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

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          <p>
            <s xml:id="echoid-s4300" xml:space="preserve">
              <pb o="477" file="0197" n="207" rhead="SUPER HUGEN. EXCEPT."/>
            quin id integrè demonſtretur; </s>
            <s xml:id="echoid-s4301" xml:space="preserve">quæ interim forma rarò à
              <lb/>
            Geometris exigitur. </s>
            <s xml:id="echoid-s4302" xml:space="preserve">Dico itaque;</s>
            <s xml:id="echoid-s4303" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4304" xml:space="preserve">Si daretur ratio Analytica (ſeu ratio notis Analyticis ex-
              <lb/>
            primenda) inter Circulum & </s>
            <s xml:id="echoid-s4305" xml:space="preserve">Diametri Quadratum, tunc Cir-
              <lb/>
            culus analyticè componeretur ex Quadratis, inſcripto & </s>
            <s xml:id="echoid-s4306" xml:space="preserve">cir-
              <lb/>
            cumſcripto. </s>
            <s xml:id="echoid-s4307" xml:space="preserve">Sed poſterius eſt abſurdum E. </s>
            <s xml:id="echoid-s4308" xml:space="preserve">Sequela Majoris
              <lb/>
            ſic probatur;</s>
            <s xml:id="echoid-s4309" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4310" xml:space="preserve">Quantitas quæſita & </s>
            <s xml:id="echoid-s4311" xml:space="preserve">determinata invenitur ex quantitati-
              <lb/>
            bus quibuſcunque eam determinantibus, in ea ratione, ſeu
              <lb/>
            relatione, quam habet quantitas determinata ad dictas quan-
              <lb/>
            titates determinantes. </s>
            <s xml:id="echoid-s4312" xml:space="preserve">Sed Quadratum inſcriptum & </s>
            <s xml:id="echoid-s4313" xml:space="preserve">cir-
              <lb/>
            cumſcriptum Circulum determinat, idemque ex illis Circu-
              <lb/>
            lus daretur in ea relatione, quam habet ad Diametri Quadra-
              <lb/>
            tum vel ejus ſemiſſem, h. </s>
            <s xml:id="echoid-s4314" xml:space="preserve">e. </s>
            <s xml:id="echoid-s4315" xml:space="preserve">ſi eſſet ratio analytica inter Cir-
              <lb/>
            culum & </s>
            <s xml:id="echoid-s4316" xml:space="preserve">diametri Quadratum; </s>
            <s xml:id="echoid-s4317" xml:space="preserve">Ex dictis quantitatibus de-
              <lb/>
            terminantibus analyticè componeretur Circulus. </s>
            <s xml:id="echoid-s4318" xml:space="preserve">Ex dictis
              <lb/>
            enim quantitatibus omnia analyticè componi poſſunt, quæ
              <lb/>
            ad ea rationem habent analyticam.</s>
            <s xml:id="echoid-s4319" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4320" xml:space="preserve">Secundi Syllogiſmi Minor eſt evidentiſſima. </s>
            <s xml:id="echoid-s4321" xml:space="preserve">Major autem
              <lb/>
            eſt axioma ab omnibus Geometris tacitè admiſſum.</s>
            <s xml:id="echoid-s4322" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4323" xml:space="preserve">Minor Syllogiſmi prioris ſic probatur.</s>
            <s xml:id="echoid-s4324" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4325" xml:space="preserve">Eodem modo componitur Circulus ex Quadrato inſcripto
              <lb/>
            & </s>
            <s xml:id="echoid-s4326" xml:space="preserve">circumſcripto, quo componitur Quadrans Circuli ex
              <lb/>
            Triangulo inſcripto & </s>
            <s xml:id="echoid-s4327" xml:space="preserve">Trapezio vel potius Quadrato cir-
              <lb/>
            cumſcripto. </s>
            <s xml:id="echoid-s4328" xml:space="preserve">Sed ex 11. </s>
            <s xml:id="echoid-s4329" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s4330" xml:space="preserve">Quadrans Circuli ſeu ſector
              <lb/>
            non poteſt componi analyticè ex Triangulo inſcripto & </s>
            <s xml:id="echoid-s4331" xml:space="preserve">Qua-
              <lb/>
            drilatero circumſcripto. </s>
            <s xml:id="echoid-s4332" xml:space="preserve">E.</s>
            <s xml:id="echoid-s4333" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4334" xml:space="preserve">Major eſt evidens. </s>
            <s xml:id="echoid-s4335" xml:space="preserve">At poterit fortaſſe diſtingui Minor,
              <lb/>
            dicendo; </s>
            <s xml:id="echoid-s4336" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s4337" xml:space="preserve">11. </s>
            <s xml:id="echoid-s4338" xml:space="preserve">veram eſſe in Methodo indefinita; </s>
            <s xml:id="echoid-s4339" xml:space="preserve">ſed
              <lb/>
            poſſe eſſe falſam in methodis Particularibus. </s>
            <s xml:id="echoid-s4340" xml:space="preserve">At inſto. </s>
            <s xml:id="echoid-s4341" xml:space="preserve">Omnis
              <lb/>
            methodus indefinita in methodos ſeu caſus Particulares eſt re-
              <lb/>
            ſolubilis. </s>
            <s xml:id="echoid-s4342" xml:space="preserve">Sed hæc methodus indefinita, nempe quod ſe-
              <lb/>
            ctor ſit terminatio datæ ſerie convergentis, in nullam parti-
              <lb/>
            culararem reſolvi poteſt. </s>
            <s xml:id="echoid-s4343" xml:space="preserve">Nulla igitur datur hic methodus
              <lb/>
            particul@ris. </s>
            <s xml:id="echoid-s4344" xml:space="preserve">Major patet, quia quantitates æquales in ſe mu-
              <lb/>
            tuò ſunt reſolubiles. </s>
            <s xml:id="echoid-s4345" xml:space="preserve">Minorem ita probo; </s>
            <s xml:id="echoid-s4346" xml:space="preserve">Si hæc </s>
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