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

Table of contents

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[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)
[121.] LEMMA. I.
Page: 92 (80)
[122.] LEMMA. I I.
Page: 93 (81)
[123.] THEOREMA 9. PROPOS. 9.
Page: 94 (82)
[124.] SCHOLIVM.
Page: 95 (83)
[125.] I.
Page: 95 (83)
[126.] II.
Page: 97 (85)
[127.] III.
Page: 97 (85)
[128.] THEOREMA 10. PROPOS. 10.
Page: 98 (86)
[129.] COROLLARIVM.
Page: 100 (88)
[130.] THEOR. 11. PROPOS. 11.
Page: 100 (88)
[131.] LEMMA.
Page: 102 (90)
[132.] SCHOLIVM.
Page: 103 (91)
[133.] COROLLARIVM.
Page: 104 (92)
[134.] THEOREMA 12. PROPOS 12.
Page: 105 (93)
[135.] SCHOLIVM.
Page: 106 (94)
[136.] THEOR. 13. PROPOS. 13.
Page: 106 (94)
[137.] SCHOLIVM.
Page: 107 (95)
[138.] THEOREMA 14. PROPOS. 14.
Page: 107 (95)
[139.] FINIS LIBRI III. THEODOSII. AD LECTOREM.
Page: 108 (96)
[140.] CHRISTOPHORI CLAVII BAMBERGENSIS E SOCIETATE IESV SINVS, VEL SEMISSES RECTARVM IN CIRCVLO SVBTENSARVM: LINEAE TANGENTES: ATQVE SECANTES.
Page: 109
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            <s xml:id="echoid-s3413" xml:space="preserve">
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            culus maximus I K. </s>
            <s xml:id="echoid-s3414" xml:space="preserve">Quoniam igitur arcus continui F I, I E, æquales ſunt, erit
              <lb/>
            H K, maior quàm K G; </s>
            <s xml:id="echoid-s3415" xml:space="preserve">atque adeo H K, maior erit dimidio ipſius H G, Qua-
              <lb/>
              <note position="left" xlink:label="note-100-01" xlink:href="note-100-01a" xml:space="preserve">6. huius.</note>
            re maior erit proportio H K, ad F I, quàm arcus dimidij ipſius H G, ad F I:
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            </s>
            <s xml:id="echoid-s3416" xml:space="preserve">
              <note position="left" xlink:label="note-100-02" xlink:href="note-100-02a" xml:space="preserve">8. quinti.</note>
            Sed vt dimidium arcus H G, ad F I, dimidium arcus F E, ita eſt totus arcus
              <lb/>
              <note position="left" xlink:label="note-100-03" xlink:href="note-100-03a" xml:space="preserve">15. quinti.</note>
            H G, ad totum arcum F E, Igitur maior erit proportio H K, ad F I, quam H G,
              <lb/>
            ad F E: </s>
            <s xml:id="echoid-s3417" xml:space="preserve">Ponitur autem, vt H G, ad F E, ita B H, ad C F. </s>
            <s xml:id="echoid-s3418" xml:space="preserve">Igitur maior erit quo-
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            que proportio H K, ad F I, quàm B H, ad C F; </s>
            <s xml:id="echoid-s3419" xml:space="preserve">atque adeo arcus H K, ad ar-
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            cum arcu F I, maiorem erit, vt B H, ad C F. </s>
            <s xml:id="echoid-s3420" xml:space="preserve">Quod eſt abſurdum. </s>
            <s xml:id="echoid-s3421" xml:space="preserve">Demonſtra-
              <lb/>
              <note position="left" xlink:label="note-100-04" xlink:href="note-100-04a" xml:space="preserve">10. quinti.</note>
            tum enim proxime ſuit in ſecunda figura, non poſſe eſſe, vt eſt arcus B H, ad
              <lb/>
            C F, ita arcum H K, ad arcum arcu F I, maiorem. </s>
            <s xml:id="echoid-s3422" xml:space="preserve">Non ergo eſt, vt B H, ad
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            C F, ita H G, ad F E: </s>
            <s xml:id="echoid-s3423" xml:space="preserve">ſed neque, vt B H, ad C F, ita eſt H G, ad arcum arcu
              <lb/>
            F E, maiorem, vt demonſtratum eſt. </s>
            <s xml:id="echoid-s3424" xml:space="preserve">Igitur erit, vt B H, ad C F, ita H G, ad
              <lb/>
            arcum arcu F E, minorem. </s>
            <s xml:id="echoid-s3425" xml:space="preserve">Quare ſi polus parallelorum ſit in circunferentia,
              <lb/>
            &</s>
            <s xml:id="echoid-s3426" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3427" xml:space="preserve">Quod oſtendendum erat.</s>
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          <head xml:id="echoid-head143" xml:space="preserve">COROLLARIVM.</head>
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            <s xml:id="echoid-s3429" xml:space="preserve">HINC ſit, maiorem eſſe proportionem arcus B H, ad atcum C F, quàm arcus H G, ad
              <lb/>
            arcum F E. </s>
            <s xml:id="echoid-s3430" xml:space="preserve">Cum enim ſit, vt B H, ad C F, ita H G, ad atcum arcu F E, minorem: </s>
            <s xml:id="echoid-s3431" xml:space="preserve">Sit autem
              <lb/>
              <note position="left" xlink:label="note-100-05" xlink:href="note-100-05a" xml:space="preserve">10. huius.</note>
            maior proportio arcus H G, ad arcum arcu F E, minorem, quàm ad F E; </s>
            <s xml:id="echoid-s3432" xml:space="preserve">erit quoque maior
              <lb/>
              <note position="left" xlink:label="note-100-06" xlink:href="note-100-06a" xml:space="preserve">8. quinti.</note>
            proportio B H, ad C F, quàm H G, ad F E.</s>
            <s xml:id="echoid-s3433" xml:space="preserve"/>
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          <head xml:id="echoid-head144" xml:space="preserve">THEOR. 11. PROPOS. 11.</head>
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            <s xml:id="echoid-s3434" xml:space="preserve">SI polus parallelorum ſit in circunferentia ma
              <lb/>
            ximi circuli, quem duo alij maximi circuli ad an-
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            gulos rectos ſecent, quorum alter ſit vnus paralle-
              <lb/>
            lorum, alter vero ſit obliquus ad parallelos; </s>
            <s xml:id="echoid-s3435" xml:space="preserve">alius
              <lb/>
            autem maximus circulus per polos parallelorum
              <lb/>
            tranſiens obliquum circulũ ſecet inter maximum
              <lb/>
            parallelorum, & </s>
            <s xml:id="echoid-s3436" xml:space="preserve">eum, quem obliquus circulus tan
              <lb/>
            git: </s>
            <s xml:id="echoid-s3437" xml:space="preserve">Diameter ſphæræ ad diametrum eius circuli,
              <lb/>
            quem tãgit obliquus circulus, maiorem rationem
              <lb/>
            habet, quàm circunferentia maximi parallelorum
              <lb/>
            intercepta inter maximum circulum primo poſi-
              <lb/>
            tum, & </s>
            <s xml:id="echoid-s3438" xml:space="preserve">maximum circulum per polos parallelo-
              <lb/>
            rum tranſeuntem, ad circunferentiam obliqui cir-
              <lb/>
            culi inter eoſdem circulos interceptam.</s>
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