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

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        <div xml:id="echoid-div197" type="section" level="1" n="95">
          <p>
            <s xml:id="echoid-s3666" xml:space="preserve">
              <pb o="444" file="0162" n="171" rhead="VERA CIRCULI"/>
            ut ſemper quilibet terminus unius ſeriei ſit major quam idem
              <lb/>
            numero terminus alterius ſeriei; </s>
            <s xml:id="echoid-s3667" xml:space="preserve">ſed in talibus ſeriebus quò
              <lb/>
            longius producuntur, eò minor eſt eorundem numero termi-
              <lb/>
            norum differentia: </s>
            <s xml:id="echoid-s3668" xml:space="preserve">ſed è contra noſtræ ſeries quò longius
              <lb/>
            producuntur, eò magis differunt iidem numero termini, ſicut
              <lb/>
            facillimè demonſtrari poteſt.</s>
            <s xml:id="echoid-s3669" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3670" xml:space="preserve">Experientia obſervo differentiam inter ſecundam duarum
              <lb/>
            mediarum arithmetice proportionalium & </s>
            <s xml:id="echoid-s3671" xml:space="preserve">ſecundam duarum
              <lb/>
            mediarum geometricè proportionalium ſemper eſſe multò
              <lb/>
            majorem differentia inter ſecundam duarum mediarum geo-
              <lb/>
            metricè proportionalium & </s>
            <s xml:id="echoid-s3672" xml:space="preserve">ſectorem circuli, ellipſeos vel
              <lb/>
            hyperbolæ; </s>
            <s xml:id="echoid-s3673" xml:space="preserve">quod notatu dignum exiſtimo, hinc enim col-
              <lb/>
            ligitur ſectorem differre vix ultra unitatem à ſecunda duarum
              <lb/>
            mediarum arithmeticè continuè proportionalium, quando
              <lb/>
            medium arithmeticum non excedit medium geometricum ul-
              <lb/>
            tra unitatem, quod ſummopere notandum, nam ex hoc evi-
              <lb/>
            dens eſt approximationem audacter eſſe adhibendam, quan-
              <lb/>
            do ita continuatur ſeries ut medietas prima notarum ſit
              <lb/>
            eadem in utroque termino convergente, quod experientia
              <lb/>
            etiam evincit; </s>
            <s xml:id="echoid-s3674" xml:space="preserve">nunquam enim in hoc caſu differt ſector
              <lb/>
            unitate à ſecunda duarum mediarum arithmeticè continuè
              <lb/>
            proportionalium.</s>
            <s xml:id="echoid-s3675" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3676" xml:space="preserve">Eſt etiam alia approximatio omnium breviſſima & </s>
            <s xml:id="echoid-s3677" xml:space="preserve">maximè
              <lb/>
            admiranda, etiamſi mihi non contingat illam demonſtratio-
              <lb/>
            ne geometrica munire; </s>
            <s xml:id="echoid-s3678" xml:space="preserve">nempe ſi primus notarum triens in
              <lb/>
            utroque termino convergente ſit eadem, ſector circuli, el-
              <lb/>
            lipſeos vel hyperbolæ ſemper differt infra unitatem à maxi-
              <lb/>
            mo quatuor arithmeticè continuè proportionalium inter ter-
              <lb/>
            minos noſtræ approximationis.</s>
            <s xml:id="echoid-s3679" xml:space="preserve"/>
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        <div xml:id="echoid-div199" type="section" level="1" n="96">
          <head xml:id="echoid-head132" xml:space="preserve">PROP. XXVI. THEOREMA.</head>
          <p>
            <s xml:id="echoid-s3680" xml:space="preserve">Sit hyperbola quæcunque C F N cujus centrum A, aſym-
              <lb/>
              <note position="left" xlink:label="note-0162-01" xlink:href="note-0162-01a" xml:space="preserve">TAB. XLIII.
                <lb/>
              fig. 4.</note>
            ptota A B, A O; </s>
            <s xml:id="echoid-s3681" xml:space="preserve">ſitque ejus ſector A F G L cum triangulo
              <lb/>
            circum ſcripto A F L: </s>
            <s xml:id="echoid-s3682" xml:space="preserve">aſymptotorum uni A B parallellæ du-
              <lb/>
            cantur rectæ F D, I M; </s>
            <s xml:id="echoid-s3683" xml:space="preserve">& </s>
            <s xml:id="echoid-s3684" xml:space="preserve">compleantur </s>
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