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

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            <s xml:id="echoid-s1795" xml:space="preserve">
              <pb o="48" file="060" n="60" rhead=""/>
            Igitur arcus B E, A G, ſimiles erunt: </s>
            <s xml:id="echoid-s1796" xml:space="preserve">Ponuntur autem & </s>
            <s xml:id="echoid-s1797" xml:space="preserve">ſimiles B E, A D.
              <lb/>
            </s>
            <s xml:id="echoid-s1798" xml:space="preserve">Similes ergo ſunt inter ſe A G, A D; </s>
            <s xml:id="echoid-s1799" xml:space="preserve">ac proinde, cum ſint eiuſdem circuli,
              <lb/>
            inter ſe æquales erunt, totum, & </s>
            <s xml:id="echoid-s1800" xml:space="preserve">pars. </s>
            <s xml:id="echoid-s1801" xml:space="preserve">Quod eſt abſurdũ. </s>
            <s xml:id="echoid-s1802" xml:space="preserve">Nullus ergo alius
              <lb/>
            circulus maximus per E, ductus præter D E F, parallelum B E, tangit in E,
              <lb/>
            ſi A B C, eundem in B, tangit. </s>
            <s xml:id="echoid-s1803" xml:space="preserve">Quare ſi A B C, tangit B E, tanget & </s>
            <s xml:id="echoid-s1804" xml:space="preserve">D E F,
              <lb/>
            eundem B E.</s>
            <s xml:id="echoid-s1805" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1806" xml:space="preserve">POSTREMO maximi circuli A B C, D E F, auferant ex parallelis
              <lb/>
            A D C, G H, circunferentias ſimiles A D, G H; </s>
            <s xml:id="echoid-s1807" xml:space="preserve">& </s>
            <s xml:id="echoid-s1808" xml:space="preserve">neuter illorum per paral-
              <lb/>
            lelorum polos ducatur, aut alterum eorum tangat. </s>
            <s xml:id="echoid-s1809" xml:space="preserve">Dico circulos maximos
              <lb/>
              <figure xlink:label="fig-060-01" xlink:href="fig-060-01a" number="68">
                <image file="060-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/060-01"/>
              </figure>
            A B C, D E F, tangere alium quendam pa-
              <lb/>
            rallelum ipſis A D C, B E, minorẽ. </s>
            <s xml:id="echoid-s1810" xml:space="preserve">Quo-
              <lb/>
            niam enim circulus maximus A B C, neque
              <lb/>
            tranſit per polos parallelorum, neque alte
              <lb/>
            rum ipſorum tangit, erit circulus maximus
              <lb/>
            A B C, ad vtrumque parallelorum A D C,
              <lb/>
            G H, obliquus. </s>
            <s xml:id="echoid-s1811" xml:space="preserve">Sienim rectus eſſet, tranſi-
              <lb/>
            ret per ipſorum polos, quod non ponitur.
              <lb/>
            </s>
            <s xml:id="echoid-s1812" xml:space="preserve">
              <note position="left" xlink:label="note-060-01" xlink:href="note-060-01a" xml:space="preserve">13 .1. huius.</note>
            Tanget igitur A B C, duos circulos æqua-
              <lb/>
            les inter ſe, & </s>
            <s xml:id="echoid-s1813" xml:space="preserve">parallelos vtrique A D C,
              <lb/>
              <note position="left" xlink:label="note-060-02" xlink:href="note-060-02a" xml:space="preserve">2. huius.</note>
            G H. </s>
            <s xml:id="echoid-s1814" xml:space="preserve">Tangat ergo parallelum B E, qui mi
              <lb/>
            nor erit vtroque A D C, G H; </s>
            <s xml:id="echoid-s1815" xml:space="preserve">(cum A B C,
              <lb/>
            ipſos ſecet) atque adeo & </s>
            <s xml:id="echoid-s1816" xml:space="preserve">alter ſibi æqua-
              <lb/>
            lis, & </s>
            <s xml:id="echoid-s1817" xml:space="preserve">parallelus minor erit vtroque A D C, G H: </s>
            <s xml:id="echoid-s1818" xml:space="preserve">ac {pro}inde paralleli A D C,
              <lb/>
            G H, poſiti erũt inter illos duos, quos circulus A B C, tangit. </s>
