Clavius, Christoph, Gnomonices libri octo, in quibus non solum horologiorum solariu[m], sed aliarum quo[quam] rerum, quae ex gnomonis umbra cognosci possunt, descriptiones geometricè demonstrantur

Page concordance

< >
Scan Original
31 11
32 12
33 13
34 14
35 15
36 16
37 17
38 18
39 19
40 20
41 21
42 22
43 23
44 24
45 25
46 26
47 27
48 28
49 29
50 30
51 31
52 32
53 33
54 34
55 35
56 36
57 37
58 38
59 39
60 40
< >
page |< < (45) of 677 > >|
    <echo version="1.0RC">
      <text xml:lang="it" type="free">
        <div xml:id="echoid-div168" type="section" level="1" n="49">
          <p>
            <s xml:id="echoid-s2990" xml:space="preserve">
              <pb o="45" file="0065" n="65" rhead="LIBER PRIMVS."/>
            Dico has lineas k N, L M, rectas eſſe, ſeq́ mutuo ſecare in centro E. </s>
            <s xml:id="echoid-s2991" xml:space="preserve">Cum enim circulus maximus
              <lb/>
            A N C k, per centrum E, tranſeat, per propoſ. </s>
            <s xml:id="echoid-s2992" xml:space="preserve">6. </s>
            <s xml:id="echoid-s2993" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2994" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2995" xml:space="preserve">Theodoſii, ſecabit vtique conicas ſuperfi-
              <lb/>
            cies E F G, E H I, per verticem E, atque adeo per axem A C, quòd idem circulus A N C K, per po-
              <lb/>
            los mundi A, C, tranſeat. </s>
            <s xml:id="echoid-s2996" xml:space="preserve">Quare communes ſectiones circuli, & </s>
            <s xml:id="echoid-s2997" xml:space="preserve">conorum, nempe E k L, E M N,
              <lb/>
            triangula erunt, per propoſ. </s>
            <s xml:id="echoid-s2998" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2999" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3000" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3001" xml:space="preserve">Apoll. </s>
            <s xml:id="echoid-s3002" xml:space="preserve">ac propterea E k, E L, E M, E N, communes ſectiones
              <lb/>
            ciuídem circuli, & </s>
            <s xml:id="echoid-s3003" xml:space="preserve">conicarum ſuperficierum, rectæ lineæ erunt. </s>
            <s xml:id="echoid-s3004" xml:space="preserve">Dico adhuc rectas E K, E N, & </s>
            <s xml:id="echoid-s3005" xml:space="preserve">EL,
              <lb/>
            E M, in directum eſſe conſtitutas.
              <lb/>
            </s>
            <s xml:id="echoid-s3006" xml:space="preserve">
              <figure xlink:label="fig-0065-01" xlink:href="fig-0065-01a" number="48">
                <image file="0065-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0065-01"/>
              </figure>
            Cum enim duo latera E C, E L, trian-
              <lb/>
            guli E C L, (coniunctis prius rectis
              <lb/>
            A M, C L) ęqualia ſint duobus lateri-
              <lb/>
              <note position="left" xlink:label="note-0065-01" xlink:href="note-0065-01a" xml:space="preserve">10</note>
            bus E A, E M, trianguli E A M, quòd
              <lb/>
            omnia ducantur è centro ſphæræ ad
              <lb/>
            eius ſuperficiem: </s>
            <s xml:id="echoid-s3007" xml:space="preserve">ſint autem & </s>
            <s xml:id="echoid-s3008" xml:space="preserve">baſes
              <lb/>
            C L, A M, æquales, ex theorem. </s>
            <s xml:id="echoid-s3009" xml:space="preserve">2.
