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

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          <p>
            <s xml:id="echoid-s4477" xml:space="preserve">
              <pb o="117" file="129" n="129" rhead=""/>
            quadrantis, quorum alter tanto minor ſit arcu
              <lb/>
              <note position="right" xlink:label="note-129-01" xlink:href="note-129-01a" xml:space="preserve">Differentia
                <lb/>
              inter ſinus
                <lb/>
              duorũ ar-
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              cuum, quo-
                <lb/>
              rum alter
                <lb/>
              tanto ſit
                <lb/>
              minorarcu
                <lb/>
              grad. 60.
                <lb/>
              quãto alter
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              maior eſt,
                <lb/>
              ęqua@ ſinui
                <lb/>
              arcus, quo
                <lb/>
              alteruter di
                <lb/>
              ctorũar@@ũ
                <lb/>
              differt ab
                <lb/>
              a@cu grad.
                <lb/>
              60.</note>
            grad. </s>
            <s xml:id="echoid-s4478" xml:space="preserve">60. </s>
            <s xml:id="echoid-s4479" xml:space="preserve">quanto alter maior eſt, æqualis eſt ſinui
              <lb/>
            arcus, quo alteruter dictorũ arcuum ab arcu grad.
              <lb/>
            </s>
            <s xml:id="echoid-s4480" xml:space="preserve">60. </s>
            <s xml:id="echoid-s4481" xml:space="preserve">differt.</s>
            <s xml:id="echoid-s4482" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4483" xml:space="preserve">IN quadrante ABC, ſit arcus CD, grad. </s>
            <s xml:id="echoid-s4484" xml:space="preserve">60. </s>
            <s xml:id="echoid-s4485" xml:space="preserve">arcus vero CE, eo tanto
              <lb/>
            minor, quanto arcus CF, maior eſt: </s>
            <s xml:id="echoid-s4486" xml:space="preserve">quorum ſinus recti EG, FH. </s>
            <s xml:id="echoid-s4487" xml:space="preserve">Dico horum
              <lb/>
            ſinuum differẽtiam æqualem eſſe ſinui arcus DE, vel DF. </s>
            <s xml:id="echoid-s4488" xml:space="preserve">Producto enim qua-
              <lb/>
            drante, vna cum ſinubus EG, FH, ad I, K; </s>
            <s xml:id="echoid-s4489" xml:space="preserve">ſumatur arcus CL, arcui CD,
              <lb/>
            æqualis, ita vt totus arcus
              <lb/>
              <figure xlink:label="fig-129-01" xlink:href="fig-129-01a" number="126">
                <image file="129-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/129-01"/>
              </figure>
            DCL, cõtineat grad. </s>
            <s xml:id="echoid-s4490" xml:space="preserve">120.
              <lb/>
            </s>
            <s xml:id="echoid-s4491" xml:space="preserve">Et quia & </s>
            <s xml:id="echoid-s4492" xml:space="preserve">arcus CI, CK,
              <lb/>
            æquales ſunt arcubus CE,
              <lb/>
            CF; </s>
            <s xml:id="echoid-s4493" xml:space="preserve">quòd per lemma in
              <lb/>
            definitionibus poſitum re-
              <lb/>
            cta BC, ſecet arcus ECI,
              <lb/>
            FCK, bifariam, cum & </s>
            <s xml:id="echoid-s4494" xml:space="preserve">re-
              <lb/>
            ctas EI, FK, bifariam ſe-
              <lb/>
              <note position="right" xlink:label="note-129-02" xlink:href="note-129-02a" xml:space="preserve">3. tertij.</note>
            cet: </s>
            <s xml:id="echoid-s4495" xml:space="preserve">erunt quoque reliqui
              <lb/>
            arcus LI, LK, reliquis ar
              <lb/>
            cubus DE, DF, æquales.
