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

Table of contents

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[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)
[101.] SCHOLIVM.
Page: 67 (55)
[102.] I.
Page: 67 (55)
[103.] II.
Page: 69 (57)
[104.] III.
Page: 69 (57)
[105.] IIII.
Page: 71 (59)
[106.] V.
Page: 72 (60)
[107.] THEOREMA 20. PROPOS. 22.
Page: 73 (61)
[108.] THEOR. 21. PROPOS. 23.
Page: 75 (63)
[109.] FINIS LIBRI I I. THEODOSII.
Page: 76 (64)
[110.] THEODOSII SPHAERICORVM LIBER TERTIVS.
Page: 77 (65)
[111.] THEOREMA 1. PROPOS. 1.
Page: 77 (65)
[112.] THEOREMA 2. PROPOS. 2.
Page: 79 (67)
[113.] THEOREMA 3. PROPOS. 3.
Page: 80 (68)
[114.] THEOREMA 4. PROPOS. 4.
Page: 81 (69)
[115.] LEMMA.
Page: 83 (71)
[116.] THEOR. 5. PROPOS. 5.
Page: 84 (72)
[117.] THEOREMA 6. PROPOS. 6.
Page: 85 (73)
[118.] LEMMA.
Page: 86 (74)
[119.] THEOR. 7. PROPOS. 7.
Page: 88 (76)
[120.] THEOREMA 8. PROPOS. 8.
Page: 90 (78)
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              <figure xlink:label="fig-056-01" xlink:href="fig-056-01a" number="62">
                <image file="056-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/056-01"/>
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            pterea & </s>
            <s xml:id="echoid-s1667" xml:space="preserve">arcus parallelo
              <lb/>
              <note position="left" xlink:label="note-056-01" xlink:href="note-056-01a" xml:space="preserve">28. tertij.</note>
            rum C V L, D X E, æ-
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            quales erunt. </s>
            <s xml:id="echoid-s1668" xml:space="preserve">Cum ergo
              <lb/>
              <note position="left" xlink:label="note-056-02" xlink:href="note-056-02a" xml:space="preserve">9. huius.</note>
            ſecẽtur bifariam in V, X,
              <lb/>
            vt dictum eſt, æquales e-
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            runt eorum medietates,
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            nimirum quatuor arcus
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            C V, V L, D X, X E. </s>
            <s xml:id="echoid-s1669" xml:space="preserve">Si
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            igitur arcubus ęqualibus
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            C V, D X, communis ar-
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            cus addatur V D, æqua-
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            les erunt arcus C D, V X:
              <lb/>
            </s>
            <s xml:id="echoid-s1670" xml:space="preserve">Eſt autem arcus V X, ar
              <lb/>
              <note position="left" xlink:label="note-056-03" xlink:href="note-056-03a" xml:space="preserve">10. huius.</note>
            cui A B, ſimilis. </s>
            <s xml:id="echoid-s1671" xml:space="preserve">Igitur
              <lb/>
            & </s>
            <s xml:id="echoid-s1672" xml:space="preserve">C D, eidem A B, ſimi
              <lb/>
            lis erit. </s>
            <s xml:id="echoid-s1673" xml:space="preserve">Non ſecus oſten
              <lb/>
            demus F G, eidem A B,
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            ſimilem eſſE; </s>
            <s xml:id="echoid-s1674" xml:space="preserve">nec non & </s>
            <s xml:id="echoid-s1675" xml:space="preserve">
              <lb/>
            arcus E L, H M, eidem
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            arcui A B, eſſe ſimiles. </s>
            <s xml:id="echoid-s1676" xml:space="preserve">Quod ſecundo loco proponebatur demonſtrandum.
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            </s>
            <s xml:id="echoid-s1677" xml:space="preserve">Siergo in ſphæra ſint paralleli circuli, &</s>
            <s xml:id="echoid-s1678" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1679" xml:space="preserve">Quod oſtendendum erat.</s>
            <s xml:id="echoid-s1680" xml:space="preserve"/>
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          <head xml:id="echoid-head102" xml:space="preserve">PROBL. 1. PROP. 14.</head>
          <note position="left" xml:space="preserve">17.</note>
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            <s xml:id="echoid-s1681" xml:space="preserve">CIRCVLO in ſphæra dato, qui minor ſit
              <lb/>
            quàm circulus maximus, datoq́ aliquo puncto
              <lb/>
            in eius circunferentia, per illud punctum deſcri-
              <lb/>
            bere circulum maximum, qui tangat datum cir-
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            culum.</s>
            <s xml:id="echoid-s1682" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1683" xml:space="preserve">IN ſphæra datus circulus ſit non maximus A B, cuius polus C, opor-
              <lb/>
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                <image file="056-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/056-02"/>
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            teatq́; </s>
            <s xml:id="echoid-s1684" xml:space="preserve">per A, punctum in eius circũferentia
              <lb/>
            datum, deſcribere maximum circulum, qui
              <lb/>
            circulum A B, tangat. </s>
            <s xml:id="echoid-s1685" xml:space="preserve">Per polum C, & </s>
            <s xml:id="echoid-s1686" xml:space="preserve">pun
              <lb/>
              <note position="left" xlink:label="note-056-05" xlink:href="note-056-05a" xml:space="preserve">20. i. huius.</note>
            ctum A, deſcribatur circulus maximus
              <lb/>
            C A D E B, in quo ſumatur quadrans A D,
              <lb/>
            & </s>
            <s xml:id="echoid-s1687" xml:space="preserve">polo D, interuallo D A, circulus deſcri-
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            batur A E, qui maximus erit, quòd recta
              <lb/>
              <note position="left" xlink:label="note-056-06" xlink:href="note-056-06a" xml:space="preserve">17. 1. huius.</note>
            ſubtenſa D A, latus ſit quadrati in maxi-
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            mo circulo deſcripti. </s>
            <s xml:id="echoid-s1688" xml:space="preserve">Dico circulum maxi-
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            mum A E, tangere circulum A B, in A. </s>
            <s xml:id="echoid-s1689" xml:space="preserve">Quo-
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            niam enim duo circuli A B, A E, eundem
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            circulum C A D, per eorum polos </s>
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