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

Page concordance

< >
Scan Original
121
122
123 399
124 400
125 401
126 402
127 403
128 404
129
130
131
132
133
134
135
136
137
138
139
140 413
141 414
142 415
143 416
144 417
145 418
146 419
147 420
148 421
149 422
150 423
< >
page |< < (422) of 568 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div157" type="section" level="1" n="72">
          <p>
            <s xml:id="echoid-s2992" xml:space="preserve">
              <pb o="422" file="0140" n="149" rhead="VERA CIRCULI"/>
            eſſe termino
              <emph style="sub">a</emph>
            , quoniam termino
              <emph style="super">a</emph>
            additur {bd - ad/c} ut fiat termi-
              <lb/>
            nus {ca + bd - ad/c}: </s>
            <s xml:id="echoid-s2993" xml:space="preserve">manifeſtum quoque eſt terminum {ca + bd - ad/c} mi-
              <lb/>
            norem eſſe termino b, quoniam differentia inter
              <emph style="super">a</emph>
            & </s>
            <s xml:id="echoid-s2994" xml:space="preserve">
              <emph style="super">b</emph>
            eſt ad
              <lb/>
            differentiam inter a & </s>
            <s xml:id="echoid-s2995" xml:space="preserve">{ca + bd - ad/c} in ratione majoris inæqualita-
              <lb/>
            tis: </s>
            <s xml:id="echoid-s2996" xml:space="preserve">evidens quoque eſt terminum {bc - be + ae/c} minorem eſſe ter-
              <lb/>
            mino b. </s>
            <s xml:id="echoid-s2997" xml:space="preserve">quoniam ex
              <emph style="sub">b</emph>
            ſubſtrahitur {be - ae/c} ut fiat {bc - be + ae/c}; </s>
            <s xml:id="echoid-s2998" xml:space="preserve">ma-
              <lb/>
            nifeſtum etiam eſt terminum {bc - be + ae/c} majorem eſſe termino
              <emph style="super">a</emph>
            ,
              <lb/>
            quoniam differentia inter
              <emph style="super">a</emph>
            & </s>
            <s xml:id="echoid-s2999" xml:space="preserve">
              <emph style="sub">b</emph>
            eſt ad differentiam inter
              <lb/>
            {bc - be + ae/c} & </s>
            <s xml:id="echoid-s3000" xml:space="preserve">
              <emph style="super">b</emph>
            in ratione majoris inæqualitatis: </s>
            <s xml:id="echoid-s3001" xml:space="preserve">evidens igitur
              <lb/>
            eſt differentiam inter terminos convergentes
              <emph style="super">a</emph>
            & </s>
            <s xml:id="echoid-s3002" xml:space="preserve">
              <emph style="super">b</emph>
            majorem
              <lb/>
            eſſe differentiâ inter terminos convergentes {ca + bd - ad/c} & </s>
            <s xml:id="echoid-s3003" xml:space="preserve">{bc - be + ae/c}.
              <lb/>
            </s>
            <s xml:id="echoid-s3004" xml:space="preserve">fed quoniam termini convergentes
              <emph style="super">a</emph>
            & </s>
            <s xml:id="echoid-s3005" xml:space="preserve">
              <emph style="super">b</emph>
            ponuntur indefiniti,
              <lb/>
            poſſunt
              <emph style="super">a</emph>
            & </s>
            <s xml:id="echoid-s3006" xml:space="preserve">
              <emph style="super">b</emph>
            ſumi loco quorumlibet terminorum convergen-
              <lb/>
            tium totius hujus ſeriei; </s>
            <s xml:id="echoid-s3007" xml:space="preserve">& </s>
            <s xml:id="echoid-s3008" xml:space="preserve">poſitis
              <emph style="super">a</emph>
            & </s>
            <s xml:id="echoid-s3009" xml:space="preserve">
              <emph style="super">b</emph>
            pro terminis hujus
              <lb/>
            ſeriei convergentibus quibuſcunque, ſequitur neceſſario ex
              <lb/>
            ſeriei compoſitione {ca + bd - ad.</s>
            <s xml:id="echoid-s3010" xml:space="preserve">/c}, {bc - be + ae/c} eſſe terminos conver-
              <lb/>
            gentes immediatè ſequentes: </s>
            <s xml:id="echoid-s3011" xml:space="preserve">cumque differentia terminorum
              <lb/>
              <emph style="super">a</emph>
            & </s>
            <s xml:id="echoid-s3012" xml:space="preserve">
              <emph style="super">b</emph>
            major ſit differentia terminorum {ca + bd - ad/c} & </s>
            <s xml:id="echoid-s3013" xml:space="preserve">{bc - be + ae/c},
              <lb/>
            evidens eſt differentiam terminorum convergentium priorum
              <lb/>
            ſemper eſſe majorem differentia terminorum convergentium
              <lb/>
            immediatè ſequentium; </s>
            <s xml:id="echoid-s3014" xml:space="preserve">& </s>
            <s xml:id="echoid-s3015" xml:space="preserve">igitur quò magis continuatur hæc
              <lb/>
            ſeries convergens eò minor fit differentia terminorum con-
              <lb/>
            vergentium: </s>
            <s xml:id="echoid-s3016" xml:space="preserve">& </s>
            <s xml:id="echoid-s3017" xml:space="preserve">quoniam hæc differentiarum diminutio ſem-
              <lb/>
            per fit proportionaliter nempe in ratione
              <emph style="super">b-a</emph>
            ad {bc - be + ae - ca - bd + ad;</s>
            <s xml:id="echoid-s3018" xml:space="preserve">/c}
              <lb/>
            igitur poſſunt inveniri hujus ſeriei termini convergentes quo-
              <lb/>
            rum differentia ſit omni exhibita quantitate minor; </s>
            <s xml:id="echoid-s3019" xml:space="preserve">& </s>
            <s xml:id="echoid-s3020" xml:space="preserve">igitur
              <lb/>
            imaginando hanc ſeriem in infinitum continuari, poſſumus
              <lb/>
            imaginari ultimos terminos convergentes eſſe </s>
          </p>
        </div>
      </text>
    </echo>
Impressum