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

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            <s xml:id="echoid-s3187" xml:space="preserve">
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            & </s>
            <s xml:id="echoid-s3188" xml:space="preserve">ex K I, ſumatur K N, ipſi M L, æqualis; </s>
            <s xml:id="echoid-s3189" xml:space="preserve">& </s>
            <s xml:id="echoid-s3190" xml:space="preserve">per N, & </s>
            <s xml:id="echoid-s3191" xml:space="preserve">A, circulus maximus
              <lb/>
            deſeribatur A O N, ſecans circulum C D, & </s>
            <s xml:id="echoid-s3192" xml:space="preserve">in O. </s>
            <s xml:id="echoid-s3193" xml:space="preserve">Deinde per lemma 2. </s>
            <s xml:id="echoid-s3194" xml:space="preserve">præ-
              <lb/>
              <note position="right" xlink:label="note-095-01" xlink:href="note-095-01a" xml:space="preserve">10. 1. huius.</note>
            cedentis propoſ. </s>
            <s xml:id="echoid-s3195" xml:space="preserve">inueniatur arcus F P, maior quidem, quàm F O, minor ve-
              <lb/>
              <figure xlink:label="fig-095-01" xlink:href="fig-095-01a" number="101">
                <image file="095-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/095-01"/>
              </figure>
            rò quàm F E, & </s>
            <s xml:id="echoid-s3196" xml:space="preserve">ipſi F G, commenſurabilis:
              <lb/>
            </s>
            <s xml:id="echoid-s3197" xml:space="preserve">ſitque G Q, ipſi F P, (qui minor eſt, quàm
              <lb/>
            E F, atque adeo minor etiam quàm G H, ip-
              <lb/>
            ſi E F, æqualis.) </s>
            <s xml:id="echoid-s3198" xml:space="preserve">æqualis: </s>
            <s xml:id="echoid-s3199" xml:space="preserve">& </s>
            <s xml:id="echoid-s3200" xml:space="preserve">per P, Q, & </s>
            <s xml:id="echoid-s3201" xml:space="preserve">A,
              <lb/>
            circuli maximi deſcribantur A P R, A Q S. </s>
            <s xml:id="echoid-s3202" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-095-02" xlink:href="note-095-02a" xml:space="preserve">20. 1. huius</note>
            Quoniam igitur arcus P F, G Q, æquales
              <lb/>
            ſunt non continui, eſtq́ue vtrique illorum
              <lb/>
            commenſurabilis arcus intermedius F G; </s>
            <s xml:id="echoid-s3203" xml:space="preserve">erit,
              <lb/>
            vt demon ſtratum iam eſt in prima ſigura, ar-
              <lb/>
            cus S L, maior arcu K R. </s>
            <s xml:id="echoid-s3204" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s3205" xml:space="preserve">multo
              <lb/>
            maior erit, quàm K N; </s>
            <s xml:id="echoid-s3206" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s3207" xml:space="preserve">M L, mul
              <lb/>
            to maior erit, quàm K N: </s>
            <s xml:id="echoid-s3208" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s3209" xml:space="preserve">K N, ipſi
              <lb/>
            M L, æqualis poſitus eſt. </s>
            <s xml:id="echoid-s3210" xml:space="preserve">Quod eſt abſurdum. </s>
            <s xml:id="echoid-s3211" xml:space="preserve">Non ergo M L, minor eſt
              <lb/>
            quàm K I.</s>
            <s xml:id="echoid-s3212" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3213" xml:space="preserve">SIT deinde, ſi fieri poteſt, arcus M L, æqualis arcui K I, vt in tertia figura.