              <lb/>
            </s>
            <s xml:id="echoid-s4496" xml:space="preserve">Sumptis quoque arcubus
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            EM, FN, qui arcubus DE,
              <lb/>
            DF, æquales ſint, ducan-
              <lb/>
            tur chordæ LM, LN. </s>
            <s xml:id="echoid-s4497" xml:space="preserve">Et
              <lb/>
            quoniam arcus FN, arcui
              <lb/>
            LK, & </s>
            <s xml:id="echoid-s4498" xml:space="preserve">arcus EM, arcui
              <lb/>
            LI, ęqualis eſt; </s>
            <s xml:id="echoid-s4499" xml:space="preserve">additis com
              <lb/>
            munibus FL, MI, erit tam arcus NL, arcui FK, quàm arcus ML, arcui EI,
              <lb/>
            æqualis: </s>
            <s xml:id="echoid-s4500" xml:space="preserve">ac proinde tan chorda NL, chordæ FK, quam chorda ML, chordæ
              <lb/>
              <note position="right" xlink:label="note-129-03" xlink:href="note-129-03a" xml:space="preserve">29. tertij.</note>
            EI, æqualis. </s>
            <s xml:id="echoid-s4501" xml:space="preserve">Quoniam igitur arcus LM, tanto minor eſt arcu LD, grad. </s>
            <s xml:id="echoid-s4502" xml:space="preserve">120.
              <lb/>
            </s>
            <s xml:id="echoid-s4503" xml:space="preserve">quanto arcus LN, eodem maior eſt; </s>
            <s xml:id="echoid-s4504" xml:space="preserve">erit per propoſ. </s>
            <s xml:id="echoid-s4505" xml:space="preserve">6. </s>
            <s xml:id="echoid-s4506" xml:space="preserve">differentia chor-
              <lb/>
            darum LN, LM, chordæ DN, vel DM, æqualis; </s>
            <s xml:id="echoid-s4507" xml:space="preserve">hoc eſt, recta k F, rectam
              <lb/>
            IE, ſuperabit chorda DN, vel DM. </s>
            <s xml:id="echoid-s4508" xml:space="preserve">Quare per antecedentem propoſ. </s>
            <s xml:id="echoid-s4509" xml:space="preserve">ſemiſ-
              <lb/>
            ſis HF, hoc eſt, ſinus arcus CF, ſuperabit ſemiſſem GE, id eſt, ſinum arcus CE,
              <lb/>
            ſemiſſe chordæ DN, vel DM, hoc eſt, ſinu arcus DF, vel DE. </s>
            <s xml:id="echoid-s4510" xml:space="preserve">Quod de-
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            monſtrandum erat.</s>
            <s xml:id="echoid-s4511" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4512" xml:space="preserve">ALITER. </s>
            <s xml:id="echoid-s4513" xml:space="preserve">In quadrante ABD, arcus BE, ſit grad. </s>
            <s xml:id="echoid-s4514" xml:space="preserve">60. </s>
            <s xml:id="echoid-s4515" xml:space="preserve">& </s>
            <s xml:id="echoid-s4516" xml:space="preserve">arcus EF,
              <lb/>
            EG, æquales, ac proinde arcus BF, tanto minor arcu BE, quanto arcus BG,
              <lb/>
            eodem arcu BE, maior eſt: </s>
            <s xml:id="echoid-s4517" xml:space="preserve">ducanturq́ue FH, GI, ad BD, perpendiculares,
              <lb/>
            quæ ſinus erunt arcuum BF, BG. </s>
            <s xml:id="echoid-s4518" xml:space="preserve">Ducta autem chorda FG, ſecet eam ſemi-
              <lb/>
            diameter ducta DE, in L. </s>
            <s xml:id="echoid-s4519" xml:space="preserve">Et quoniam arcus FG, bifariam ſectus eſt in E, erit
              <lb/>
            quoque recta FG, bifariam ſecta in L, ex lemmate in definitionibus demon-
              <lb/>
            ſtrato; </s>
            <s xml:id="echoid-s4520" xml:space="preserve">ac propterea & </s>
            <s xml:id="echoid-s4521" xml:space="preserve">ad angulos rectos. </s>
            <s xml:id="echoid-s4522" xml:space="preserve">Eſt ergo FL, ſinus arcus EF; </s>
            <s xml:id="echoid-s4523" xml:space="preserve">& </s>
            <s xml:id="echoid-s4524" xml:space="preserve">GL,
              <lb/>
              <note position="right" xlink:label="note-129-04" xlink:href="note-129-04a" xml:space="preserve">3. terttj.</note>
            ſinus arcus EG. </s>
            <s xml:id="echoid-s4525" xml:space="preserve">Ducta quoque recta FK, ad GI, perpendiculari, erit IK, </s>
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