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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            _ergo_ H I, K L, _ponantur æquales, minor erit_ O I, _quàm_ K P. </s>
            <s xml:id="echoid-s3301" xml:space="preserve">_Quod eſt abſurdum._
              <lb/>
            </s>
            <s xml:id="echoid-s3302" xml:space="preserve">_Quia enim arcus_ E M, F N, _dimidij æqualium_ D E, F G, _æquales ſunt, & </s>
            <s xml:id="echoid-s3303" xml:space="preserve">non con=_
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            _tinui, non poterit_ O I, _minor eſſe, quam_ K P, _vt in ſecunda figura demonſtratum_
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            _eſt. </s>
            <s xml:id="echoid-s3304" xml:space="preserve">Nonergo arcus_ H I, _arcui_ K L, _æqualis eſt: </s>
            <s xml:id="echoid-s3305" xml:space="preserve">Sed nequeminor eſt oſtenſus. </s>
            <s xml:id="echoid-s3306" xml:space="preserve">Maior_
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            _igitur eſt. </s>
            <s xml:id="echoid-s3307" xml:space="preserve">Quod eſt propoſitum._</s>
            <s xml:id="echoid-s3308" xml:space="preserve"/>
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        <div xml:id="echoid-div272" type="section" level="1" n="126">
          <head xml:id="echoid-head140" xml:space="preserve">II.</head>
          <p>
            <s xml:id="echoid-s3309" xml:space="preserve">SI in ſphæra maximus circulus tangat aliquem ſphæræ circu-
              <lb/>
              <note position="right" xlink:label="note-097-01" xlink:href="note-097-01a" xml:space="preserve">9.</note>
            lum, alius autem maximus circulus ad parallelos obliquus ſit, tan-
              <lb/>
            gatque circulos maiores illis, quos tangit maximus circulus primò
              <lb/>
            poſitus, fuerintque eorum contactus in maximo circulo primo poſi-
              <lb/>
            to; </s>
            <s xml:id="echoid-s3310" xml:space="preserve">& </s>
            <s xml:id="echoid-s3311" xml:space="preserve">ſumantur à circulo obliquo circun ferentiæ æquales, quæ con-
              <lb/>
            tinuæ quidem non ſint, ſed tamen ſintad eaſdem partes maximi pa-
              <lb/>
            rallelorum; </s>
            <s xml:id="echoid-s3312" xml:space="preserve">per puncta autem terminantia æquales circunferentias
              <lb/>
            deſcribantur paralleli circuli: </s>
            <s xml:id="echoid-s3313" xml:space="preserve">HI circunferentias inæ quales interci-
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            pient de maximo circulo primò poſito, quarum ea, quæ propior erit
              <lb/>
            maximo parallelorum, maior erit remotiore.</s>
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            <s xml:id="echoid-s3315" xml:space="preserve">HOC _Theorema demonſtrabitur ex propoſ. </s>
            <s xml:id="echoid-s3316" xml:space="preserve">7. </s>
            <s xml:id="echoid-s3317" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s3318" xml:space="preserve">quemadmodum præce=_
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            _dens Theorema ex propoſ. </s>
            <s xml:id="echoid-s3319" xml:space="preserve">5. </s>
            <s xml:id="echoid-s3320" xml:space="preserve">demonſtratũ ſuit: </s>
            <s xml:id="echoid-s3321" xml:space="preserve">dummodo duo circuli maximi_ A B, A C,
              <lb/>
            _præcedentis Theorematis tangant duos parallelos, vt in propoſ. </s>
            <s xml:id="echoid-s3322" xml:space="preserve">7. </s>
            <s xml:id="echoid-s3323" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s3324" xml:space="preserve">dictum_
              <lb/>
            _eſt. </s>
            <s xml:id="echoid-s3325" xml:space="preserve">Reliqua conſtructio figuræ à conſtructione præcedentis Theorematis non dif=_
              <lb/>
            _fert, &</s>
            <s xml:id="echoid-s3326" xml:space="preserve">c._</s>
            <s xml:id="echoid-s3327" xml:space="preserve"/>
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        <div xml:id="echoid-div274" type="section" level="1" n="127">
          <head xml:id="echoid-head141" xml:space="preserve">III.</head>
          <p>
            <s xml:id="echoid-s3328" xml:space="preserve">SI in ſphæra maximus circulus aliquem ſphæræ circulum tan-
              <lb/>
              <note position="right" xlink:label="note-097-02" xlink:href="note-097-02a" xml:space="preserve">10.</note>
            gat, aliquis autem alius maximus circulus obliquus ad parallelos tan-
              <lb/>
            gat circulos maiores illis, quos tangebat maximus circulus primo
              <lb/>
            poſitus, fuerintque eorum contactus in maximo circulo primo poſi-
              <lb/>
            to; </s>
            <s xml:id="echoid-s3329" xml:space="preserve">ſumantur autem de obliquo circulo æquales circunferentiæ, quæ
              <lb/>
            continuæ quidem non ſint, ſed tamen ſint ad eaſdem partes maximi
              <lb/>
            parallelorum, per que puncta terminantia æquales circunferentias
              <lb/>
            deſcribantur maximi circuli, qui & </s>
            <s xml:id="echoid-s3330" xml:space="preserve">tangant eundem circulum, quem
              <lb/>
            tangebat maximus circulus primo poſitus, & </s>
            <s xml:id="echoid-s3331" xml:space="preserve">ſimiles parallelorum
              <lb/>
            circunferentias intercipiant, habeantque eos ſemicirculos, qui ten-
              <lb/>
            dunt à punctis contactuum ad puncta terminantia æquales obliqui
              <lb/>
            circuli circunferentias, per quæ deſcribuntur, eiuſmodi, vt minimè
              <lb/>
            cõueniant cum illo circuli maximi primò poſiti ſemicirculo, in quo
              <lb/>
            eſt contactus obliqui circuli inter apparentem polum, & </s>
            <s xml:id="echoid-s3332" xml:space="preserve">maximum
              <lb/>
            parallelorum: </s>
            <s xml:id="echoid-s3333" xml:space="preserve">Inæquales intercipient circunferentias de maximo
              <lb/>
            parallelorum, quarum propior circulo maximo primò poſito, ſem-
              <lb/>
            per erit maior remotiore.</s>
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