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

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            <s xml:id="echoid-s3365" xml:space="preserve">
              <pb o="87" file="099" n="99" rhead=""/>
            K F, F I, I E, æquales ſunt, erit arcus B O, maior quàm O N, & </s>
            <s xml:id="echoid-s3366" xml:space="preserve">O N, maior
              <lb/>
              <note position="right" xlink:label="note-099-01" xlink:href="note-099-01a" xml:space="preserve">6. huius.</note>
            quàm N H, &</s>
            <s xml:id="echoid-s3367" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3368" xml:space="preserve">Igitur maior erit proportio B O, ad C L, quàm O N, ad
              <lb/>
              <note position="right" xlink:label="note-099-02" xlink:href="note-099-02a" xml:space="preserve">8. quinti.</note>
            L K; </s>
            <s xml:id="echoid-s3369" xml:space="preserve">& </s>
            <s xml:id="echoid-s3370" xml:space="preserve">maior proportio O N, ad L K, quàm N H, ad K F, &</s>
            <s xml:id="echoid-s3371" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3372" xml:space="preserve">Quare, cum
              <lb/>
            ſint quotcunque magnitudines B O, O N, N H, & </s>
            <s xml:id="echoid-s3373" xml:space="preserve">totidem numero C L, L K,
              <lb/>
              <figure xlink:label="fig-099-01" xlink:href="fig-099-01a" number="104">
                <image file="099-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/099-01"/>
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            K F, ſitq́ue maior proportio primæ B O, ad primã C L, quàm ſecundæ O N,
              <lb/>
            ad ſecundam L K; </s>
            <s xml:id="echoid-s3374" xml:space="preserve">& </s>
            <s xml:id="echoid-s3375" xml:space="preserve">maior ſecundæ O N, ad ſecundam L K, quàm tertiæ
              <lb/>
            N H, ad tertiam K F; </s>
            <s xml:id="echoid-s3376" xml:space="preserve">maior erit proportio B H, ad C F, quàm N H, ad K F:
              <lb/>
            </s>
            <s xml:id="echoid-s3377" xml:space="preserve">
              <note position="right" xlink:label="note-099-03" xlink:href="note-099-03a" xml:space="preserve">34. quinti.</note>
            Sed proportio N H, ad K F, maior adhuc eſt proportione H M, ad F I, vt
              <lb/>
              <note position="right" xlink:label="note-099-04" xlink:href="note-099-04a" xml:space="preserve">8. quinti.</note>
            oſtenſum eſt. </s>
            <s xml:id="echoid-s3378" xml:space="preserve">Multo ergo maior eſt proportio B H, ad C F, quàm H M, ad
              <lb/>
            F I: </s>
            <s xml:id="echoid-s3379" xml:space="preserve">Sed adhuc maior eſt proportio H M, ad F I, quàm H G, ad F E; </s>
            <s xml:id="echoid-s3380" xml:space="preserve">propte-
              <lb/>
              <note position="right" xlink:label="note-099-05" xlink:href="note-099-05a" xml:space="preserve">34. quinti.</note>
            rea quòd arcus H M, M G, multitudine æquales ſunt arcubus F I, I E; </s>
            <s xml:id="echoid-s3381" xml:space="preserve">eſtq́ue
              <lb/>
            maior proportio primæ H M, ad primam F I, quæ ſecundæ M G, ad ſecundam
              <lb/>
              <note position="right" xlink:label="note-099-06" xlink:href="note-099-06a" xml:space="preserve">8. quinti.</note>
            I E, vt dictum eſt. </s>
            <s xml:id="echoid-s3382" xml:space="preserve">Multo igitur maior eſt proportio B H, ad C F, quàm H G,
              <lb/>
            ad F E. </s>
            <s xml:id="echoid-s3383" xml:space="preserve">Sit vt B H, ad C F, ita H G, ad P. </s>
            <s xml:id="echoid-s3384" xml:space="preserve">Erit ergo maior proportio quoque
              <lb/>
            H G, ad P, quam H G, ad F E; </s>
            <s xml:id="echoid-s3385" xml:space="preserve">ac proinde P, arcus minor erit arcu F E. </s>
            <s xml:id="echoid-s3386" xml:space="preserve">Qua-
              <lb/>
              <note position="right" xlink:label="note-099-07" xlink:href="note-099-07a" xml:space="preserve">10. quinti.</note>
            re eſt, vt arcus B H, ad arcum C F, ita arcus H G, ad arcum P, arcu F E, mi-
              <lb/>
            norem. </s>
            <s xml:id="echoid-s3387" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s3388" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3389" xml:space="preserve">SED iam ſint arcus C F, F E, incommenſurabiles, vt in ſecunda figura.
