            <s xml:id="echoid-s7054" xml:space="preserve">0. </s>
            <s xml:id="echoid-s7055" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7056" xml:space="preserve">45. </s>
            <s xml:id="echoid-s7057" xml:space="preserve">inueniemus
              <lb/>
            ex hac, per doctrinam propoſ. </s>
            <s xml:id="echoid-s7058" xml:space="preserve">14. </s>
            <s xml:id="echoid-s7059" xml:space="preserve">eiusq́; </s>
            <s xml:id="echoid-s7060" xml:space="preserve">coroll. </s>
            <s xml:id="echoid-s7061" xml:space="preserve">chordas omnium arcuum ſe-
              <lb/>
            ſe continue Minutis 45. </s>
            <s xml:id="echoid-s7062" xml:space="preserve">ſuperantium, ſi primo inueſtigemus chordam arcus
              <lb/>
            grad. </s>
            <s xml:id="echoid-s7063" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7064" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7065" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7066" xml:space="preserve">ex duobus arcubus Min. </s>
            <s xml:id="echoid-s7067" xml:space="preserve">45. </s>
            <s xml:id="echoid-s7068" xml:space="preserve">& </s>
            <s xml:id="echoid-s7069" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7070" xml:space="preserve">45. </s>
            <s xml:id="echoid-s7071" xml:space="preserve">compoſiti: </s>
            <s xml:id="echoid-s7072" xml:space="preserve">Deinde ve
              <lb/>
            ro chordam arcus grad. </s>
            <s xml:id="echoid-s7073" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7074" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7075" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7076" xml:space="preserve">qui ex duobus arcubus grad. </s>
            <s xml:id="echoid-s7077" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7078" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7079" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7080" xml:space="preserve">& </s>
            <s xml:id="echoid-s7081" xml:space="preserve">
              <lb/>
            Min. </s>
            <s xml:id="echoid-s7082" xml:space="preserve">45. </s>
            <s xml:id="echoid-s7083" xml:space="preserve">componitur: </s>
            <s xml:id="echoid-s7084" xml:space="preserve">Et poſtea chordam arcus grad. </s>
            <s xml:id="echoid-s7085" xml:space="preserve">3. </s>
            <s xml:id="echoid-s7086" xml:space="preserve">qui componitur ex
              <lb/>
            arcu grad. </s>
            <s xml:id="echoid-s7087" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7088" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7089" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7090" xml:space="preserve">& </s>
            <s xml:id="echoid-s7091" xml:space="preserve">ex arcu Min. </s>
            <s xml:id="echoid-s7092" xml:space="preserve">45. </s>
            <s xml:id="echoid-s7093" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s7094" xml:space="preserve">ita deinceps, apponendo ſemper
              <lb/>
            arcui antecedenti arcum Min. </s>
            <s xml:id="echoid-s7095" xml:space="preserve">45.</s>
            <s xml:id="echoid-s7096" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7097" xml:space="preserve">POSTREMO aliorum arcuum chordas inueſtigabimus hac arte. </s>
            <s xml:id="echoid-s7098" xml:space="preserve">Sit in
              <lb/>
              <note position="right" xlink:label="note-195-02" xlink:href="note-195-02a" xml:space="preserve">Supputatio
                <lb/>
              chordæ ar-
                <lb/>
              cus grad. 1.</note>
            ſemicirculo ABCDE, chorda AB, arcus Min.
              <lb/>
            </s>
            <s xml:id="echoid-s7099" xml:space="preserve">
              <figure xlink:label="fig-195-01" xlink:href="fig-195-01a" number="146">
                <image file="195-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/195-01"/>
              </figure>
            45. </s>
            <s xml:id="echoid-s7100" xml:space="preserve">& </s>
            <s xml:id="echoid-s7101" xml:space="preserve">AD, chorda arcus grad. </s>
            <s xml:id="echoid-s7102" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7103" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7104" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7105" xml:space="preserve">at AC,
              <lb/>
            chorda arcus grad. </s>
            <s xml:id="echoid-s7106" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7107" xml:space="preserve">quæ inueſtiganda propo-
              <lb/>
            natur. </s>
            <s xml:id="echoid-s7108" xml:space="preserve">Quoniam igitur maior eſt proportio arcus
              <lb/>
            AC, ad arcum AB, quam chordæ AC, ad chor-
              <lb/>
              <note position="right" xlink:label="note-195-03" xlink:href="note-195-03a" xml:space="preserve">10. huius.</note>
            dam AB: </s>
            <s xml:id="echoid-s7109" xml:space="preserve">Habet autem arcus AC, ad arcum AB,
              <lb/>
            proportionẽ ſesquitertiam; </s>
            <s xml:id="echoid-s7110" xml:space="preserve">habebit chorda AC,
              <lb/>
            ad chordam AB, proportionem minorem, quàm
              <lb/>
            ſeſquitertiam. </s>
            <s xml:id="echoid-s7111" xml:space="preserve">Cum ergo chorda AB, arcus Min.
              <lb/>
            </s>
            <s xml:id="echoid-s7112" xml:space="preserve">45. </s>
            <s xml:id="echoid-s7113" xml:space="preserve">ex præcedentibus inuenta ſit partium ferè 130899. </s>
            <s xml:id="echoid-s7114" xml:space="preserve">erit chorda AC, ar-
              <lb/>
            cus grad. </s>
            <s xml:id="echoid-s7115" xml:space="preserve">1 (quæ nimirum ad chordam AB, hoc eſt, ad 130899. </s>
            <s xml:id="echoid-s7116" xml:space="preserve">minorem pro-
              <lb/>
            portionem habet, quam ſeſquitertiam.) </s>
            <s xml:id="echoid-s7117" xml:space="preserve">minor, quàm 174532. </s>
            <s xml:id="echoid-s7118" xml:space="preserve">cum hic nume
              <lb/>
              <note position="right" xlink:label="note-195-04" xlink:href="note-195-04a" xml:space="preserve">10. quinti.</note>
            rus ad illum proportionem habeat ſeſquitertiam. </s>
            <s xml:id="echoid-s7119" xml:space="preserve">Rurſus quia maior eſt pro-
              <lb/>
            portio arcus AD, ad arcum AC, quam chordæ AD, ad chordam AC: </s>
            <s xml:id="echoid-s7120" xml:space="preserve">Habet
              <lb/>
              <note position="right" xlink:label="note-195-05" xlink:href="note-195-05a" xml:space="preserve">10. huius.</note>
            </s>
          </p>
        </div>
      </text>
    </echo>
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