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-s2607" xml:space="preserve">ITEM quia L A, minor eſt, quàm L I, Lk, L C; </s>
            <s xml:id="echoid-s2608" xml:space="preserve">erunt quadrata ex F L,
              <lb/>
              <note position="right" xlink:label="note-079-01" xlink:href="note-079-01a" xml:space="preserve">7. tertij.</note>
            L A, minora quadratis ex F L, L I: </s>
            <s xml:id="echoid-s2609" xml:space="preserve">Eſt autem tam quadratum ex F A, qua-
              <lb/>
            dratis ex F L, L A, quam quadratum ex F I, quadratis ex F L, L I, æqua-
              <lb/>
              <note position="right" xlink:label="note-079-02" xlink:href="note-079-02a" xml:space="preserve">47. primi.</note>
            le. </s>
            <s xml:id="echoid-s2610" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s2611" xml:space="preserve">quadratum ex F A, minus erit quadrato ex F I; </s>
            <s xml:id="echoid-s2612" xml:space="preserve">atque ob id re-
              <lb/>
            cta quoque F A, minor erit quàm recta F I. </s>
            <s xml:id="echoid-s2613" xml:space="preserve">Eodem modo oſtendemus, rectam
              <lb/>
            F A, maiorem eſſe, quàm F K, F C. </s>
            <s xml:id="echoid-s2614" xml:space="preserve">Eſt ergo F A, omnium rectarum ex F, in
              <lb/>
            arcum A C, cadentium minima.</s>
            <s xml:id="echoid-s2615" xml:space="preserve"/>
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            <s xml:id="echoid-s2616" xml:space="preserve">DENIQVE quia L I, minor eſt, quàm L K; </s>
            <s xml:id="echoid-s2617" xml:space="preserve">erunt quadrata ex F L, L I,
              <lb/>
              <note position="right" xlink:label="note-079-03" xlink:href="note-079-03a" xml:space="preserve">7. tertij.</note>
            minora quadratis ex F L, L K: </s>
            <s xml:id="echoid-s2618" xml:space="preserve">Eſtautem tam quadratum ex F I, quadra-
              <lb/>
            tis ex F L, L I, quàm quadratum ex F K, quadratis ex F L, L K, æquale. </s>
            <s xml:id="echoid-s2619" xml:space="preserve">Igi-
              <lb/>
              <note position="right" xlink:label="note-079-04" xlink:href="note-079-04a" xml:space="preserve">47. primi.</note>
            tur & </s>
            <s xml:id="echoid-s2620" xml:space="preserve">quadratum ex F I, minus erit quadrato ex F K, ideoque & </s>
            <s xml:id="echoid-s2621" xml:space="preserve">recta F I, mi-
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            nor erit, quàm recta F K.</s>
            <s xml:id="echoid-s2622" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2623" xml:space="preserve">QVOD ſi recta A B, ſecet circulum A C B D, bifariam, ita vt ſit eius
              <lb/>
            diameter, demonſtratum à nobis iam eſt theoremate tertio ſcholij propoſ.</s>
            <s xml:id="echoid-s2624" xml:space="preserve">21.
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            </s>
            <s xml:id="echoid-s2625" xml:space="preserve">præcedentis libri, rectam F B, minimam eſſe, & </s>
            <s xml:id="echoid-s2626" xml:space="preserve">F A, maximam. </s>
            <s xml:id="echoid-s2627" xml:space="preserve">Vnde non eſt
              <lb/>
            neceſſe, idem hoc loco demonſtrare. </s>
            <s xml:id="echoid-s2628" xml:space="preserve">Immo plura ibi ſunt demonſtrata, quàm
              <lb/>
            hic proponuntur. </s>
            <s xml:id="echoid-s2629" xml:space="preserve">Sirecta igitur linea circulum in partes inæquales ſecet, &</s>
            <s xml:id="echoid-s2630" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2631" xml:space="preserve">
              <lb/>
            Quod oſtendendum erat.</s>
            <s xml:id="echoid-s2632" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div237" type="section" level="1" n="112">
          <head xml:id="echoid-head126" xml:space="preserve">THEOREMA 2. PROPOS. 2.</head>
          <note position="right" xml:space="preserve">30. Secundi
            <lb/>
          huius.</note>
          <p>
            <s xml:id="echoid-s2633" xml:space="preserve">SI recta linea ſecans circulum ſegmentum au-
              <lb/>
            ferat, quod ſemicirculo minus non ſit, ſuper ipſa
              <lb/>
            autem recta linea ſtatuatur aliud circuli ſegmen-
              <lb/>
            tum, quod & </s>
            <s xml:id="echoid-s2634" xml:space="preserve">ſemicirculo maius non ſit, & </s>
            <s xml:id="echoid-s2635" xml:space="preserve">incli-
              <lb/>
            natum ſit ad alterum ſegmentum, quod ſemicircu
              <lb/>
            lo maius non eſt; </s>
            <s xml:id="echoid-s2636" xml:space="preserve">diuidatur vero inſiſtentis ſeg-
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            menti circunferentia in partes inæquales: </s>
            <s xml:id="echoid-s2637" xml:space="preserve">Recta
              <lb/>
            linea ſubtendens minorem circunferentiæ partem
              <lb/>
            minima eſtrectarum omnium ductarum ab illo
              <lb/>
            puncto, à quo ipſa ducitur, ad ſubiecti circuli cir-
              <lb/>
            cunferentiam illam, quæ ſemicirculo minor non
              <lb/>
            eſt: </s>
            <s xml:id="echoid-s2638" xml:space="preserve">& </s>
            <s xml:id="echoid-s2639" xml:space="preserve">reliqua omnia, quæ in præcedẽti, ſequuntur.</s>
            <s xml:id="echoid-s2640" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2641" xml:space="preserve">RECTA linea A B, à circulo A C B D, cuius centrum E, auferat ſeg-
              <lb/>
            mentum A C B, ſemicirculo non minus, ſed vel ſemicirculo æquale, vt in pri-
              <lb/>
            ma figura, vel maius, vt in alijs figuris; </s>
            <s xml:id="echoid-s2642" xml:space="preserve">& </s>
            <s xml:id="echoid-s2643" xml:space="preserve">ſuper recta A B, ſtatuatur ſegmen-
              <lb/>
            tum aliud circuli A F B, ſemicirculo non maius, ſed vel ſemicirculo æquale,
              <lb/>
            vt in poſtrema trium figurarum, vel minus, vt in primis duabus figuris, & </s>
            <s xml:id="echoid-s2644" xml:space="preserve">in-
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            clinatum ad ſegmentum alterum A D B, quod ſemicirculo maius non eſt, cum
              <lb/>
            A C B, vel ſemicirculo æquale, vel maius ponatur. </s>
            <s xml:id="echoid-s2645" xml:space="preserve">Diuidatur quoque </s>
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