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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            <s xml:id="echoid-s3335" xml:space="preserve">HOC _etiam Theorema demonſtrabitur ex propoſ. </s>
            <s xml:id="echoid-s3336" xml:space="preserve">8. </s>
            <s xml:id="echoid-s3337" xml:space="preserve">buius lib. </s>
            <s xml:id="echoid-s3338" xml:space="preserve">quemadmodum_
              <lb/>
            _propoſitio 9. </s>
            <s xml:id="echoid-s3339" xml:space="preserve">ex propoſ. </s>
            <s xml:id="echoid-s3340" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3341" xml:space="preserve">fuit oſtenſa, dummodo maximi circuli propoſ. </s>
            <s xml:id="echoid-s3342" xml:space="preserve">9. </s>
            <s xml:id="echoid-s3343" xml:space="preserve">ex A,_
              <lb/>
            _prodeuntes tangant eundem circulum minoremillo, quem_ D C, _tangere debet, &</s>
            <s xml:id="echoid-s3344" xml:space="preserve">c._</s>
            <s xml:id="echoid-s3345" xml:space="preserve"/>
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        <div xml:id="echoid-div276" type="section" level="1" n="128">
          <head xml:id="echoid-head142" xml:space="preserve">THEOREMA 10. PROPOS. 10.</head>
          <note position="left" xml:space="preserve">11.</note>
          <p>
            <s xml:id="echoid-s3346" xml:space="preserve">SI polus parallelorum ſit in circunferentia ma
              <lb/>
            ximi circuli, quem duo alij maximi circuli ad angu
              <lb/>
            los rectos ſecent, quorum alter ſit vnus parallelo-
              <lb/>
            rum, alter verò ſit obliquus ad parallelos; </s>
            <s xml:id="echoid-s3347" xml:space="preserve">in hoc
              <lb/>
            autein obliquo circulo ſumãtur duo quælibet pun
              <lb/>
            cta ad eaſdem partes maximi illius paralleli, perq́;
              <lb/>
            </s>
            <s xml:id="echoid-s3348" xml:space="preserve">polum parallelorum, & </s>
            <s xml:id="echoid-s3349" xml:space="preserve">per vtium que illorum pun
              <lb/>
            ctorum deſcribantur maximi circuli: </s>
            <s xml:id="echoid-s3350" xml:space="preserve">Erit, vt cir-
              <lb/>
            cunferentia maximi parallelorum intercepta inter
              <lb/>
            maximum circulum primò poſitum, & </s>
            <s xml:id="echoid-s3351" xml:space="preserve">proximum
              <lb/>
            maximum circulum per polum, & </s>
            <s xml:id="echoid-s3352" xml:space="preserve">per vnum pun-
              <lb/>
            ctorum deſcriptum, ad circunferentiam obliqui
              <lb/>
            circuli inter eoſdem circulos interceptam, ita cir-
              <lb/>
            cunferentia maximi parallelorum intercepta inter
              <lb/>
            duos magnos circulos per polum, perque vtrum-
              <lb/>
            que punctorum deſcriptos, ad circunferentiam
              <lb/>
            aliquam, quæ ſit minor, quam circunferentia obli-
              <lb/>
            qui circuli inter vtrum que punctum intercepta.</s>
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            <s xml:id="echoid-s3354" xml:space="preserve">SIT polus A, parallelorum in circunferentia maximi circuli A B, quem
              <lb/>
            duo alij maximi circuli B D, C D, ſecent ad angulos rectos, & </s>
            <s xml:id="echoid-s3355" xml:space="preserve">ſit B D, paral-
              <lb/>
            lelorum maximus, & </s>
            <s xml:id="echoid-s3356" xml:space="preserve">C D, ad parallelos obliquus; </s>
            <s xml:id="echoid-s3357" xml:space="preserve">in quo ſumptis duobus
              <lb/>
            punctis vtcunque E, F, deſcribantur per A, polum, & </s>
            <s xml:id="echoid-s3358" xml:space="preserve">per E, F, circuli ma-
              <lb/>
              <note position="left" xlink:label="note-098-02" xlink:href="note-098-02a" xml:space="preserve">20. 1. huius</note>
            ximi A E G, A F H. </s>
            <s xml:id="echoid-s3359" xml:space="preserve">Dico, vt eſt arcus B H, ad arcum C F, ita eſſe arcum H G,
              <lb/>
            ad arcum minorem arcu F E. </s>
            <s xml:id="echoid-s3360" xml:space="preserve">Aut enim arcus C F, F E, commenſurabiles
              <lb/>
            ſunt, aut incommenſurabiles. </s>
            <s xml:id="echoid-s3361" xml:space="preserve">Sint primum commenſurabiles, vt in prima fi-
              <lb/>
            gura; </s>
            <s xml:id="echoid-s3362" xml:space="preserve">& </s>
            <s xml:id="echoid-s3363" xml:space="preserve">inuenta eorum maxima menſura P, diuidantur arcus C F, F E, in ar-
              <lb/>
              <note position="left" xlink:label="note-098-03" xlink:href="note-098-03a" xml:space="preserve">3. decimi.</note>
            cus maximæ menſuræ æquales, perque puncta diuiſionum, & </s>
            <s xml:id="echoid-s3364" xml:space="preserve">polum A, circu-
              <lb/>
              <note position="left" xlink:label="note-098-04" xlink:href="note-098-04a" xml:space="preserve">20. 1. huius</note>
            li maximi ducantur I M, K N, L O. </s>
            <s xml:id="echoid-s3365" xml:space="preserve">Quoniam igitur arcus continui C L, L </s>
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