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

Table of contents

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[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)
[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)
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            <s xml:id="echoid-s2813" xml:space="preserve">
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            quod eſt propoſitum. </s>
            <s xml:id="echoid-s2814" xml:space="preserve">Ex his constat, arcum H E, in figura propoſitionis
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            minorem eſſe arcu D F. </s>
            <s xml:id="echoid-s2815" xml:space="preserve">Nam cum angulus F M K, acutus ſit, & </s>
            <s xml:id="echoid-s2816" xml:space="preserve">H N K,
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            ebtuſus, ſi ex M, N, ad D E, perpẽdiculares ducerentur, caderent hæ in ar
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            cus D F, B H, auferrentque, vt in proximo lemmatc oſtendimus, arcus
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            æquales. </s>
            <s xml:id="echoid-s2817" xml:space="preserve">Quare arcus H E, minor est arcu D F.</s>
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          <head xml:id="echoid-head130" xml:space="preserve">THEOR. 5. PROPOS. 5.</head>
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            <s xml:id="echoid-s2819" xml:space="preserve">SI in circunferentia maximi circuli ſit polus
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            parallelorum, huncque maximum circulum ſecẽt
              <lb/>
            ad angulos rectos duo alij maximi circuli, quorú
              <lb/>
            alter ſit vnus parallelorum, alter verò obliquus ſit
              <lb/>
            ad parallelos; </s>
            <s xml:id="echoid-s2820" xml:space="preserve">ab hoc autem obliquo circulo æqua
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            les circunferentiæ ſumantur deinceps ad eandem
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            partem maximi parallelorum, perque illa puncta
              <lb/>
            terminantia æquales circunferentias deſcriban-
              <lb/>
            tur paralleli circuli: </s>
            <s xml:id="echoid-s2821" xml:space="preserve">Circunferentiæ maximi illius
              <lb/>
            circuli primo poſiti inter parallelos interceptæ in-
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            æquales erunt, ſemperque ea, quæ propior fuerit
              <lb/>
            maximo parallelorum, remotiore maior erit.</s>
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            <s xml:id="echoid-s2823" xml:space="preserve">IN circunferentia maximi circuli A B C D, ſit A, polus parallelorum,
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            cumq́ue fecent duo maximi circuli B D, E C, ad angulos rectos, quorum B D,
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              <figure xlink:label="fig-084-01" xlink:href="fig-084-01a" number="92">
                <image file="084-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/084-01"/>
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            ſit maximus parallelorum, & </s>
            <s xml:id="echoid-s2824" xml:space="preserve">E C, ad paralle
              <lb/>
            los obliquus: </s>
            <s xml:id="echoid-s2825" xml:space="preserve">& </s>
            <s xml:id="echoid-s2826" xml:space="preserve">per F, G, H, puncta, quæ ex
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            obliquo circulo arcus æquales auferunt F G,
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            G H, deſcribantur paralleli I K, L M, N O, ex
              <lb/>
            polo A. </s>
            <s xml:id="echoid-s2827" xml:space="preserve">Dico arcum I L, maiorẽ eſſe arcu L N.
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            </s>
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              <note position="left" xlink:label="note-084-01" xlink:href="note-084-01a" xml:space="preserve">20. 1. huius</note>
            Per polum enim A, & </s>
            <s xml:id="echoid-s2829" xml:space="preserve">punctum G, circulus
              <lb/>
            maximus deſcribatur A P, ſecans parallelos in
              <lb/>
            P, Q. </s>
            <s xml:id="echoid-s2830" xml:space="preserve">Quoniam igitur in ſphæræ ſuperficie
              <lb/>
            intra periphæriam circuli I K, punctum G, ſi-
              <lb/>
            gnatum eſt præter polum A, & </s>
            <s xml:id="echoid-s2831" xml:space="preserve">ex G, duo ar-
              <lb/>
            cus G P, G F, circulorum maximorum ca-
              <lb/>
            dunt in circunferentiam circuli I K; </s>
            <s xml:id="echoid-s2832" xml:space="preserve">erit ar-
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              <note position="left" xlink:label="note-084-02" xlink:href="note-084-02a" xml:space="preserve">Schol. 11.
                <lb/>
              @. huius.</note>
            cus G P, omnium minimus; </s>
            <s xml:id="echoid-s2833" xml:space="preserve">atque adeo minor
              <lb/>
            quam G F: </s>
            <s xml:id="echoid-s2834" xml:space="preserve">quod arcus G P, G F, minores ſint ſemicirculo, cum ſe non inter-
              <lb/>
            ſecent, antequam parallelum I K, diuidunt. </s>
            <s xml:id="echoid-s2835" xml:space="preserve">Rurſus quia in ſuperficie ſphæræ
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            extra periphæriam circuli N O, punctum G, ſignatum eſt præter eius polum;</s>
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