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

List of thumbnails

< >
71
71 (51) 		72
72 (52)
73
73 (53) 		74
74 (54)
75
75 (55) 		76
76 (56)
77
77 (57) 		78
78 (58)
79
79 (59) 		80
80 (60)
< >
page |< < (52) of 677 > >|
    <echo version="1.0RC">
      <text xml:lang="it" type="free">
        <div xml:id="echoid-div190" type="section" level="1" n="57">
          <p>
            <s xml:id="echoid-s3446" xml:space="preserve">
              <pb o="52" file="0072" n="72" rhead="GNOMONICES"/>
            ergo duo anguli E O S, E O Q, duobus angulis F O S, F O Q, ęquales, ac proinde tam hi, quàm
              <lb/>
            illi, dimidium conſtituent quatuor angulorum ad punctum O, exiſtentium in plano circuli B C:
              <lb/>
            </s>
            <s xml:id="echoid-s3447" xml:space="preserve">Sed hi quatuor, per 2. </s>
            <s xml:id="echoid-s3448" xml:space="preserve">corollarium propoſ. </s>
            <s xml:id="echoid-s3449" xml:space="preserve">15. </s>
            <s xml:id="echoid-s3450" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3451" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3452" xml:space="preserve">Euclidis, quatuor rectis ſunt æquales. </s>
            <s xml:id="echoid-s3453" xml:space="preserve">Igi-
              <lb/>
            tur tam E O S, E O Q, quàm F O S, F O Q, duobus rectis æquales erunt, ac propterea in dire-
              <lb/>
              <note position="left" xlink:label="note-0072-01" xlink:href="note-0072-01a" xml:space="preserve">14. primi.</note>
              <note position="left" xlink:label="note-0072-02" xlink:href="note-0072-02a" xml:space="preserve">2. vndec.</note>
            ctum erunt rectæ S O, O Q, Triangulum ergo eſt Q R S, atque adeo in vno plano erit, in eo ſci-
              <lb/>
            licet, quod per S Q, Q R, ducitur. </s>
            <s xml:id="echoid-s3454" xml:space="preserve">Ducitur autem planum circuli L M, per has rectas S Q, Q R,
              <lb/>
            vt patet. </s>
            <s xml:id="echoid-s3455" xml:space="preserve">In eodem ergo plano cireuli L M, erit recta R S; </s>
            <s xml:id="echoid-s3456" xml:space="preserve">ac proinde circulus L M, per rectam
              <lb/>
            I k, tranſibit, ita vt per eandem ſecet duos circulos tangentes E G, F H. </s>
            <s xml:id="echoid-s3457" xml:space="preserve">Quare I k, communis ſe-
              <lb/>
            ctio eſt trium circulorum E G, F H, L M. </s>
            <s xml:id="echoid-s3458" xml:space="preserve">Quapropter ſi in Sphæra duo circuli maximi, &</s>
            <s xml:id="echoid-s3459" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s3460" xml:space="preserve">Quod demonſtrandum erat. </s>
            <s xml:id="echoid-s3461" xml:space="preserve">
              <lb/>
            </s>
          </p>
        </div>
        <div xml:id="echoid-div193" type="section" level="1" n="58">
          <head xml:id="echoid-head61" xml:space="preserve">LEMMA.</head>
          <p style="it">
            <s xml:id="echoid-s3462" xml:space="preserve">QVOD autem K I, coeat cum vtra-
              <lb/>
              <figure xlink:label="fig-0072-01" xlink:href="fig-0072-01a" number="55">
                <image file="0072-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0072-01"/>
              </figure>
            que E S, F S, hac ratione demonſtrabimus.
              <lb/>
            </s>
            <s xml:id="echoid-s3463" xml:space="preserve">Si enim K I, E S, non conueniunt, erunt vti-
              <lb/>
            que parallelæ, per definitionem 34. </s>
            <s xml:id="echoid-s3464" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3465" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3466" xml:space="preserve">
              <lb/>
            Euclidis, cum ſint in eodem plano circuli E G. </s>
            <s xml:id="echoid-s3467" xml:space="preserve">
              <lb/>
            Nam E S, tangens circulum E G, in eodem eſt
              <lb/>
              <note position="left" xlink:label="note-0072-04" xlink:href="note-0072-04a" xml:space="preserve">20</note>
            circuli plano, in quo videlicet ctiam eſt K I.
