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

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            <s xml:id="echoid-s2051" xml:space="preserve">
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            culum B N D, inclinatiorem eſſe ad circulum A B C D, quàm F O H,
              <lb/>
            ad E F G H. </s>
            <s xml:id="echoid-s2052" xml:space="preserve">Deſcribantur enim per L, P, polos, & </s>
            <s xml:id="echoid-s2053" xml:space="preserve">per polos, M, Q, cir-
              <lb/>
              <note position="left" xlink:label="note-066-01" xlink:href="note-066-01a" xml:space="preserve">30. i. huius</note>
            culi maximi A N C, E O G; </s>
            <s xml:id="echoid-s2054" xml:space="preserve">ſitque communis ſectio circulorum A B C D,
              <lb/>
            B N D, recta B D; </s>
            <s xml:id="echoid-s2055" xml:space="preserve">circulorum autem A B C D, A N C, recta A C; </s>
            <s xml:id="echoid-s2056" xml:space="preserve">& </s>
            <s xml:id="echoid-s2057" xml:space="preserve">circulo-
              <lb/>
            rum B N D, A N C, recta N I: </s>
            <s xml:id="echoid-s2058" xml:space="preserve">quæ omnes rectæ per centrum ſphæræ I, tran-
              <lb/>
            ſibunt, cum circuli maximi per idem centrum ſphæræ ducantur. </s>
            <s xml:id="echoid-s2059" xml:space="preserve">Eodem ordi-
              <lb/>
              <note position="left" xlink:label="note-066-02" xlink:href="note-066-02a" xml:space="preserve">6. 1. huius.</note>
            dine ſint in alia ſphæra communes ſectiones circulorum, vt recta F H, circu-
              <lb/>
            lorum E F G H, F O H; </s>
            <s xml:id="echoid-s2060" xml:space="preserve">recta vero E G, circulorum E F G H, E O G; </s>
            <s xml:id="echoid-s2061" xml:space="preserve">& </s>
            <s xml:id="echoid-s2062" xml:space="preserve">re-
              <lb/>
            cta O K, circulorum F O H, E O G: </s>
            <s xml:id="echoid-s2063" xml:space="preserve">quæ omnes rectæ ſimiliter per centrum
              <lb/>
            ſphæræ K, tranſibunt. </s>
            <s xml:id="echoid-s2064" xml:space="preserve">Et quoniam circulus A N C, per polos circulorum
              <lb/>
            A B C D, B N D, tranſiens, eos ſecat ad angulos rectos; </s>
            <s xml:id="echoid-s2065" xml:space="preserve">erit viciſsim vterque
              <lb/>
              <note position="left" xlink:label="note-066-03" xlink:href="note-066-03a" xml:space="preserve">15. 1. huius</note>
            circulus A B C D, B N D, ad circulum A N C, rectus, atque adeo & </s>
            <s xml:id="echoid-s2066" xml:space="preserve">recta B D,
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            communis eorum ſectio, ad eundem circulum A N C, perpendicularis erit.