              <lb/>
            </s>
            <s xml:id="echoid-s3010" xml:space="preserve">ſcholij propoſ. </s>
            <s xml:id="echoid-s3011" xml:space="preserve">21. </s>
            <s xml:id="echoid-s3012" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3013" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3014" xml:space="preserve">Theodoſii,
              <lb/>
            propterea quòd circuli F G, HI, ſunt
              <lb/>
            æquales; </s>
            <s xml:id="echoid-s3015" xml:space="preserve">erunt anguli C E L, A E M,
              <lb/>
            æquales: </s>
            <s xml:id="echoid-s3016" xml:space="preserve">Ac proinde cum A C, ſit re-
              <lb/>
              <note position="right" xlink:label="note-0065-02" xlink:href="note-0065-02a" xml:space="preserve">8. primi.</note>
            cta linea, nempeaxis, conſtituent quo-
              <lb/>
            que rectæ E L, E M, per ea, quæ ad pro-
              <lb/>
              <note position="left" xlink:label="note-0065-03" xlink:href="note-0065-03a" xml:space="preserve">20</note>
            poſ. </s>
            <s xml:id="echoid-s3017" xml:space="preserve">15. </s>
            <s xml:id="echoid-s3018" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3019" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3020" xml:space="preserve">Euclidis ex Proclo oſten-
              <lb/>
            dimus, vnam lineam rectam L M. </s>
            <s xml:id="echoid-s3021" xml:space="preserve">Eſt
              <lb/>
            igitur linea L M, communis nimirum
              <lb/>
            ſectio conicarum ſuperficierum, & </s>
            <s xml:id="echoid-s3022" xml:space="preserve">cir
              <lb/>
            culi A N C K, recta. </s>
            <s xml:id="echoid-s3023" xml:space="preserve">Eademq́ ratione
              <lb/>
            & </s>
            <s xml:id="echoid-s3024" xml:space="preserve">k N, recta erit linea, nec non & </s>
            <s xml:id="echoid-s3025" xml:space="preserve">com
              <lb/>
            munes ſectiones reliquorum circulo-
              <lb/>
            rum horariorum, & </s>
            <s xml:id="echoid-s3026" xml:space="preserve">dictarum ſuper-
              <lb/>
            ficierum conicarum, ſecantes ſeſe mutuo in centro E, per quod tranſeunt. </s>
            <s xml:id="echoid-s3027" xml:space="preserve">Quod primo loco
              <lb/>
            erat oſtendendum.</s>
            <s xml:id="echoid-s3028" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">30</note>
          <p>
            <s xml:id="echoid-s3029" xml:space="preserve">SINT rurſus circuli horarum ab ortu, vel occaſu K R N Q, L P M O, tangentes parallelos
              <lb/>
            F G, H I, in punctis K, L, M, N, in quibus eoſdem ſecat circulus horarius à meridie, vel media no-
              <lb/>
            cte A N C K, vt propoſ. </s>
            <s xml:id="echoid-s3030" xml:space="preserve">9. </s>
            <s xml:id="echoid-s3031" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s3032" xml:space="preserve">eſt demonſtratum. </s>
            <s xml:id="echoid-s3033" xml:space="preserve">Dico eos conicas ſuperficies tangere in
              <lb/>
            lineis rectis K N, L M, in quibus eaſdem ſuperficies ſecari demonſtrauimus à circulo A N C k.
