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

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            <s xml:id="echoid-s2813" xml:space="preserve">
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            quod eſt propoſitum. </s>
            <s xml:id="echoid-s2814" xml:space="preserve">Ex his constat, arcum H E, in figura propoſitionis
              <lb/>
            minorem eſſe arcu D F. </s>
            <s xml:id="echoid-s2815" xml:space="preserve">Nam cum angulus F M K, acutus ſit, & </s>
            <s xml:id="echoid-s2816" xml:space="preserve">H N K,
              <lb/>
            ebtuſus, ſi ex M, N, ad D E, perpẽdiculares ducerentur, caderent hæ in ar
              <lb/>
            cus D F, B H, auferrentque, vt in proximo lemmatc oſtendimus, arcus
              <lb/>
            æquales. </s>
            <s xml:id="echoid-s2817" xml:space="preserve">Quare arcus H E, minor est arcu D F.</s>
            <s xml:id="echoid-s2818" xml:space="preserve"/>
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        <div xml:id="echoid-div246" type="section" level="1" n="116">
          <head xml:id="echoid-head130" xml:space="preserve">THEOR. 5. PROPOS. 5.</head>
          <p>
            <s xml:id="echoid-s2819" xml:space="preserve">SI in circunferentia maximi circuli ſit polus
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            parallelorum, huncque maximum circulum ſecẽt
              <lb/>
            ad angulos rectos duo alij maximi circuli, quorú
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            alter ſit vnus parallelorum, alter verò obliquus ſit
              <lb/>
            ad parallelos; </s>
            <s xml:id="echoid-s2820" xml:space="preserve">ab hoc autem obliquo circulo æqua
              <lb/>
            les circunferentiæ ſumantur deinceps ad eandem
              <lb/>
            partem maximi parallelorum, perque illa puncta
              <lb/>
            terminantia æquales circunferentias deſcriban-
              <lb/>
            tur paralleli circuli: </s>
            <s xml:id="echoid-s2821" xml:space="preserve">Circunferentiæ maximi illius
              <lb/>
            circuli primo poſiti inter parallelos interceptæ in-
              <lb/>
            æquales erunt, ſemperque ea, quæ propior fuerit
              <lb/>
            maximo parallelorum, remotiore maior erit.</s>
            <s xml:id="echoid-s2822" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2823" xml:space="preserve">IN circunferentia maximi circuli A B C D, ſit A, polus parallelorum,
              <lb/>
            cumq́ue fecent duo maximi circuli B D, E C, ad angulos rectos, quorum B D,
              <lb/>
              <figure xlink:label="fig-084-01" xlink:href="fig-084-01a" number="92">
                <image file="084-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/084-01"/>
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            ſit maximus parallelorum, & </s>
            <s xml:id="echoid-s2824" xml:space="preserve">E C, ad paralle
              <lb/>
            los obliquus: </s>
            <s xml:id="echoid-s2825" xml:space="preserve">& </s>
            <s xml:id="echoid-s2826" xml:space="preserve">per F, G, H, puncta, quæ ex
              <lb/>
            obliquo circulo arcus æquales auferunt F G,
              <lb/>
            G H, deſcribantur paralleli I K, L M, N O, ex
              <lb/>
            polo A. </s>
            <s xml:id="echoid-s2827" xml:space="preserve">Dico arcum I L, maiorẽ eſſe arcu L N.
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            </s>
            <s xml:id="echoid-s2828" xml:space="preserve">
              <note position="left" xlink:label="note-084-01" xlink:href="note-084-01a" xml:space="preserve">20. 1. huius</note>
            Per polum enim A, & </s>
            <s xml:id="echoid-s2829" xml:space="preserve">punctum G, circulus
              <lb/>
            maximus deſcribatur A P, ſecans parallelos in
              <lb/>
            P, Q. </s>
            <s xml:id="echoid-s2830" xml:space="preserve">Quoniam igitur in ſphæræ ſuperficie
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            intra periphæriam circuli I K, punctum G, ſi-
              <lb/>
            gnatum eſt præter polum A, & </s>
            <s xml:id="echoid-s2831" xml:space="preserve">ex G, duo ar-
              <lb/>
            cus G P, G F, circulorum maximorum ca-
              <lb/>
            dunt in circunferentiam circuli I K; </s>
            <s xml:id="echoid-s2832" xml:space="preserve">erit ar-
              <lb/>
              <note position="left" xlink:label="note-084-02" xlink:href="note-084-02a" xml:space="preserve">Schol. 11.
                <lb/>
              @. huius.</note>
            cus G P, omnium minimus; </s>
            <s xml:id="echoid-s2833" xml:space="preserve">atque adeo minor
              <lb/>
            quam G F: </s>
            <s xml:id="echoid-s2834" xml:space="preserve">quod arcus G P, G F, minores ſint ſemicirculo, cum ſe non inter-
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            ſecent, antequam parallelum I K, diuidunt. </s>
            <s xml:id="echoid-s2835" xml:space="preserve">Rurſus quia in ſuperficie ſphæræ
              <lb/>
            extra periphæriam circuli N O, punctum G, ſignatum eſt præter eius polum;</s>
            <s xml:id="echoid-s2836" xml:space="preserve"/>
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