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

Table of figures

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          <head xml:id="echoid-head572" xml:space="preserve">THEOR. 37. PROPOS. 39.</head>
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            <s xml:id="echoid-s13692" xml:space="preserve">ANGVLI ſphærici eandem habẽt rationem,
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            quam eorum arcus.</s>
            <s xml:id="echoid-s13693" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s13694" xml:space="preserve">SINT duo anguli ſphærici BAC, EDF, quorum arcus BC, EF. </s>
            <s xml:id="echoid-s13695" xml:space="preserve">Dico
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            ita eſſe angulum A, ad angulum D, vt eſt arcus BC, ad arcum EF. </s>
            <s xml:id="echoid-s13696" xml:space="preserve">Erunt
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              <note position="right" xlink:label="note-409-01" xlink:href="note-409-01a" xml:space="preserve">Defin. 6.
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              huius.</note>
            enim A, D, poli arcuum BC, EF; </s>
            <s xml:id="echoid-s13697" xml:space="preserve">& </s>
            <s xml:id="echoid-s13698" xml:space="preserve">arcus AB, AC, DE, DF, quadrantes.
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            </s>
            <s xml:id="echoid-s13699" xml:space="preserve">Productis igitur arcu-
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              <figure xlink:label="fig-409-01" xlink:href="fig-409-01a" number="258">
                <image file="409-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/409-01"/>
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            bus BC, EF, ſuman-
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            tur quotcunque arcus
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            BG, GH, arcui BC,
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            & </s>
            <s xml:id="echoid-s13700" xml:space="preserve">quotcũq; </s>
            <s xml:id="echoid-s13701" xml:space="preserve">arcus FI,
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            IK, KL, arcui EF,
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            æquales; </s>
            <s xml:id="echoid-s13702" xml:space="preserve">ac per puncta
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            G, H, I, K, L, & </s>
            <s xml:id="echoid-s13703" xml:space="preserve">po-
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            los A, D, arcus circu-
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              <note position="right" xlink:label="note-409-02" xlink:href="note-409-02a" xml:space="preserve">20.1 Theod.</note>
            lorum maximorũ du-
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            cantur AG, AH, DI,
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            DK, DL, qui omnes
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            quadrãtes erunt, nem-
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            pe quadrantibus AB,
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              <note position="right" xlink:label="note-409-03" xlink:href="note-409-03a" xml:space="preserve">28. tertij.</note>
            AC, DE, DF, æquales, propterea quòd & </s>
            <s xml:id="echoid-s13704" xml:space="preserve">rectæ ſubtenſæ AG, AH, DI,
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            DK, DL, rectis ſubtenſis AB, AC, DE, DF, æquales ſunt, ex defin. </s>
            <s xml:id="echoid-s13705" xml:space="preserve">poli.
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            </s>
            <s xml:id="echoid-s13706" xml:space="preserve">Erunt ergo omnes anguli ad A, inter ſe æquales; </s>
            <s xml:id="echoid-s13707" xml:space="preserve">atque adeò quam multiplex
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              <note position="right" xlink:label="note-409-04" xlink:href="note-409-04a" xml:space="preserve">18. huius.</note>
            eſt arcus CH, arcus BC, tam multiplex erit aggregatum omnium angulorũ
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            ad A, anguli BAC: </s>
            <s xml:id="echoid-s13708" xml:space="preserve">Eademque ratione tam multiplex erit aggregatum om-
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            nium angulorum ad D, anguli EDF, quam multiplex eſt arcus EL, arcus
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            EF. </s>
            <s xml:id="echoid-s13709" xml:space="preserve">Quoniam verò ſi arcus CH, arcui EL, æqualis fuerit, etiam angulus
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            HAC, angulo EDL, æqualis eſt; </s>
            <s xml:id="echoid-s13710" xml:space="preserve">ſi autem arcus CH, maior ſuerit arcu EL,
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              <note position="right" xlink:label="note-409-05" xlink:href="note-409-05a" xml:space="preserve">18. huius.</note>
            etiam angulus HAC, angulo EDL, maior eſt; </s>
            <s xml:id="echoid-s13711" xml:space="preserve">& </s>
            <s xml:id="echoid-s13712" xml:space="preserve">ſi minor, minor; </s>
            <s xml:id="echoid-s13713" xml:space="preserve">deficient
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            propterea vnà arcus CH, & </s>
            <s xml:id="echoid-s13714" xml:space="preserve">angulus HAC, æquè multiplicia primæ magni-
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              <note position="right" xlink:label="note-409-06" xlink:href="note-409-06a" xml:space="preserve">12. huius.</note>
            tudinis BC, & </s>
            <s xml:id="echoid-s13715" xml:space="preserve">tertiæ BAC, ab arcu EL, & </s>
            <s xml:id="echoid-s13716" xml:space="preserve">angulo EDL, æque multiplici-
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            bus ſecundę magnitudinis EF, & </s>
            <s xml:id="echoid-s13717" xml:space="preserve">quartæ EDF; </s>
            <s xml:id="echoid-s13718" xml:space="preserve">vel vnà æqualia erunt, vel
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            vnà excedent. </s>
            <s xml:id="echoid-s13719" xml:space="preserve">Quare quę proportio eſt arcus BC, primæ magnitudinis ad
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              <note position="right" xlink:label="note-409-07" xlink:href="note-409-07a" xml:space="preserve">Defin. 6.
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              quinti.</note>
            arcum EF, ſecundam magnitudinem, ea erit anguli BAC, tertiæ magnitu-
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            dinis ad angulum EDF, quartam magnitudinem. </s>
            <s xml:id="echoid-s13720" xml:space="preserve">Itaque anguli ſphærici
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            eandem habent rationem, quam eorum arcus. </s>
            <s xml:id="echoid-s13721" xml:space="preserve">Quod erat demouſtrandum.</s>
            <s xml:id="echoid-s13722" xml:space="preserve"/>
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        <div xml:id="echoid-div1092" type="section" level="1" n="538">
          <head xml:id="echoid-head573" xml:space="preserve">COROLLARIVM.</head>
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            <s xml:id="echoid-s13723" xml:space="preserve">EX hoc ſequitur, @ta eſſe angulum ſphæricum quemcumque ad quatuor angulos rectos
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            ſphæricos, vt eſt arcus illius anguli ad totam circunferentiam circuli maximi; </s>
            <s xml:id="echoid-s13724" xml:space="preserve">& </s>
            <s xml:id="echoid-s13725" xml:space="preserve">contra.
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            </s>
            <s xml:id="echoid-s13726" xml:space="preserve">Cum enim ſit angulus ſphæricus quicunque ad angulum rectum ſphæricum, vt arcus il-
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              <note position="right" xlink:label="note-409-08" xlink:href="note-409-08a" xml:space="preserve">39. huius.</note>
            lius anguli ad quadrantem, nimirum ad arcum anguli recti, erit quoque idem angulus ad
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            quadruplum anguli recti nempe ad quatuor rectos, vt idem arcus illius anguli ad quadru-
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              <note position="right" xlink:label="note-409-09" xlink:href="note-409-09a" xml:space="preserve">Schol. 4.
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              quinti.</note>
            plum quadrantis, hoc eſt, ad totam circun ferentiam; </s>
            <s xml:id="echoid-s13727" xml:space="preserve">& </s>
            <s xml:id="echoid-s13728" xml:space="preserve">contra.</s>
            <s xml:id="echoid-s13729" xml:space="preserve"/>
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