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

Page concordance

< >
Scan Original
51 39
52 40
53 41
54 42
55 43
56 44
57 45
58 46
59 47
60 48
61 49
62 50
63 51
64 52
65 53
66 54
67 55
68 56
69 57
70 58
71 59
72 60
73 61
74 62
75 63
76 64
77 65
78 66
79 67
80 68
< >
page |< < (48) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div179" type="section" level="1" n="93">
          <p>
            <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"/>
              </figure>
            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>
        </div>
        <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>
        </div>
      </text>
    </echo>
Impressum