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

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        <div xml:id="echoid-div201" type="section" level="1" n="101">
          <head xml:id="echoid-head113" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s2104" xml:space="preserve">_HINC_ fit, ſi circulorum maximorũ ad alios inclinatorum poli equaliter diſtent
              <lb/>
            à polis maximorum, ad quos inclinantur, inclinationes eſſe equales: </s>
            <s xml:id="echoid-s2105" xml:space="preserve">cuius vero polus
              <lb/>
            vicinior ſit pola eius, ad queminclinantur, inclinationem eſſe maiorem. </s>
            <s xml:id="echoid-s2106" xml:space="preserve">Nam ſi arcus
              <lb/>
              <note position="right" xlink:label="note-067-01" xlink:href="note-067-01a" xml:space="preserve">Coroll. 16.
                <lb/>
              1. huius.</note>
            _L P, MQ_, ſint æquales, erunt & </s>
            <s xml:id="echoid-s2107" xml:space="preserve">_C P, G Q,_ æquales, cum quadrantes ſint _C L,_
              <lb/>
            _GM;_ </s>
            <s xml:id="echoid-s2108" xml:space="preserve">atque adeo poli _P, Q,_ circulorum inclinatorum æqualiter diſtabunt à ſubie-
              <lb/>
            ctis planis circulorum _A B C D, E F G H._ </s>
            <s xml:id="echoid-s2109" xml:space="preserve">Quare, vt demonſtratum eſt in hac propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s2110" xml:space="preserve">æqualeserunt inclinationes circulorum _B N D, F O H,_ ad circulos _A B C D, E F G H._ </s>
            <s xml:id="echoid-s2111" xml:space="preserve">
              <lb/>
            Si vero arcus _L P,_ minor ſit arcu _M Q,_ erit reliquus arcus _C P,_ ex quadrante
              <lb/>
            maior arcu _G Q,_ reliquo ex quadrante. </s>
            <s xml:id="echoid-s2112" xml:space="preserve">Igitur, vt oſtendimus in hac propeſ. </s>
            <s xml:id="echoid-s2113" xml:space="preserve">maior
              <lb/>
            erit inclinatio circuli _B N D,_ ad circulum _A B C D,_ quam circuli _F O H,_ ad cir-
              <lb/>
            culum _E F G H._</s>
            <s xml:id="echoid-s2114" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2115" xml:space="preserve">_CONVERSVM_ quoque huius Theorematis, & </s>
            <s xml:id="echoid-s2116" xml:space="preserve">ſcholij demonſtrabimus in
              <lb/>
            bunc modum.</s>
            <s xml:id="echoid-s2117" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2118" xml:space="preserve">SI in ſphæris æqualibus maximi circuli ad maximos circulos
              <lb/>
            æqualiter inclinentur, erunt diſtantiæ polorum ipſorum à ſubiectis
              <lb/>
            planis æquales: </s>
            <s xml:id="echoid-s2119" xml:space="preserve">Illius verò, qui magis inclinatur, ſublimior erit po-
              <lb/>
            lus. </s>
            <s xml:id="echoid-s2120" xml:space="preserve">Item diſtantiæ polorum illorum circulorum, qui æqualiter incli
              <lb/>
            nantur, à polis circulorum, ad quos inclinantur, æquales erunt: </s>
            <s xml:id="echoid-s2121" xml:space="preserve">Di-
              <lb/>
            ſtantia vero poli illius circuli, qui magis inclinatur, à polo circuli,
              <lb/>
            ad quem inclinatur, minor erit.</s>
            <s xml:id="echoid-s2122" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2123" xml:space="preserve">_SI_ namque circuli _B N D, F O H,_ al circulos _A B C D, E F G H,_ æqualiter in-
              <lb/>
            clinentur, erunt anguli _A I N, E K O,_ æquales, ex defin 7 lib. </s>
            <s xml:id="echoid-s2124" xml:space="preserve">11. </s>
            <s xml:id="echoid-s2125" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s2126" xml:space="preserve">ac propterea
              <lb/>
              <note position="right" xlink:label="note-067-02" xlink:href="note-067-02a" xml:space="preserve">26. tertij.</note>
