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

Table of contents

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[41.] THEOR. 10. PROP. 11.
Page: 28 (16)
[42.] THEOR. 11. PROP. 12.
Page: 28 (16)
[43.] SCHOLIVM.
Page: 29 (17)
[44.] THEOREMA 12. PROPOS. 13.
Page: 29 (17)
[45.] SCHOLIVM.
Page: 30 (18)
[46.] THEOR. 13. PROPOS. 14.
Page: 30 (18)
[47.] THEOREMA 14. PROPOS. 15.
Page: 31 (19)
[48.] SCHOLIVM.
Page: 31 (19)
[49.] I.
Page: 31 (19)
[50.] II.
Page: 32 (20)
[51.] III.
Page: 32 (20)
[52.] IIII.
Page: 33 (21)
[53.] THEOREMA 15. PROPOS. 16.
Page: 33 (21)
[54.] COROLLARIVM.
Page: 34 (22)
[55.] SCHOLIVM.
Page: 34 (22)
[56.] LEMMA.
Page: 35 (23)
[57.] THEOR. 16. PROPOS. 17.
Page: 35 (23)
[58.] PROBL. 2. PROP. 18.
Page: 36 (24)
[59.] PROBL. 3. PROPOS. 19.
Page: 36 (24)
[60.] SCHOLIVM.
Page: 37 (25)
[61.] PROBL. 4. PROP. 20.
Page: 38 (26)
[62.] PROBL. 5. PROP. 21.
Page: 39 (27)
[63.] SCHOLIVM.
Page: 39 (27)
[64.] I.
Page: 39 (27)
[65.] II.
Page: 40 (28)
[66.] THEOR. 17. PROPOS. 22.
Page: 41 (29)
[67.] SCHOLIVM.
Page: 41 (29)
[68.] FINIS LIBRI PRIMI THEODOSII.
Page: 41 (29)
[69.] THEODOSII SPHAE RICORVM LIBER SECVNDVS.
Page: 42
[70.] DEFINITIO.
Page: 42
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            <s xml:id="echoid-s1077" xml:space="preserve">
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            tur æquale: </s>
            <s xml:id="echoid-s1078" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s1079" xml:space="preserve">ſemidiametri F H, E I, æquales erunt, atque adeo & </s>
            <s xml:id="echoid-s1080" xml:space="preserve">cir-
              <lb/>
              <note position="right" xlink:label="note-041-01" xlink:href="note-041-01a" xml:space="preserve">26. primi.</note>
            culi B F, C E, æquales. </s>
            <s xml:id="echoid-s1081" xml:space="preserve">quod primo loco propoſitum eſt.</s>
            <s xml:id="echoid-s1082" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1083" xml:space="preserve">_SINT_ iam circuli B F, C E, æquales. </s>
            <s xml:id="echoid-s1084" xml:space="preserve">Dico & </s>
            <s xml:id="echoid-s1085" xml:space="preserve">rectas A F, D E, ab eorum po-
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            lis ad circunferentias ductas eſſe æquales. </s>
            <s xml:id="echoid-s1086" xml:space="preserve">Conſtructis enim eiſdem, erunt ſemidiame-
              <lb/>
            tri F H, E I, æquales, & </s>
            <s xml:id="echoid-s1087" xml:space="preserve">circuli ipſi æqualiter acentro ſphæræ diſtabunt. </s>
            <s xml:id="echoid-s1088" xml:space="preserve">Perpen-
              <lb/>
              <note position="right" xlink:label="note-041-02" xlink:href="note-041-02a" xml:space="preserve">6. huius.</note>
            diculares ergo G H, G I, æquales erunt; </s>
            <s xml:id="echoid-s1089" xml:space="preserve">atque adeo & </s>
            <s xml:id="echoid-s1090" xml:space="preserve">reliquæ lineæ A H, D I,
              <lb/>
            erunt æquales. </s>
            <s xml:id="echoid-s1091" xml:space="preserve">Quoniam igitur latera A H, H F, lateribus D I, I E, æqualia
              <lb/>
            ſunt, continentq́; </s>
            <s xml:id="echoid-s1092" xml:space="preserve">angulos H, I, æquales, cum recti ſint ex defin. </s>
            <s xml:id="echoid-s1093" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1094" xml:space="preserve">lib, 11. </s>
            <s xml:id="echoid-s1095" xml:space="preserve">Eucl, erũt
              <lb/>
              <note position="right" xlink:label="note-041-03" xlink:href="note-041-03a" xml:space="preserve">4. primi,</note>
            baſes A F, D E, æquales. </s>
            <s xml:id="echoid-s1096" xml:space="preserve">Quod ſecundo loco propoſitum erat.</s>
            <s xml:id="echoid-s1097" xml:space="preserve"/>
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        <div xml:id="echoid-div121" type="section" level="1" n="66">
          <head xml:id="echoid-head77" xml:space="preserve">THEOR. 17. PROPOS. 22.</head>
          <note position="right" xml:space="preserve">0</note>
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            <s xml:id="echoid-s1098" xml:space="preserve">SI in ſphæra recta linea per centrum ducta re-
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            ctam aliquam lineam non per centrum ductam
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            bifariam ſecet, ad angulos rectos ipſam ſecabit.