            <s xml:id="echoid-s1819" xml:space="preserve">Dico & </s>
            <s xml:id="echoid-s1820" xml:space="preserve">D E F,
              <lb/>
            eundem B E, tangere. </s>
            <s xml:id="echoid-s1821" xml:space="preserve">Si enim non tangit, deſcribatur per punctum H, quod
              <lb/>
            eſt inter circulum B E, & </s>
            <s xml:id="echoid-s1822" xml:space="preserve">ſibi æqualem, ac parallelum, ut oſtendimus, cir-
              <lb/>
              <note position="left" xlink:label="note-060-03" xlink:href="note-060-03a" xml:space="preserve">15. huius.</note>
            culus maximus K H, tangens B E, in I; </s>
            <s xml:id="echoid-s1823" xml:space="preserve">eruntq́; </s>
            <s xml:id="echoid-s1824" xml:space="preserve">ſemicirculi, quorum alter ex
              <lb/>
            I, per H, alter vero ex B, per G, tranſit, non coeuntes, vt conſtat ex figura
              <lb/>
              <figure xlink:label="fig-060-02" xlink:href="fig-060-02a" number="69">
                <image file="060-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/060-02"/>
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            propoſi. </s>
            <s xml:id="echoid-s1825" xml:space="preserve">13. </s>
            <s xml:id="echoid-s1826" xml:space="preserve">huius libri, & </s>
            <s xml:id="echoid-s1827" xml:space="preserve">ex demonſtra-
              <lb/>
              <note position="left" xlink:label="note-060-04" xlink:href="note-060-04a" xml:space="preserve">13. huius.</note>
            tis ibidem. </s>
            <s xml:id="echoid-s1828" xml:space="preserve">Igitur arcus A K, G H, ſimi-
              <lb/>
            les erunt: </s>
            <s xml:id="echoid-s1829" xml:space="preserve">Ponuntur autem & </s>
            <s xml:id="echoid-s1830" xml:space="preserve">A D, G H,
              <lb/>
            ſimiles. </s>
            <s xml:id="echoid-s1831" xml:space="preserve">Similes igitur ſunt A K, A D; </s>
            <s xml:id="echoid-s1832" xml:space="preserve">atque
              <lb/>
            adeo, cum ſint eiuſdem circuli, inter ſe æ-
              <lb/>
            quales erunt, totum & </s>
            <s xml:id="echoid-s1833" xml:space="preserve">pars. </s>
            <s xml:id="echoid-s1834" xml:space="preserve">Quod eſt ab-
              <lb/>
            ſurdum. </s>
            <s xml:id="echoid-s1835" xml:space="preserve">Nullus ergo alius circulus maxi-
              <lb/>
            mus per H, deſcriptus, præter D E F, paral-
              <lb/>
            lelum B E, tangit, ſi A B C, eundem tangit
              <lb/>
            in B. </s>
            <s xml:id="echoid-s1836" xml:space="preserve">Quare ſi A B C, tangit circulum B E,
              <lb/>
            tanget & </s>
            <s xml:id="echoid-s1837" xml:space="preserve">D E F, eundem B E. </s>
            <s xml:id="echoid-s1838" xml:space="preserve">Quapropter
              <lb/>
            maximi circuli, qui ſimiles circunferentias,
              <lb/>
            &</s>
            <s xml:id="echoid-s1839" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1840" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s1841" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div183" type="section" level="1" n="94">
          <head xml:id="echoid-head106" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s1842" xml:space="preserve">_MANIFESTVM_ autem eſt, circulos maximos _A B C, D E F,_ ita tangere
              <lb/>
            eundem parallelum _B E,_ vt ſemicirculi eorum à contactibus per arcus ſimiles proce-
              <lb/>
            dentes non coeant. </s>
            <s xml:id="echoid-s1843" xml:space="preserve">Alias non eſſent arcus ablati ſimiles, vt conſtat ex propoſ.</s>
            <s xml:id="echoid-s1844" xml:space="preserve">13.
              <lb/>
            </s>
            <s xml:id="echoid-s1845" xml:space="preserve">buius libri.</s>
            <s xml:id="echoid-s1846" xml:space="preserve"/>
          </p>
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