            & </s>
            <s xml:id="echoid-s2127" xml:space="preserve">arcus _A N, E O,_ æquales erunt. </s>
            <s xml:id="echoid-s2128" xml:space="preserve">Additis igitur quadrantibus _N P, O Q,_ æqudo
              <lb/>
            les erunt arcus _A P, E Q;_ </s>
            <s xml:id="echoid-s2129" xml:space="preserve">ac propterea & </s>
            <s xml:id="echoid-s2130" xml:space="preserve">reliqui _C P, G Q,_ ex ſemicirculis
              <lb/>
            æquales erunt.</s>
            <s xml:id="echoid-s2131" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2132" xml:space="preserve">_SI_ verò circulus _B N D,_ ad circulum _A B C D,_ magis inclinetur, quam circulus
              <lb/>
            _F O H,_ ad circulum _E F G H,_ erit minor angulus _A I N,_ angulo _E K O,_ vt in defi-
              <lb/>
            nitionem 7. </s>
            <s xml:id="echoid-s2133" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2134" xml:space="preserve">11 Eucl. </s>
            <s xml:id="echoid-s2135" xml:space="preserve">ſeripſimus; </s>
            <s xml:id="echoid-s2136" xml:space="preserve">ac propterea & </s>
            <s xml:id="echoid-s2137" xml:space="preserve">arcus _A H,_ minor erit arcu _F O._
              <lb/>
            </s>
            <s xml:id="echoid-s2138" xml:space="preserve">
              <note position="right" xlink:label="note-067-03" xlink:href="note-067-03a" xml:space="preserve">Scho. 26.
                <lb/>
              tcrtij.</note>
            Additis igitur quadrantibus _N P, O Q,_ minor erit arcus _A P,_ arcu _EQ;_ </s>
            <s xml:id="echoid-s2139" xml:space="preserve">ac proin-
              <lb/>
            de reliquus _C P,_ ex ſemicirculo _A N C,_ reliquo _G Q,_ ex ſemicirculo _F O G,_ maior erit.</s>
            <s xml:id="echoid-s2140" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2141" xml:space="preserve">_RVRSVS,_ ſi circuli æqualiter inclinentur, erunt arcus _C P, G Q,_ vt pro-
              <lb/>
            xime oſtendimus, æquales. </s>
            <s xml:id="echoid-s2142" xml:space="preserve">Cum ergo quadrantes ſint _C L, G M;_ </s>
            <s xml:id="echoid-s2143" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s2144" xml:space="preserve">arcus
              <lb/>
              <note position="right" xlink:label="note-067-04" xlink:href="note-067-04a" xml:space="preserve">Coroll. 16.
                <lb/>
              1. huius.</note>
            _L P, M Q,_ æquales.</s>
            <s xml:id="echoid-s2145" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2146" xml:space="preserve">_SI_ denique circulus _B N D,_ magis inclinetur, erit exproxime demoſtratis, ar@
              <lb/>
            cus _C P,_ maior arcu _G Q._ </s>
            <s xml:id="echoid-s2147" xml:space="preserve">Reliquus igitur _L P,_ ex quadrante _C L,_ minor erit re-
              <lb/>
            lique _M Q,_ ex quadrante _G M,_ &</s>
            <s xml:id="echoid-s2148" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2149" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2150" xml:space="preserve">_DVO_ quoque alia Theoremata in alia verſione hoc loco adiecta ſunt, vide-
              <lb/>
            licet.</s>
            <s xml:id="echoid-s2151" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div206" type="section" level="1" n="102">
          <head xml:id="echoid-head114" xml:space="preserve">I.</head>
          <p>
            <s xml:id="echoid-s2152" xml:space="preserve">CIRCVLI maximi tangentes eundem parallelum, æqualiter
              <lb/>
              <note position="right" xlink:label="note-067-05" xlink:href="note-067-05a" xml:space="preserve">26.</note>
            inclinantur ad maximum parallelorum: </s>
            <s xml:id="echoid-s2153" xml:space="preserve">qui vero maiorem paralle-
              <lb/>
            lum tangit, inclinatior eſt ad maximum parallelorum. </s>
            <s xml:id="echoid-s2154" xml:space="preserve">Et </s>
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