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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            <s xml:id="echoid-s2471" xml:space="preserve">
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            æquales; </s>
            <s xml:id="echoid-s2472" xml:space="preserve">atque adeò cum H Q, ſit quadrans, omnes illi arcus quadrantes
              <lb/>
            erunt. </s>
            <s xml:id="echoid-s2473" xml:space="preserve">Quare cum demonſtratum ſit eos tranſire per polos tangentium, erunt
              <lb/>
            puncta Q, S, T, V, R, poli circulorum tangentium, quæ quidem omnia
              <lb/>
              <note position="right" xlink:label="note-075-01" xlink:href="note-075-01a" xml:space="preserve">Coroll. 16.
                <lb/>
              1. huius.</note>
            ſunt in parallelo Q T R, quod vltimo loco proponebatur demonſtrandum.
              <lb/>
            </s>
            <s xml:id="echoid-s2474" xml:space="preserve">Iam vero quia arcus circulorum maximorũ ex E, polo circuli maximi A B C D,
              <lb/>
            ad Q, S, T, V, R, polos tangentium ducti metiuntur diſtantias poli E, à
              <lb/>
            polis tangentium; </s>
            <s xml:id="echoid-s2475" xml:space="preserve">eſtq́ue omnium maximus E Q; </s>
            <s xml:id="echoid-s2476" xml:space="preserve">minimus autem E R; </s>
            <s xml:id="echoid-s2477" xml:space="preserve">æqua
              <lb/>
              <note position="right" xlink:label="note-075-02" xlink:href="note-075-02a" xml:space="preserve">Schol. 21.
                <lb/>
              huius.</note>
            les verò E S, E T; </s>
            <s xml:id="echoid-s2478" xml:space="preserve">& </s>
            <s xml:id="echoid-s2479" xml:space="preserve">denique E T, maior, quàm E V, quòd omnes hi arcùs
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            ſint ſemicirculo minores; </s>
            <s xml:id="echoid-s2480" xml:space="preserve">(eſt enim E Q, quadrante E A, minor; </s>
            <s xml:id="echoid-s2481" xml:space="preserve">atque adeo
              <lb/>
            reliqui eum non ſecabunt citra punctum Q, ideoque ſemicirculo minores
              <lb/>
            erunt.) </s>
            <s xml:id="echoid-s2482" xml:space="preserve">erit circulus H K, minimè inclinatus ad circulum maximum A B C D;
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            </s>
            <s xml:id="echoid-s2483" xml:space="preserve">
              <note position="right" xlink:label="note-075-03" xlink:href="note-075-03a" xml:space="preserve">Schol. 21.
                <lb/>
              huius.</note>
            & </s>
            <s xml:id="echoid-s2484" xml:space="preserve">G L, maximè; </s>
            <s xml:id="echoid-s2485" xml:space="preserve">at M P, N K, æqualiter, ſeu ſimiliter; </s>
            <s xml:id="echoid-s2486" xml:space="preserve">& </s>
            <s xml:id="echoid-s2487" xml:space="preserve">O L, magis quàm
              <lb/>
            N K, quod primo loco demonſtrandum proponebatur. </s>
            <s xml:id="echoid-s2488" xml:space="preserve">Quocirca ſi in ſphæ-
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            ra maximus circulus. </s>
            <s xml:id="echoid-s2489" xml:space="preserve">&</s>
            <s xml:id="echoid-s2490" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2491" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s2492" xml:space="preserve"/>
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        <div xml:id="echoid-div227" type="section" level="1" n="108">
          <head xml:id="echoid-head120" xml:space="preserve">THEOR. 21. PROPOS. 23.</head>
          <note position="right" xml:space="preserve">34.</note>
          <p>
            <s xml:id="echoid-s2493" xml:space="preserve">IISDEM poſitis, ſi circunferétiæ circulorum
              <lb/>
            tangentium à contactibus ad nodos ſint æqua-
              <lb/>
            les;</s>
            <s xml:id="echoid-s2494" xml:space="preserve">prædicti circuli maximi ſimiliter inclinati erút.</s>
            <s xml:id="echoid-s2495" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2496" xml:space="preserve">RVRSVS in ſphæra maximus circulus A B C D, cuius polus E, tangat
              <lb/>
            circulum A F, ſecet autem alium huic parallelum G B H D, poſitum inter
              <lb/>
            ſphæræ centrum, & </s>
            <s xml:id="echoid-s2497" xml:space="preserve">circulum A F, ita vt G B H D, maior ſit, quàm A F; </s>
            <s xml:id="echoid-s2498" xml:space="preserve">ſit-
              <lb/>
            que E, polus maximi circuli A B C D, inter vtrumque circulum A F, G B H D:
              <lb/>
            </s>
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              <figure xlink:label="fig-075-01" xlink:href="fig-075-01a" number="84">
                <image file="075-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/075-01"/>
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            Tangãt deinde in punctis
              <lb/>
            M, N, circuli maximi
              <lb/>
            M O, N P, circulũ G B H D,
              <lb/>
            ſecantes A B C D, in O,
              <lb/>
            P, nodis, ſintq́ue arcus
              <lb/>
            M O, N P, æquales. </s>
            <s xml:id="echoid-s2500" xml:space="preserve">Di-
              <lb/>
            co circulos M O, N P,
              <lb/>
            ſimiliter inclinari ad ma-
              <lb/>
            ximum circulum A B C D.
              <lb/>
            </s>
            <s xml:id="echoid-s2501" xml:space="preserve">Ducatur enim per E,po-
              <lb/>
              <note position="right" xlink:label="note-075-05" xlink:href="note-075-05a" xml:space="preserve">20. 1. huius.</note>
            lum circuli A B C D, & </s>
            <s xml:id="echoid-s2502" xml:space="preserve">I,
              <lb/>
            polum parallelorum cir-
              <lb/>
            culus maximus G A C: </s>
            <s xml:id="echoid-s2503" xml:space="preserve">Itẽ
              <lb/>
            per I, polum parallelorũ,
              <lb/>
            & </s>
            <s xml:id="echoid-s2504" xml:space="preserve">puncta contactuum cir
              <lb/>
            culi maximi I M, I N, qui
              <lb/>
            per polos quoque circu-
              <lb/>
              <note position="right" xlink:label="note-075-06" xlink:href="note-075-06a" xml:space="preserve">5. huius.</note>
            lorum tangentium tran-
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            ſibũt;</s>
            <s xml:id="echoid-s2505" xml:space="preserve">atque adeo ipſos ad
              <lb/>
            angulos rectos ſecabunt.
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            </s>
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              <note position="right" xlink:label="note-075-07" xlink:href="note-075-07a" xml:space="preserve">15. 1. huius.</note>
            Quoniam igitur ſegmenta circulorum æqualia, nempe ſemicirculi, qui ten-
              <lb/>
            dunt ex M, & </s>
            <s xml:id="echoid-s2507" xml:space="preserve">N, per I, donec iterum ſecent circulos tangentes M O, N P,
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            inſiſtunt diametris circulorum M O, N P, (eſt enim communis ſectio </s>
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