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

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            <s xml:id="echoid-s3064" xml:space="preserve">
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            clinatus eſt ad partes R, & </s>
            <s xml:id="echoid-s3065" xml:space="preserve">viciſsim B E, atque adeò & </s>
            <s xml:id="echoid-s3066" xml:space="preserve">ſibi parallelus V X, ad
              <lb/>
            M N, ad eaſdem partes R, erit inclinatus. </s>
            <s xml:id="echoid-s3067" xml:space="preserve">Item ſegmentum incipiens ab X, & </s>
            <s xml:id="echoid-s3068" xml:space="preserve">
              <lb/>
            per V, vſque ad alteram ſectionem tranſiens ſectum eſt inæqualiter in T, eſt-
              <lb/>
            q́ue minor pars T X, vt mox oſtcndemus. </s>
            <s xml:id="echoid-s3069" xml:space="preserve">Igitur recta T X, minor eſt, quàm
              <lb/>
              <note position="left" xlink:label="note-092-01" xlink:href="note-092-01a" xml:space="preserve">2. huius.</note>
            recta T F: </s>
            <s xml:id="echoid-s3070" xml:space="preserve">Sed recta T F, æqualis eſt rectæ H S. </s>
            <s xml:id="echoid-s3071" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s3072" xml:space="preserve">recta T X, minor erit
              <lb/>
              <note position="left" xlink:label="note-092-02" xlink:href="note-092-02a" xml:space="preserve">3. huius.</note>
            quàm recta H S; </s>
            <s xml:id="echoid-s3073" xml:space="preserve">atquo adeo, vt in lemmate propoſ. </s>
            <s xml:id="echoid-s3074" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3075" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s3076" xml:space="preserve">demonſtratum
              <lb/>
            eſt, maior erit arcus H S, quàm vt ſimilis eſſe poſsit arcui T X. </s>
            <s xml:id="echoid-s3077" xml:space="preserve">Cum ergo ar-
              <lb/>
            cus I L, arcui H S, & </s>
            <s xml:id="echoid-s3078" xml:space="preserve">arcus L N, arcui T X, ſit ſimilis, maior erit quoque ar-
              <lb/>
              <note position="left" xlink:label="note-092-03" xlink:href="note-092-03a" xml:space="preserve">13. 2. huius.</note>
            cus I L, quàm vt ſimilis ſit arcui L N; </s>
            <s xml:id="echoid-s3079" xml:space="preserve">atque adeo, cum in eodem circulo ſint,
              <lb/>
            erit I L, maior, quam L N. </s>
            <s xml:id="echoid-s3080" xml:space="preserve">Si igitur ſphæra maximus circulus aliquem ſphæræ
              <lb/>
            circulum tangat, &</s>
            <s xml:id="echoid-s3081" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3082" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s3083" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div258" type="section" level="1" n="121">
          <head xml:id="echoid-head135" xml:space="preserve">LEMMA. I.</head>
          <p style="it">
            <s xml:id="echoid-s3084" xml:space="preserve">QVOD autem arcus T X, minor ſit ſemiſſe ſegmenti, quod ab X, inci
              <lb/>
            pit, et per V, vſque ad alteram ſectionẽ protenditur, it a demonſtrabimus.
              <lb/>
            </s>
            <s xml:id="echoid-s3085" xml:space="preserve">Per E, ducatur circulus maximus E Z, tangens parallelum A C, in Z, pun
              <lb/>
            cto, quod ſit ad dexteram cir culimaximi N Y: </s>
            <s xml:id="echoid-s3086" xml:space="preserve">cùmex E, duo circuli tan-
              <lb/>
              <figure xlink:label="fig-092-01" xlink:href="fig-092-01a" number="98">
                <image file="092-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/092-01"/>
              </figure>
            gẽtes A C, deſcribi poſſint,
              <lb/>
            vnus ad ſinistram circuli
              <lb/>
              <note position="left" xlink:label="note-092-04" xlink:href="note-092-04a" xml:space="preserve">schol. 13. 3
                <lb/>
              huius.</note>
            N Y, et ad dexteram alter.
              <lb/>
            </s>
            <s xml:id="echoid-s3087" xml:space="preserve">Eritq́ E Z, quadrans. </s>
            <s xml:id="echoid-s3088" xml:space="preserve">Nam
              <lb/>
            circulus maximus Z Y, per
              <lb/>
            Y, polum circuli A C, & </s>
            <s xml:id="echoid-s3089" xml:space="preserve">
              <lb/>
            per Z, cõtactum deſcriptus
              <lb/>
            trãſit quoq; </s>
            <s xml:id="echoid-s3090" xml:space="preserve">per polum cir-
              <lb/>
              <note position="left" xlink:label="note-092-05" xlink:href="note-092-05a" xml:space="preserve">5. 2. huius.</note>
            culi tangentis E Z. </s>
            <s xml:id="echoid-s3091" xml:space="preserve">Quare
              <lb/>
            idem circulus Y Z, ſecabit
              <lb/>
            ſegmenta circulorum B E,
              <lb/>
              <note position="left" xlink:label="note-092-06" xlink:href="note-092-06a" xml:space="preserve">5. 2. huius.</note>
            E Z, bifariam. </s>
            <s xml:id="echoid-s3092" xml:space="preserve">Cum ergo hi
              <lb/>
              <note position="left" xlink:label="note-092-07" xlink:href="note-092-07a" xml:space="preserve">13. 1. huius</note>
            maximi cir culi ſe bifariam
              <lb/>
            ſecent, ſecabitur ſegmẽtum
              <lb/>
            à puncto E, per Z, vſque ad
              <lb/>
            alter am ſectionem, in duos
              <lb/>
            quadrantes in puncto Z;
              <lb/>
            </s>
            <s xml:id="echoid-s3093" xml:space="preserve">atque adeo E Z, quadrans
              <lb/>
            erit. </s>
            <s xml:id="echoid-s3094" xml:space="preserve">Eodem modo quadrans erit E D, ſi per polum Y, & </s>
            <s xml:id="echoid-s3095" xml:space="preserve">contactum D,
              <lb/>
            circulus maximus Y D, deſcribatur. </s>
            <s xml:id="echoid-s3096" xml:space="preserve">Eſt autem & </s>
            <s xml:id="echoid-s3097" xml:space="preserve">arcus cir culi maximi
              <lb/>
            inter E, & </s>
            <s xml:id="echoid-s3098" xml:space="preserve">Y, polum, quadrans. </s>
            <s xml:id="echoid-s3099" xml:space="preserve">lgitur cir culus maximus ex E, tanquam
              <lb/>
              <note position="left" xlink:label="note-092-08" xlink:href="note-092-08a" xml:space="preserve">Cotol. 16.1
                <lb/>
              huius.</note>
            polo, & </s>
            <s xml:id="echoid-s3100" xml:space="preserve">interuallo E Z, deſcriptus tranſibit per puncta Y, D. </s>
            <s xml:id="echoid-s3101" xml:space="preserve">Non aliter
              <lb/>
            oſtendemus N M, eſſe quadrantem; </s>
            <s xml:id="echoid-s3102" xml:space="preserve">atque adeo circulum maximum ex
              <lb/>
            N, polo, & </s>
            <s xml:id="echoid-s3103" xml:space="preserve">interuallo N M, deſcriptum tranſire per Y, polum paralle-
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            lorum, qualis eſt M Y, atque adeo ſecare arcum B D, vltra punctum </s>
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