              <lb/>
            </s>
            <s xml:id="echoid-s2067" xml:space="preserve">
              <note position="left" xlink:label="note-066-04" xlink:href="note-066-04a" xml:space="preserve">19. vndec.</note>
            Quare anguli A I D, N I D, recti erunt, ex defin. </s>
            <s xml:id="echoid-s2068" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2069" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2070" xml:space="preserve">11. </s>
            <s xml:id="echoid-s2071" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s2072" xml:space="preserve">ac pro-
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              <figure xlink:label="fig-066-01" xlink:href="fig-066-01a" number="77">
                <image file="066-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/066-01"/>
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            inde A I N, angulus
              <lb/>
            erit inclinationis cir-
              <lb/>
            culi B N D, ad circu-
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            lum A B C D, ex de-
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            fin. </s>
            <s xml:id="echoid-s2073" xml:space="preserve">6. </s>
            <s xml:id="echoid-s2074" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2075" xml:space="preserve">11. </s>
            <s xml:id="echoid-s2076" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s2077" xml:space="preserve">Eo-
              <lb/>
            dem modo erit E K O,
              <lb/>
            angulus inclinationis
              <lb/>
            circuli F O H, ad cir-
              <lb/>
            circulũ E F G H. </s>
            <s xml:id="echoid-s2078" xml:space="preserve">Quo-
              <lb/>
            niam vero P, polus cir
              <lb/>
            culi B N D, ſublimior
              <lb/>
            ponitur ſupra circu-
              <lb/>
            lum A B C D, quàm
              <lb/>
            polus Q, circuli F O H,
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            ſupra circulum E F G H, erit maior arcus C P, arcu G Q. </s>
            <s xml:id="echoid-s2079" xml:space="preserve">Hi enim arcus,
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            cum ſint perpendiculares ad circulos A B C D, E F G H, altitudines polo-
              <lb/>
            rum P, Q, ſupra ipſos circulos metiuntur. </s>
            <s xml:id="echoid-s2080" xml:space="preserve">Sunt autem arcus P N, Q O,
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            æquales, cum ſint quadrantes. </s>
            <s xml:id="echoid-s2081" xml:space="preserve">Poli enim P, Q, à circulis maximis B N D,
              <lb/>
            F O H, per quadrantem abſunt. </s>
            <s xml:id="echoid-s2082" xml:space="preserve">Arcus ergo C N, maior erit arcu G O, ac pro
              <lb/>
              <note position="left" xlink:label="note-066-05" xlink:href="note-066-05a" xml:space="preserve">Coroll. 16.
                <lb/>
              huius.</note>
            rea A N, reliquus ex ſemicirculo A N C, minor erit reliquo E O, ex ſemicir
              <lb/>
            culo E O G. </s>
            <s xml:id="echoid-s2083" xml:space="preserve">Quare angulus A I N, angulo E K O, minor erit, ac proinde
              <lb/>
              <note position="left" xlink:label="note-066-06" xlink:href="note-066-06a" xml:space="preserve">Schol. 27.
                <lb/>
              tertij.</note>
            magis inclinatus erit circulus B N D, ad circulum A B C D, quam circulus
              <lb/>
            F O H, ad circulum E F G H, vt in explicatione definitionis 7. </s>
            <s xml:id="echoid-s2084" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2085" xml:space="preserve">11.
              <lb/>
            </s>
            <s xml:id="echoid-s2086" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s2087" xml:space="preserve">ſcripſimus.</s>
            <s xml:id="echoid-s2088" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2089" xml:space="preserve">SED ſintiam arcus C P, G Q, æquales, hoc eſt, poli B, Q, æqualiter di
              <lb/>
            ſtent à planis circulorum A B C D, E F G H. </s>
            <s xml:id="echoid-s2090" xml:space="preserve">Dico circulos B N D, F O H,
              <lb/>
            æqualiter inclinari ad circulos A B C D, E F G H. </s>
            <s xml:id="echoid-s2091" xml:space="preserve">Quoniam enim arcus C P,
              <lb/>
            G Q, æquales ſunt, ſi addantur quadrantes P N, Q O, erunt & </s>
            <s xml:id="echoid-s2092" xml:space="preserve">arcus C H,
              <lb/>
            G O, æquales; </s>
            <s xml:id="echoid-s2093" xml:space="preserve">ac propterea & </s>
            <s xml:id="echoid-s2094" xml:space="preserve">reliqui arcus A N, E O, ex ſęmicirculis æqua-
              <lb/>
            les erunt, Anguli igitur A I N, E K O, æquales erunt, ac propterea, ex defin.
              <lb/>
            </s>
            <s xml:id="echoid-s2095" xml:space="preserve">
              <note position="left" xlink:label="note-066-07" xlink:href="note-066-07a" xml:space="preserve">27. tertij.</note>
            7. </s>
            <s xml:id="echoid-s2096" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2097" xml:space="preserve">11. </s>
            <s xml:id="echoid-s2098" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s2099" xml:space="preserve">ſimiles, ſiue æquales erunt inclinationes circulorũ B N D, F O H,
              <lb/>
            ad circulos A B C D, E F G H. </s>
            <s xml:id="echoid-s2100" xml:space="preserve">Si igitur in ſphæris ęqualibus maximi circuli
              <lb/>
            ad maximos circulos, &</s>
            <s xml:id="echoid-s2101" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2102" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s2103" xml:space="preserve"/>
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