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

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          <p>
            <s xml:id="echoid-s14548" xml:space="preserve">
              <pb o="418" file="430" n="430" rhead=""/>
            arcuum quadrans. </s>
            <s xml:id="echoid-s14549" xml:space="preserve">Dico ita eſſe ſinum complementi arcus AC, ad ſinum com
              <lb/>
            plementi arcus v. </s>
            <s xml:id="echoid-s14550" xml:space="preserve">g. </s>
            <s xml:id="echoid-s14551" xml:space="preserve">AB, vt eſt, ſinus complementi reliqui arcus BC, ad ſi-
              <lb/>
            num totum. </s>
            <s xml:id="echoid-s14552" xml:space="preserve">Quoniam enim nullus arcuum
              <lb/>
              <figure xlink:label="fig-430-01" xlink:href="fig-430-01a" number="282">
                <image file="430-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/430-01"/>
              </figure>
            ponitur quadrans, nullus reliquorum angu-
              <lb/>
            lorum erit rectus. </s>
            <s xml:id="echoid-s14553" xml:space="preserve">Alias triangulum ABC,
              <lb/>
            duos angulos habens rectos haberet duos ar-
              <lb/>
              <note position="left" xlink:label="note-430-01" xlink:href="note-430-01a" xml:space="preserve">Schol. 25.
                <lb/>
              huius.</note>
            cus quadrantes. </s>
            <s xml:id="echoid-s14554" xml:space="preserve">quod non ponitur. </s>
            <s xml:id="echoid-s14555" xml:space="preserve">Sit ergo
              <lb/>
            primum angulus A, acutus, & </s>
            <s xml:id="echoid-s14556" xml:space="preserve">arcus AB, ipſi
              <lb/>
            & </s>
            <s xml:id="echoid-s14557" xml:space="preserve">recto angulo B, adiacens quadrante minor.
              <lb/>
            </s>
            <s xml:id="echoid-s14558" xml:space="preserve">Quo poſito, erit & </s>
            <s xml:id="echoid-s14559" xml:space="preserve">angulus C, acutus; </s>
            <s xml:id="echoid-s14560" xml:space="preserve">atque
              <lb/>
              <note position="left" xlink:label="note-430-02" xlink:href="note-430-02a" xml:space="preserve">33. huius.</note>
            adeo omnes arcus trianguli ABC, quadran-
              <lb/>
              <note position="left" xlink:label="note-430-03" xlink:href="note-430-03a" xml:space="preserve">28. huius.</note>
            te minores. </s>
            <s xml:id="echoid-s14561" xml:space="preserve">Producantur arcus AB, AC, & </s>
            <s xml:id="echoid-s14562" xml:space="preserve">
              <lb/>
            fiant quadrantes AD, AE; </s>
            <s xml:id="echoid-s14563" xml:space="preserve">ac per puncta D,
              <lb/>
            E, arcus DE, circuli maximi ducatur DE,
              <lb/>
              <note position="left" xlink:label="note-430-04" xlink:href="note-430-04a" xml:space="preserve">20. 1 Theod.</note>
            conueniens cum arcu BC, producto in F. </s>
            <s xml:id="echoid-s14564" xml:space="preserve">Erit
              <lb/>
            ergo vterque angulus D, E, rectus, ob quadrantes AD, AE; </s>
            <s xml:id="echoid-s14565" xml:space="preserve">atque adeo, cum
              <lb/>
              <note position="left" xlink:label="note-430-05" xlink:href="note-430-05a" xml:space="preserve">25. huius.</note>
            & </s>
            <s xml:id="echoid-s14566" xml:space="preserve">angulus B, ponatur rectus, erit vterq; </s>
            <s xml:id="echoid-s14567" xml:space="preserve">arcus BF, DF, quadrans, ob rectos
              <lb/>
            angulos B, D. </s>
            <s xml:id="echoid-s14568" xml:space="preserve">Præterea BD, erit arcus anguli F; </s>
            <s xml:id="echoid-s14569" xml:space="preserve">propterea quòd F, polus eſt
              <lb/>
              <note position="left" xlink:label="note-430-06" xlink:href="note-430-06a" xml:space="preserve">26. huius.</note>
            arcus BD, ob quadrantes BF, DF. </s>
            <s xml:id="echoid-s14570" xml:space="preserve">Item CF, complementum erit arcus BC;
              <lb/>
            </s>
            <s xml:id="echoid-s14571" xml:space="preserve">& </s>
            <s xml:id="echoid-s14572" xml:space="preserve">BD, CE, complementa arcuum AB, AC, ob quadrantes BF, AD, AE. </s>
            <s xml:id="echoid-s14573" xml:space="preserve">
              <lb/>
            Manifeſtum autem eſt in triangulo CEF, ita eſſe ſinum arcus CE, hoc eſt, ſi-
              <lb/>
              <note position="left" xlink:label="note-430-07" xlink:href="note-430-07a" xml:space="preserve">41. huius.</note>
            num complementi arcus AC, ad ſinum anguli F, hoc eſt, ad ſinum arcus BD,
              <lb/>
            ſeu complementi arcus AB, vt eſt ſinus arcus CF, hoc eſt, ſinus complemen
              <lb/>
            ti arcus BC, ad ſinum anguli recti E, id eſt, ad ſinum totum. </s>
            <s xml:id="echoid-s14574" xml:space="preserve">Quod eſt pro-
              <lb/>
            poſitum.</s>
            <s xml:id="echoid-s14575" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14576" xml:space="preserve">SIT deinde angulus A, obtuſus, & </s>
            <s xml:id="echoid-s14577" xml:space="preserve">adhuc arcus AB, quadrante minor.
