Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

Table of contents

< >
< >
page |< < (739) of 568 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div488" type="section" level="1" n="174">
          <pb o="739" file="0483" n="505" rhead="IN LUDO ALEÆ."/>
          <p>
            <s xml:id="echoid-s10309" xml:space="preserve">Qui ſex vicibus idem ſuſcipit, ſors ejus eſt {31031/46656}a, & </s>
            <s xml:id="echoid-s10310" xml:space="preserve">po-
              <lb/>
            teſt 31031 contra 15625 deponere; </s>
            <s xml:id="echoid-s10311" xml:space="preserve">id eſt, paulò minus
              <lb/>
            quàm 2 ad 1.</s>
            <s xml:id="echoid-s10312" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10313" xml:space="preserve">Atque ita conſequenter quilibet jactuum numerus inueniri
              <lb/>
            poteſt. </s>
            <s xml:id="echoid-s10314" xml:space="preserve">Sed licet majori compendio progredi, ut in ſequen-
              <lb/>
            ti Propoſitione oſtendetur; </s>
            <s xml:id="echoid-s10315" xml:space="preserve">ſine quo calculus aliàs multo pro-
              <lb/>
            lixior foret.</s>
            <s xml:id="echoid-s10316" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div489" type="section" level="1" n="175">
          <head xml:id="echoid-head247" xml:space="preserve">
            <emph style="sc">Propositio</emph>
          XI.</head>
          <head xml:id="echoid-head248" style="it" xml:space="preserve">Invenire, quot vicibus ſuſcipere quis poſſit, ut dua-
            <lb/>
          bus teſſeris 12 puncta jaciat.</head>
          <p>
            <s xml:id="echoid-s10317" xml:space="preserve">SI quis primâ vice duos ſenarios jacere contendat, ap-
              <lb/>
            paret unum eſſe caſum, quo vincat, id eſt, ad ob-
              <lb/>
            tinendum a; </s>
            <s xml:id="echoid-s10318" xml:space="preserve">& </s>
            <s xml:id="echoid-s10319" xml:space="preserve">35 eſſe caſus, quibus perdat ſive nihil ha-
              <lb/>
            beat, quoniam 36 ſunt jactus. </s>
            <s xml:id="echoid-s10320" xml:space="preserve">Itaque habet, per 2
              <emph style="super">dam</emph>
              <lb/>
            Propoſitionem, {1/36}a.</s>
            <s xml:id="echoid-s10321" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10322" xml:space="preserve">Qui duabus vicibus idem ſuſcipit, ſi primâ vice duos
              <lb/>
            ſenarios jaciat, obtinebit a; </s>
            <s xml:id="echoid-s10323" xml:space="preserve">ſi verò primâ vice diver-
              <lb/>
            ſum eveniat, unus ipſi reſtat jactus, id quod ipſi, per
              <lb/>
            illud quod jam dictum eſt, valet {1/36}a.</s>
            <s xml:id="echoid-s10324" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10325" xml:space="preserve">Atqui ut primâ vice duos ſenarios jaciat, unus tan-
              <lb/>
            tum eſt caſus, ſed 35 caſus, quibus diverſum eveniat.
              <lb/>
            </s>
            <s xml:id="echoid-s10326" xml:space="preserve">Itaque ab initio unus caſus eſt, qui det ipſi a, & </s>
            <s xml:id="echoid-s10327" xml:space="preserve">35
              <lb/>
            qui dent {1/36}a; </s>
            <s xml:id="echoid-s10328" xml:space="preserve">id quod per 2
              <emph style="super">dam</emph>
            Propoſitionem valet
              <lb/>
            {71/2296}a Et remanet contracertanti {1225/1296}a.</s>
            <s xml:id="echoid-s10329" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10330" xml:space="preserve">Ex his invenire licet, qualis ſit ei ſors aut pars, qui
              <lb/>
            idem ſuſcipit quaternis jactibus, prætereundo caſum eum,
              <lb/>
            cùm quis illud ternis jactibus ſuſcipit.</s>
            <s xml:id="echoid-s10331" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10332" xml:space="preserve">Etenim, qui 4
              <emph style="super">or</emph>
            vicibus duos ſenarios jacere conten-
              <lb/>
            dit, ſi illud 1
              <emph style="super">ma</emph>
            aut 2
              <emph style="super">da</emph>
            vice faciat, obtinet a; </s>
            <s xml:id="echoid-s10333" xml:space="preserve">ſin mi-
              <lb/>
            nùs, reſtant ipſi duo jactus, qui per illud quod ſupe-
              <lb/>
            riùs dictum eſt, valent {71/1296}a. </s>
            <s xml:id="echoid-s10334" xml:space="preserve">Sed propter eandem </s>
          </p>
        </div>
      </text>
    </echo>
Impressum