              <lb/>
            </s>
            <s xml:id="echoid-s1099" xml:space="preserve">Quod ſi ad angulos rectos eam ſecet, bifariam
              <lb/>
            quoqueipſam ſecabit.</s>
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          </p>
          <p>
            <s xml:id="echoid-s1101" xml:space="preserve">IN ſphæra, cuius centrum A, recta A B, per centrum ducta rectam C D,
              <lb/>
              <figure xlink:label="fig-041-01" xlink:href="fig-041-01a" number="42">
                <image file="041-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/041-01"/>
              </figure>
            non per centrum ductam ſecet bifariam in
              <lb/>
            B. </s>
            <s xml:id="echoid-s1102" xml:space="preserve">Dico ipſam C D, ſecari ad angulos re-
              <lb/>
            ctos. </s>
            <s xml:id="echoid-s1103" xml:space="preserve">Ducto enim per rectas A B, C D, pla-
              <lb/>
              <note position="right" xlink:label="note-041-05" xlink:href="note-041-05a" xml:space="preserve">1. huius.</note>
            no, quod circulum faciat C D, qui maxi-
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              <note position="right" xlink:label="note-041-06" xlink:href="note-041-06a" xml:space="preserve">6. huius.</note>
            mus erit, cum per centrum ſphæræ tranſeat.
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            </s>
            <s xml:id="echoid-s1104" xml:space="preserve">Quoniam igitur in circulo C D, recta A B,
              <lb/>
            per eius centrum A, tranſiens rectam C D,
              <lb/>
            non per centrum ductam ſecat bifariam in
              <lb/>
            B, ad angulos rectos ipſam ſecabit. </s>
            <s xml:id="echoid-s1105" xml:space="preserve">Et ſi ad
              <lb/>
              <note position="right" xlink:label="note-041-07" xlink:href="note-041-07a" xml:space="preserve">3. tertij.</note>
            angulos rectos ipſam ſecet, bifariam ipſam
              <lb/>
            ſecabit. </s>
            <s xml:id="echoid-s1106" xml:space="preserve">Si igitur in ſphæra recta linea, &</s>
            <s xml:id="echoid-s1107" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s1108" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s1109" xml:space="preserve"/>
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        <div xml:id="echoid-div123" type="section" level="1" n="67">
          <head xml:id="echoid-head78" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s1110" xml:space="preserve">_ADDITVR_ hic in exemplari græco theorema aliud, quod id em prorſus eſt,
              <lb/>
            quod prop. </s>
            <s xml:id="echoid-s1111" xml:space="preserve">7. </s>
            <s xml:id="echoid-s1112" xml:space="preserve">demonſtratum eſt. </s>
            <s xml:id="echoid-s1113" xml:space="preserve">Vnde ſuperuacaneũ eſſe duximus, illud hic repetere.</s>
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          </p>
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        <div xml:id="echoid-div124" type="section" level="1" n="68">
          <head xml:id="echoid-head79" xml:space="preserve">FINIS LIBRI PRIMI THEODOSII.</head>
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