              <lb/>
            </s>
            <s xml:id="echoid-s3468" xml:space="preserve">Quare ſi ducatur & </s>
            <s xml:id="echoid-s3469" xml:space="preserve">R T, ipſi S F, paral-
              <lb/>
            lela, erit planum per K R, R T, ductum pla-
              <lb/>
              <note position="left" xlink:label="note-0072-05" xlink:href="note-0072-05a" xml:space="preserve">15. vndec.</note>
            no per S E, S F, ducto parallelum, atque adeò
              <lb/>
            rectæ K I, F S, in illis planis parallelis exiſten-
              <lb/>
            tes nunquam conuenient, cum nec ipſa plana
              <lb/>
            coeant vnquam. </s>
            <s xml:id="echoid-s3470" xml:space="preserve">I gitur K I, F S, non conue-
              <lb/>
            nientes, & </s>
            <s xml:id="echoid-s3471" xml:space="preserve">in codem plano circuli F H, exi-
              <lb/>
            ſtentes (Nam F S, tangens circulum F H, in
              <lb/>
              <note position="left" xlink:label="note-0072-06" xlink:href="note-0072-06a" xml:space="preserve">30</note>
            eodem eſt circuli plano, in quo ni mirum eſt quoque K I.) </s>
            <s xml:id="echoid-s3472" xml:space="preserve">parallelæ ſunt, per definitionem
              <lb/>
            34. </s>
            <s xml:id="echoid-s3473" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3474" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3475" xml:space="preserve">Euclidis. </s>
            <s xml:id="echoid-s3476" xml:space="preserve">Ac proi nde & </s>
            <s xml:id="echoid-s3477" xml:space="preserve">E S, F S, inter ſe parallelæ erunt, cum vtraque ipſi
              <lb/>
              <note position="left" xlink:label="note-0072-07" xlink:href="note-0072-07a" xml:space="preserve">9. vndec.</note>
            I K, parallela ſit, quod eſt abſurdum. </s>
            <s xml:id="echoid-s3478" xml:space="preserve">Oſtenſum eſt enim, rectas E S, F S, in puncto S, coi-
              <lb/>
            re. </s>
            <s xml:id="echoid-s3479" xml:space="preserve">Conuenient ergo rectæ K I, E S, cum non ſint parallelæ, in eodemq́ existant plano, vt
              <lb/>
            demonſtratum est. </s>
            <s xml:id="echoid-s3480" xml:space="preserve">Eademq́ ratione oſtendemus K I, F S, conuenire.</s>
            <s xml:id="echoid-s3481" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div195" type="section" level="1" n="59">
          <head xml:id="echoid-head62" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s3482" xml:space="preserve">QVAE in hac, & </s>
            <s xml:id="echoid-s3483" xml:space="preserve">præcedenti propoſ. </s>
            <s xml:id="echoid-s3484" xml:space="preserve">oſtendimus, demonſtrabimus alio modo, & </s>
            <s xml:id="echoid-s3485" xml:space="preserve">fortaſſis facilio-
              <lb/>
              <note position="left" xlink:label="note-0072-08" xlink:href="note-0072-08a" xml:space="preserve">40</note>
            vi, in ſcholio propoſ. </s>
            <s xml:id="echoid-s3486" xml:space="preserve">20. </s>
            <s xml:id="echoid-s3487" xml:space="preserve">hui{us} lib.</s>
            <s xml:id="echoid-s3488" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div197" type="section" level="1" n="60">
          <head xml:id="echoid-head63" xml:space="preserve">THEOREMA 16. PROPOSITIO 18.</head>
          <note position="left" xml:space="preserve">Planum ſecans
            <lb/>
          quotcunque pla
            <lb/>
          na eandem cõ-
            <lb/>
          munem ſectio-
            <lb/>
          nẽ habentia, cui
            <lb/>
          planũ illud æ-
            <lb/>
          quidiſtet, facit
            <lb/>
          communes ſe-
            <lb/>
          ctiones paralle-
            <lb/>
          las: ſi vero com-
            <lb/>
          munẽ illam ſe-
            <lb/>
          ctionẽ: ſecet, fa-
            <lb/>
          git communes
            <lb/>
          ſectiones coeun
            <lb/>
          tes in illo pun-
            <lb/>
          cto, in quo pla-
            <lb/>
          nũ ſecans com-
            <lb/>
          munẽ illorum
            <lb/>
          ſectionem diui-
            <lb/>
          dit.</note>
          <p>
            <s xml:id="echoid-s3489" xml:space="preserve">SI PLANA quotcunq; </s>
            <s xml:id="echoid-s3490" xml:space="preserve">vnam eandemq́; </s>
            <s xml:id="echoid-s3491" xml:space="preserve">habentia ſectionem com-
              <lb/>
            munem ſecentur plano quopiam alio, quod vni corum, vel communi
              <lb/>
            illorum ſectioni æquidiſtet, erunt omnium illorũ planorum, & </s>
            <s xml:id="echoid-s3492" xml:space="preserve">plani
              <lb/>
            ſecantis communes ſectiones, lineæ parallelæ: </s>
            <s xml:id="echoid-s3493" xml:space="preserve">Si verò eadem plana ſe-
              <lb/>
              <note position="left" xlink:label="note-0072-10" xlink:href="note-0072-10a" xml:space="preserve">50</note>
            centur plano, quod non æquidiſtet communi illorum ſectioni, coi-
              <lb/>
            bunt communes omnium illorum, & </s>
            <s xml:id="echoid-s3494" xml:space="preserve">plani ſecantis ſectiones in illo
              <lb/>
            puncto ſectionis communis, in quo planum ſecans ipſam interſecat.</s>
            <s xml:id="echoid-s3495" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3496" xml:space="preserve">PLANA quotcunque A B, C D, E F, R S, habentia eandem communem ſectionem G H,
              <lb/>
            ſecentur plano I K, quod æquidiſter primum, vt in priori figura, plano R S, vel communi ſectio-
              <lb/>
            ni G H, (Voco autem planum rectæ cuipiam æquidiſtans, quod infinitè productum nunquam
              <lb/>
            conuenlt cum linea illa recta infinitè quoque producta: </s>
            <s xml:id="echoid-s3497" xml:space="preserve">vel cui per rectam illam lineam planum
              <lb/>
            aliquod æquidiſtans duci poteſt.) </s>
            <s xml:id="echoid-s3498" xml:space="preserve">ſintq́ue communes ſectiones planorum A B, C D, E F, & </s>
            <s xml:id="echoid-s3499" xml:space="preserve">plani
              <lb/>
            ſecantis I k, rectæ L M, N O, P Q. </s>
            <s xml:id="echoid-s3500" xml:space="preserve">Dico has communes ſectiones parallelas eſſe. </s>
            <s xml:id="echoid-s3501" xml:space="preserve">Ducto </s>
          </p>
        </div>
      </text>
    </echo>
Impressum