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

List of thumbnails

< >
151
151 (424) 		152
152 (425)
153
153 (426) 		154
154 (427)
155
155 (428) 		156
156 (429)
157
157 (430) 		158
158 (431)
159
159 (432) 		160
160 (433)
< >
page |< < (428) of 568 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div164" type="section" level="1" n="76">
          <p>
            <s xml:id="echoid-s3132" xml:space="preserve">
              <pb o="428" file="0146" n="155" rhead="VERA CIRCULI"/>
            ſequentes Vqab, {aa.</s>
            <s xml:id="echoid-s3133" xml:space="preserve">/Vqab} ſumma terminorum convergentium
              <emph style="super">a + b</emph>
              <lb/>
            multiplicata in terminum convergentem primum
              <emph style="sub">a</emph>
            efficit
              <lb/>
            aa + ab: </s>
            <s xml:id="echoid-s3134" xml:space="preserve">& </s>
            <s xml:id="echoid-s3135" xml:space="preserve">ſumma terminorum convergentium immediate ſe-
              <lb/>
            quentium nempe Vqab + {aa/Vqab} multiplicata in primum terminum
              <lb/>
            convergentem
              <emph style="super">Vqab</emph>
            efficit etiam aa + ab; </s>
            <s xml:id="echoid-s3136" xml:space="preserve">ex his invenienda ſit ſe-
              <lb/>
            riei propoſitæ terminatio. </s>
            <s xml:id="echoid-s3137" xml:space="preserve">manifeſtum eſt quantitatem aa + ab
              <lb/>
            eodem modo fieri à terminis convergentibus
              <emph style="super">a, b,</emph>
            quo à termi-
              <lb/>
            nis convergentibus immediatè ſequentibus Vqab, {aa/Vqab:</s>
            <s xml:id="echoid-s3138" xml:space="preserve">} & </s>
            <s xml:id="echoid-s3139" xml:space="preserve">quo-
              <lb/>
            niam quantitates
              <emph style="super">a, b,</emph>
            indefinitæ ponuntur pro quibuslibet to-
              <lb/>
            tius ſeriei terminis convergentibus, evidens eſt ſummam quo-
              <lb/>
            rumcunque terminorum convergentium propoſitæ ſeriei mul-
              <lb/>
            tiplicatam in primum terminum convergentem efficere quan-
              <lb/>
            titatem æqualem illi, quæ fit à ſumma terminorum conver-
              <lb/>
            gentium immediatè ſequentium multiplicata etiam in primum
              <lb/>
            ſuum terminum convergentem; </s>
            <s xml:id="echoid-s3140" xml:space="preserve">cumque duo termini conver-
              <lb/>
            gentes duos terminos convergentes ſemper immediatè ſe-
              <lb/>
            quuntur, manifeſtum eſt ſummam duorum quorumlibet ter-
              <lb/>
            minorum convergentium multiplicatam in primum ſemper
              <lb/>
            efficere eandem quantitatem nempe aa + ab, atque ultimi ter-
              <lb/>
            mini convergentes ſunt æquales, & </s>
            <s xml:id="echoid-s3141" xml:space="preserve">proinde ſit ultimus ille
              <lb/>
            terminus ſeu ſeriei terminatio
              <emph style="super">z</emph>
            , quæ ſibi addita & </s>
            <s xml:id="echoid-s3142" xml:space="preserve">in ſum-
              <lb/>
            mam multiplicata efficit
              <emph style="super">2 zz</emph>
            , quæ quantitas debet eſſe æqua-
              <lb/>
            lis quantitati aa + ab, & </s>
            <s xml:id="echoid-s3143" xml:space="preserve">æquatione reſoluta dabitur
              <emph style="super">z</emph>
            ſeu ſeriei
              <lb/>
            terminatio {Vq aa + ab,/2} quam invenire oportuit.</s>
            <s xml:id="echoid-s3144" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3145" xml:space="preserve">Et proinde ad inveniendam cujuscunque ſeriei convergen-
              <lb/>
            tis terminationem; </s>
            <s xml:id="echoid-s3146" xml:space="preserve">opus eſt ſolummodo invenire quantitatem
              <lb/>
            eodem modo compoſitam ex terminis convergentibus primis,
              <lb/>
            quo componitur eadem quantitas ex terminis convergentibus
              <lb/>
            ſecundis.</s>
            <s xml:id="echoid-s3147" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div165" type="section" level="1" n="77">
          <head xml:id="echoid-head113" xml:space="preserve">CONSECTARIUM.</head>
          <p>
            <s xml:id="echoid-s3148" xml:space="preserve">Quoniam non refert in problemate ſive termini conver-
              <lb/>
            gentes a, b, ſint primi, ſecundi, vel tertii &</s>
            <s xml:id="echoid-s3149" xml:space="preserve">c; </s>
            <s xml:id="echoid-s3150" xml:space="preserve">manifeſtum </s>
          </p>
        </div>
      </text>
    </echo>
Impressum