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

Table of contents

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[71.] THEOREMA 1. PROPOS. 1.
Page: 42
[72.] THEOREMA 2. PROPOS. 2.
Page: 42
[73.] SCHOLIVM.
Page: 43 (31)
[74.] THEOREMA 3. PROPOS. 3.
Page: 43 (31)
[75.] THEOREMA 4. PROPOS. 4.
Page: 44 (32)
[76.] THEOR. 5. PROPOS. 5.
Page: 44 (32)
[77.] THEOREMA 6. PROPOS. 6.
Page: 45 (33)
[78.] COROLLARIVM.
Page: 46 (34)
[79.] THEOREMA 7. PROPOS. 7.
Page: 46 (34)
[80.] SCHOLIVM.
Page: 46 (34)
[81.] THEOR. 8. PROP. 8.
Page: 47 (35)
[82.] SCHOLIVM.
Page: 47 (35)
[83.] THEOR. 9. PROPOS. 9.
Page: 48 (36)
[84.] SCHOLIVM.
Page: 49 (37)
[85.] I.
Page: 49 (37)
[86.] THEOR, 10. PROP. 10.
Page: 50 (38)
[87.] THEOR. 11. PROP. 11
Page: 51 (39)
[88.] THEOR. 12. PROPOS. 12.
Page: 53 (41)
[89.] THEOREMA 13. PROPOS. 13.
Page: 54 (42)
[90.] PROBL. 1. PROP. 14.
Page: 56 (44)
[91.] PROBL. 2. PROPOS. 15.
Page: 57 (45)
[92.] SCHOLIVM.
Page: 58 (46)
[93.] THEOR. 14. PROPOS. 16.
Page: 58 (46)
[94.] SCHOLIVM.
Page: 60 (48)
[95.] THEOREMA 15. PROPOS. 17.
Page: 61 (49)
[96.] THEOR 16. PROPOS. 18.
Page: 62 (50)
[97.] THEOR. 17. PROPOS. 19.
Page: 63 (51)
[98.] THEOREMA 18. PROPOS. 20.
Page: 64 (52)
[99.] COROLLARIVM.
Page: 65 (53)
[100.] THEOREMA 19. PROPOS. 21.
Page: 65 (53)
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            lorum maximorum I M, M O, diameter vtriuſque, cum ſe mutuo ſecent bifa-
              <lb/>
              <note position="left" xlink:label="note-076-01" xlink:href="note-076-01a" xml:space="preserve">@1. 1. huius.</note>
            riam) ad angulos rectos, & </s>
            <s xml:id="echoid-s2508" xml:space="preserve">diuiduntur non bifariam in I, quod I, polus paral-
              <lb/>
            lelorum non ſit polus tangentium; </s>
            <s xml:id="echoid-s2509" xml:space="preserve">ponunturque arcus M O, N P, æquales;
              <lb/>
            </s>
            <s xml:id="echoid-s2510" xml:space="preserve">erunt ductæ rectæ I O, I B, æquales. </s>
            <s xml:id="echoid-s2511" xml:space="preserve">Si igitur ex I, polo parallelus deſcriba-
              <lb/>
              <note position="left" xlink:label="note-076-02" xlink:href="note-076-02a" xml:space="preserve">12. 1. huius.</note>
            tur O K, ad interuallum I O, tranſibit is quoque per P. </s>
            <s xml:id="echoid-s2512" xml:space="preserve">Et quia circulus
              <lb/>
            maximus I M, tranſiens per polos circulorum M O, O Q, ſe ſecantium in
              <lb/>
            O, Q, ſecat eorum ſegmenta bifariam, æquales erunt arcus M O, M Q, & </s>
            <s xml:id="echoid-s2513" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-076-03" xlink:href="note-076-03a" xml:space="preserve">9. huius.</note>
            S O, S Q; </s>
            <s xml:id="echoid-s2514" xml:space="preserve">Eodemque argumento æquales erunt arcus N P, N R, & </s>
            <s xml:id="echoid-s2515" xml:space="preserve">T P,
              <lb/>
            T R; </s>
            <s xml:id="echoid-s2516" xml:space="preserve">nec non K O, K P, & </s>
            <s xml:id="echoid-s2517" xml:space="preserve">C O, C P; </s>
            <s xml:id="echoid-s2518" xml:space="preserve">propterea quòd circulus maximus IkC,
              <lb/>
            tranſiens per polos circulorum O K P, O C P, ſecat eorum ſegmenta bifa-
              <lb/>
              <note position="left" xlink:label="note-076-04" xlink:href="note-076-04a" xml:space="preserve">9. huius.</note>
            riam in K, & </s>
            <s xml:id="echoid-s2519" xml:space="preserve">C. </s>
            <s xml:id="echoid-s2520" xml:space="preserve">Cum ergo arcus M O, N P, ponantur æquales, erunt & </s>