              <lb/>
            </s>
            <s xml:id="echoid-s3214" xml:space="preserve">Diuiſis autẽ arcubus E F, G H, bifariã in N, O, deſcribantur per N, O, & </s>
            <s xml:id="echoid-s3215" xml:space="preserve">A, cir
              <lb/>
              <note position="right" xlink:label="note-095-03" xlink:href="note-095-03a" xml:space="preserve">20. 1. huius</note>
            culi maximi A N P, A O Q. </s>
            <s xml:id="echoid-s3216" xml:space="preserve">Erit igitur arcus M Q, maior arcu Q L, & </s>
            <s xml:id="echoid-s3217" xml:space="preserve">K P,
              <lb/>
              <figure xlink:label="fig-095-02" xlink:href="fig-095-02a" number="102">
                <image file="095-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/095-02"/>
              </figure>
              <note position="right" xlink:label="note-095-04" xlink:href="note-095-04a" xml:space="preserve">6. huius.</note>
            maior quàm P I. </s>
            <s xml:id="echoid-s3218" xml:space="preserve">Quare Q L, minor erit, quàm
              <lb/>
            dimidiũ ipſius M L; </s>
            <s xml:id="echoid-s3219" xml:space="preserve">& </s>
            <s xml:id="echoid-s3220" xml:space="preserve">K P, maior, quàm dimi-
              <lb/>
            dium ipſius K I. </s>
            <s xml:id="echoid-s3221" xml:space="preserve">Cum ergo M L, K I, ponãtur
              <lb/>
            æquales; </s>
            <s xml:id="echoid-s3222" xml:space="preserve">erit Q L, minor, quàm K P, quod eſt
              <lb/>
            abſurdum. </s>
            <s xml:id="echoid-s3223" xml:space="preserve">Quoniam enim arcus F N, G O,
              <lb/>
            dimidij æqualium arcuum E F, G H, æquales
              <lb/>
            ſunt non continui, non poterit Q L, minor
              <lb/>
            eſſe, quàm K B; </s>
            <s xml:id="echoid-s3224" xml:space="preserve">vt proximè in ſecunda figura
              <lb/>
            demonſtratum eſt. </s>
            <s xml:id="echoid-s3225" xml:space="preserve">Non ergo arcus M L, ar-
              <lb/>
            cui K I, æqualis eſt: </s>
            <s xml:id="echoid-s3226" xml:space="preserve">ſed neque minor eſt oſten
              <lb/>
            ſus. </s>
            <s xml:id="echoid-s3227" xml:space="preserve">Maior ergo eſt. </s>
            <s xml:id="echoid-s3228" xml:space="preserve">Si igitur polus paralle-
              <lb/>
            lorum ſit in circunferentia, &</s>
            <s xml:id="echoid-s3229" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3230" xml:space="preserve">Quod erat
              <lb/>
            demonſtrandum.</s>
            <s xml:id="echoid-s3231" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div267" type="section" level="1" n="124">
          <head xml:id="echoid-head138" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s3232" xml:space="preserve">_SICVT_ Theodoſius in hac propoſitione 9. </s>
            <s xml:id="echoid-s3233" xml:space="preserve">idem demonſtrauit de arcubus non
              <lb/>
            continuis, quod de continuis propoſ. </s>
            <s xml:id="echoid-s3234" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3235" xml:space="preserve">docuit, ita in alia verſione demonſtrantur tris
              <lb/>
            bus Theorematibus eadem de arcubus non continuis, quæ Theodoſius de continuis de-
              <lb/>
            monſtrauit propoſ. </s>
            <s xml:id="echoid-s3236" xml:space="preserve">5. </s>
            <s xml:id="echoid-s3237" xml:space="preserve">7. </s>
            <s xml:id="echoid-s3238" xml:space="preserve">& </s>
            <s xml:id="echoid-s3239" xml:space="preserve">8. </s>
            <s xml:id="echoid-s3240" xml:space="preserve">Primum autem theorema eiuſmodi eſt.</s>
            <s xml:id="echoid-s3241" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div268" type="section" level="1" n="125">
          <head xml:id="echoid-head139" xml:space="preserve">I.</head>
          <p>
            <s xml:id="echoid-s3242" xml:space="preserve">SI polus parallelorum ſit in circunferentia maximi circuli, quem
              <lb/>
              <note position="right" xlink:label="note-095-05" xlink:href="note-095-05a" xml:space="preserve">7.</note>
            duo alij maximi circuli ad angulos rectos ſecẽt, quorum circulorum
              <lb/>
            alter ſit vnus parallelorum, alter verò ad parallelos obliquus ſit, & </s>
            <s xml:id="echoid-s3243" xml:space="preserve">ab
              <lb/>
            hoc obliquo circulo ſumantur æquales circunferentię, quę continuę
              <lb/>
            quidem non ſint, ſed tamen ſint ad eaſdem partes maximi illius </s>
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