              <lb/>
            </s>
            <s xml:id="echoid-s14578" xml:space="preserve">Fiat angulus BAD, rectus, ſecetq́; </s>
            <s xml:id="echoid-s14579" xml:space="preserve">arcus AD, arcum BC, in D. </s>
            <s xml:id="echoid-s14580" xml:space="preserve">Producto
              <lb/>
            quoque arcu AB, fiat quadrans AE, & </s>
            <s xml:id="echoid-s14581" xml:space="preserve">per puncta E, D, ducatur arcus ED,
              <lb/>
              <note position="left" xlink:label="note-430-08" xlink:href="note-430-08a" xml:space="preserve">20. 1 Theod.</note>
            circuli maximi ſecans arcum AC, in F. </s>
            <s xml:id="echoid-s14582" xml:space="preserve">Et quia duo anguli DAB, DBA,
              <lb/>
            recti ſunt, erunt arcus AD, BD, quadrantes; </s>
            <s xml:id="echoid-s14583" xml:space="preserve">atque adeo cum AE, quoque
              <lb/>
              <note position="left" xlink:label="note-430-09" xlink:href="note-430-09a" xml:space="preserve">Schol. 25.
                <lb/>
              huius.</note>
            ſit quadrans, & </s>
            <s xml:id="echoid-s14584" xml:space="preserve">angulus DAE, rectus, erit & </s>
            <s xml:id="echoid-s14585" xml:space="preserve">
              <lb/>
            arcus DE, quadrans; </s>
            <s xml:id="echoid-s14586" xml:space="preserve">ac proinde BE, ob qua-
              <lb/>
              <figure xlink:label="fig-430-02" xlink:href="fig-430-02a" number="283">
                <image file="430-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/430-02"/>
              </figure>
              <note position="left" xlink:label="note-430-10" xlink:href="note-430-10a" xml:space="preserve">26. huius.</note>
            drantes BD, ED, erit arcus anguli BDE,
              <lb/>
            hoc eſt, anguli CDF, qui illi ad verticem eſt
              <lb/>
              <note position="left" xlink:label="note-430-11" xlink:href="note-430-11a" xml:space="preserve">6. huius.</note>
            æqualis. </s>
            <s xml:id="echoid-s14587" xml:space="preserve">Quoniam vero A, polus eſt arcus
              <lb/>
              <note position="left" xlink:label="note-430-12" xlink:href="note-430-12a" xml:space="preserve">26. huius.</note>
            ED, erit & </s>
            <s xml:id="echoid-s14588" xml:space="preserve">arcus AF, quadrans, cum arcus
              <lb/>
              <note position="left" xlink:label="note-430-13" xlink:href="note-430-13a" xml:space="preserve">Coroll. 16.</note>
            EF, quadrante ſemper abſit à ſuo polo; </s>
            <s xml:id="echoid-s14589" xml:space="preserve">nec-
              <lb/>
              <note position="left" xlink:label="note-430-14" xlink:href="note-430-14a" xml:space="preserve">1. Theod.</note>
            non & </s>
            <s xml:id="echoid-s14590" xml:space="preserve">angulus AFE, & </s>
            <s xml:id="echoid-s14591" xml:space="preserve">angulus CFD, re-
              <lb/>
              <note position="left" xlink:label="note-430-15" xlink:href="note-430-15a" xml:space="preserve">25. 1. Theod.</note>
            ctus. </s>
            <s xml:id="echoid-s14592" xml:space="preserve">Præterea erit arcus CE, complemen-
              <lb/>
            tum arcus AC; </s>
            <s xml:id="echoid-s14593" xml:space="preserve">& </s>
            <s xml:id="echoid-s14594" xml:space="preserve">arcus BE, complementum
              <lb/>
            arcus AB; </s>
            <s xml:id="echoid-s14595" xml:space="preserve">& </s>
            <s xml:id="echoid-s14596" xml:space="preserve">arcus CD, complementum ar-
              <lb/>
            cus BC, ob quadrantes AF, AE, BD. </s>
            <s xml:id="echoid-s14597" xml:space="preserve">Per-
              <lb/>
            ſpicuum autem eſt in triãgulo CDF, ita eſſe
              <lb/>
            ſinum arcus CF, hoc eſt, ſinum complementi
              <lb/>
              <note position="left" xlink:label="note-430-16" xlink:href="note-430-16a" xml:space="preserve">41. huius.</note>
            arcus AC, ad ſinum anguli CDF, hoc eſt, ad ſinum arcus BE, ſiue comple-
              <lb/>
            menti arcus AB, vt eſt ſinus arcus CD, nempe ſinus complementi arcus BC,
              <lb/>
            ad ſinum anguli recti F, hoc eſt, ad ſinum totum. </s>
            <s xml:id="echoid-s14598" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s14599" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14600" xml:space="preserve">TERTIO ſit angulus A, acutus, & </s>
            <s xml:id="echoid-s14601" xml:space="preserve">arcus AB, quadrante maior. </s>
            <s xml:id="echoid-s14602" xml:space="preserve"/>
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