            <s xml:id="echoid-s2521" xml:space="preserve">toti
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              <figure xlink:label="fig-076-01" xlink:href="fig-076-01a" number="85">
                <image file="076-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/076-01"/>
              </figure>
            O M Q, P N R, quorum
              <lb/>
            ipſi dimidij ſunt, æqua-
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            les; </s>
            <s xml:id="echoid-s2522" xml:space="preserve">atque adeo & </s>
            <s xml:id="echoid-s2523" xml:space="preserve">rectæ
              <lb/>
              <note position="left" xlink:label="note-076-05" xlink:href="note-076-05a" xml:space="preserve">29. tertij.</note>
            ſubtenſę O Q, P R, æqua
              <lb/>
            les erunt. </s>
            <s xml:id="echoid-s2524" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s2525" xml:space="preserve">arcus
              <lb/>
              <note position="left" xlink:label="note-076-06" xlink:href="note-076-06a" xml:space="preserve">28. tertij.</note>
            O S Q, P T R, ęquales
              <lb/>
            erunt; </s>
            <s xml:id="echoid-s2526" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s2527" xml:space="preserve">eo-
              <lb/>
            rum dimidij O S, P T, æ-
              <lb/>
            quales erunt. </s>
            <s xml:id="echoid-s2528" xml:space="preserve">Sunt autem
              <lb/>
            & </s>
            <s xml:id="echoid-s2529" xml:space="preserve">toti K O, K P, oſtenſi
              <lb/>
            ęquales. </s>
            <s xml:id="echoid-s2530" xml:space="preserve">Reliqui ergo K S,
              <lb/>
            K T, æquales erunt; </s>
            <s xml:id="echoid-s2531" xml:space="preserve">atque
              <lb/>
            adeo, cum ſint vnius eiuſ-
              <lb/>
            demq́ue circuli, ſimiles in
              <lb/>
            ter ſe erunt. </s>
            <s xml:id="echoid-s2532" xml:space="preserve">Quia verò ar-
              <lb/>
              <note position="left" xlink:label="note-076-07" xlink:href="note-076-07a" xml:space="preserve">10. huius.</note>
            cubus K S, K T, ſimiles
              <lb/>
            ſunt arcus H M, H N; </s>
            <s xml:id="echoid-s2533" xml:space="preserve">erũt
              <lb/>
            quoq;</s>
            <s xml:id="echoid-s2534" xml:space="preserve">æquales arcus H M,
              <lb/>
            H N. </s>
            <s xml:id="echoid-s2535" xml:space="preserve">Itaque cum ſeg-
              <lb/>
            mentum B H D, bifariam
              <lb/>
              <note position="left" xlink:label="note-076-08" xlink:href="note-076-08a" xml:space="preserve">9. huius.</note>
            ſeceturin H, fintque equales arcus H M, H N; </s>
            <s xml:id="echoid-s2536" xml:space="preserve">erunt circuli M O, N P, ſimili-
              <lb/>
            ter inclinati ad circulum A B C D. </s>
            <s xml:id="echoid-s2537" xml:space="preserve">Quare ijſdem poſitis, ſi circunferentiæ à
              <lb/>
            contactibus, &</s>
            <s xml:id="echoid-s2538" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2539" xml:space="preserve">Quod erat demonſtrandum.</s>
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        <div xml:id="echoid-div229" type="section" level="1" n="109">
          <head xml:id="echoid-head121" xml:space="preserve">FINIS LIBRI I I. THEODOSII.</head>
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