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

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              <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>
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