              <lb/>
            </s>
            <s xml:id="echoid-s3390" xml:space="preserve">Dico adhuc, vt eſt arcus B H, ad arcum C F, ita eſſe arcum H G, ad arcum ar-
              <lb/>
            cu F E, minorem. </s>
            <s xml:id="echoid-s3391" xml:space="preserve">Si enim non ita ſit, erit, vt B H, ad C F, ita H G, vel ad arcũ
              <lb/>
            arcu F E, maiorem, vel ad ipſummet F E. </s>
            <s xml:id="echoid-s3392" xml:space="preserve">Sit primum, ſi fieri poteſt, vt B H, ad
              <lb/>
            C F, ita H G, ad arcum F I, arcu F E, maiorem. </s>
            <s xml:id="echoid-s3393" xml:space="preserve">Inueniatur per lemma 2. </s>
            <s xml:id="echoid-s3394" xml:space="preserve">pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s3395" xml:space="preserve">8. </s>
            <s xml:id="echoid-s3396" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s3397" xml:space="preserve">arcus F K, maior quidem quàm F E, minor autem quàm F I,
              <lb/>
            & </s>
            <s xml:id="echoid-s3398" xml:space="preserve">ipſi C F, commenſurabilis, ducaturq́ue per K, & </s>
            <s xml:id="echoid-s3399" xml:space="preserve">A, polum circulus maxi-
              <lb/>
              <note position="right" xlink:label="note-099-08" xlink:href="note-099-08a" xml:space="preserve">20. 1. huius.</note>
            mus K L. </s>
            <s xml:id="echoid-s3400" xml:space="preserve">Quoniam igitur commenſurabiles ſunt arcus C F, F K, erit, vt de-
              <lb/>
            monſtratum iam eſt in prima figura, vt B H, ad C F, ita H L, ad arcum arcu
              <lb/>
            F K, minorem: </s>
            <s xml:id="echoid-s3401" xml:space="preserve">Sed vt B H, ad C F, ita ponebatur H G, ad F I. </s>
            <s xml:id="echoid-s3402" xml:space="preserve">Igitur erit quo-
              <lb/>
            que, vt H G, ad F I, ita H L, ad arcum arcu F K, minorem: </s>
            <s xml:id="echoid-s3403" xml:space="preserve">& </s>
            <s xml:id="echoid-s3404" xml:space="preserve">permutando, vt
              <lb/>
            H G, ad H L, ita F I, ad arcum arcu F K, minorem: </s>
            <s xml:id="echoid-s3405" xml:space="preserve">Sed H G, arcus minor eſt
              <lb/>
            arcu H L. </s>
            <s xml:id="echoid-s3406" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s3407" xml:space="preserve">arcus F I, minor erit, quàm arcus arcu F K, minor, totum
              <lb/>
            quàm pars. </s>
            <s xml:id="echoid-s3408" xml:space="preserve">Quod eſt abſurdum. </s>
            <s xml:id="echoid-s3409" xml:space="preserve">Non ergo eſt, vt B H, ad C F, ita H G, ad ar-
              <lb/>
            cum arcu F E, maiorem.</s>
            <s xml:id="echoid-s3410" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3411" xml:space="preserve">SIT deinde, ſi ſieri poteſt, vt B H, ad C F, ita H G, ad F E, vt in tertia
              <lb/>
            figura. </s>
            <s xml:id="echoid-s3412" xml:space="preserve">Diuiſo arcu F E, bifariam in I, deſcribatur per I, & </s>
            <s xml:id="echoid-s3413" xml:space="preserve">per A, polum cir-
              <lb/>
              <note position="right" xlink:label="note-099-09" xlink:href="note-099-09a" xml:space="preserve">20. 1. huius</note>
            </s>
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