              <lb/>
            </s>
            <s xml:id="echoid-s3034" xml:space="preserve">Sit enim recta S T, communis ſectio planorum, in quibus circuli F G, L M, quæ per definitionem
              <lb/>
            lib. </s>
            <s xml:id="echoid-s3035" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3036" xml:space="preserve">Theodoſii, vtrumque circulum tanget. </s>
            <s xml:id="echoid-s3037" xml:space="preserve">Et quia circulus L P M O, maximus, per propoſ. </s>
            <s xml:id="echoid-s3038" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3039" xml:space="preserve">
              <lb/>
            lib. </s>
            <s xml:id="echoid-s3040" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3041" xml:space="preserve">Theodoſii, tranſit per centrum ſphæræ E, manifeſtum eſt, ipſum tranſire per rectam L M,
              <lb/>
            quæ ex L, in M, per centrum E, extenditur: </s>
            <s xml:id="echoid-s3042" xml:space="preserve">alioqui, ducta in circulo L P M O, recta ex L, in M,
              <lb/>
            clauderent duæ rectæ lineæ, nempe ea, quæ modo ducta eſt, & </s>
            <s xml:id="echoid-s3043" xml:space="preserve">L M, ſuperficiem, quod eſt abſur-
              <lb/>
            dum. </s>
            <s xml:id="echoid-s3044" xml:space="preserve">Dico iam, circulum L P M O, conicas ſuperficies tangere in recta L M, nullo autem modo
              <lb/>
              <note position="left" xlink:label="note-0065-05" xlink:href="note-0065-05a" xml:space="preserve">40</note>
            ſecare. </s>
            <s xml:id="echoid-s3045" xml:space="preserve">Si namque eas ſecaret, fierent communes ſectiones, triangula, per propoſ. </s>
            <s xml:id="echoid-s3046" xml:space="preserve">3. </s>
            <s xml:id="echoid-s3047" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3048" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3049" xml:space="preserve">Apollo-
              <lb/>
            nij, quorum baſes in parallelis F G, H I, exiſterent, quandoquidem circulus L P M O, per verticẽ
              <lb/>
            E, conicarum ſuperficierum tranſit. </s>
            <s xml:id="echoid-s3050" xml:space="preserve">Igitur communis ſectio planorum, in quibus circuli F G,
              <lb/>
            L M, ſunt, circulum F G, ſecaret, faciens nimirum baſim trianguli in circulo F G, quod eſt abſur-
              <lb/>
            dum. </s>
            <s xml:id="echoid-s3051" xml:space="preserve">Tangit enim ipſum, vt dictum eſt, ex definitione lib. </s>
            <s xml:id="echoid-s3052" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3053" xml:space="preserve">Theodoſii. </s>
            <s xml:id="echoid-s3054" xml:space="preserve">Tangit ergo circulus
              <lb/>
            L P M O, conicas ſuperficies E F G, E H I, in recta L M, eademq́; </s>
            <s xml:id="echoid-s3055" xml:space="preserve">eſt ratio in cæteris, quod ſecun-
              <lb/>
            do loco propoſitum erat. </s>
            <s xml:id="echoid-s3056" xml:space="preserve">Circuli igitur horarũ à meridie, vel media nocte, ſecant ſuperficies, &</s>
            <s xml:id="echoid-s3057" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s3058" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s3059" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div172" type="section" level="1" n="50">
          <head xml:id="echoid-head53" xml:space="preserve">THEOREMA 12. PROPOSITIO 14.</head>
          <note position="left" xml:space="preserve">50</note>
          <note position="right" xml:space="preserve">Lineæ horarum
            <lb/>
          à mer. uel med.
            <lb/>
          noc. ſecant ſe-
            <lb/>
          ct@ones coni-
            <lb/>
          cas, quas pla-
            <lb/>
          num horologii
            <lb/>
          in conis, quorú
            <lb/>
          baſes ſunt pa-
            <lb/>
          rall elus ſemper
            <lb/>
          apparentiũ ma-
            <lb/>
          ximus, & maxi-
            <lb/>
          mus ſemper la-
            <lb/>
          tentium efficit,
            <lb/>
          in punctis, in
            <lb/>
          quibus eaſdem
            <lb/>
          tangunt linez
            <unsure/>
            <lb/>
          horarum ab or.
            <lb/>
          uel occ.</note>
          <p>
            <s xml:id="echoid-s3060" xml:space="preserve">LINEAE horarum à meridie, vel media nocte ſecant communes
              <lb/>
            ſectiones plani horologij cuiuſcunque, & </s>
            <s xml:id="echoid-s3061" xml:space="preserve">ſuperficierum conicarum,
              <lb/>
            quarum vertex eſt centrum mundi, baſes autem duo paralleli tangentes
              <lb/>
            Horizontem, quorum vnus eſt maximus ſemper apparentiũ, alter vero
              <lb/>
            maximus ſemper latentium: </s>
            <s xml:id="echoid-s3062" xml:space="preserve">In punctis autem ſectionum eaſdem com-
              <lb/>
            munes ſectiones tangunt lineæ horarum ab ortu, vel occaſu.</s>
            <s xml:id="echoid-s3063" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3064" xml:space="preserve">QVONIAM circuli horarum à meridie, vel media nocte ſecant ſuperficies has conicas </s>
          </p>
        </div>
      </text>
    </echo>
Impressum