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

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            <s xml:id="echoid-s4205" xml:space="preserve">
              <pb o="473" file="0193" n="203" rhead="AD RESP. JAC. GREG."/>
            terit, quoniam tunc ignotum erit, quomodo terminatio com-
              <lb/>
            poſita ſit ex primis & </s>
            <s xml:id="echoid-s4206" xml:space="preserve">ſecundis terminis. </s>
            <s xml:id="echoid-s4207" xml:space="preserve">E. </s>
            <s xml:id="echoid-s4208" xml:space="preserve">G. </s>
            <s xml:id="echoid-s4209" xml:space="preserve">Si a ſit 1 & </s>
            <s xml:id="echoid-s4210" xml:space="preserve">b, 2
              <lb/>
            quomodo probabitur per
              <emph style="sc">XI</emph>
            ejus Propoſitionem, termina-
              <lb/>
            tionem non eſſe {7/3}. </s>
            <s xml:id="echoid-s4211" xml:space="preserve">Ut ergo concludatur, rationem Circu-
              <lb/>
            li ad quadratum diametri ejus non eſſe analyticam, demon-
              <lb/>
            ftrari non ſolum debet, quod ſector Circuli non ſit ana-
              <lb/>
            lyticus indefinite ad figuram ſuam inſcriptam, licet illa de-
              <lb/>
            monſtratio non careat ſuâ pulchritudine, ſed quod illud etiam
              <lb/>
            verum ſit in omni caſu definito.</s>
            <s xml:id="echoid-s4212" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4213" xml:space="preserve">Dico præterea, ſi quantitates a & </s>
            <s xml:id="echoid-s4214" xml:space="preserve">b maneant indetermi-
              <lb/>
            natæ, terminationem forte reduci ad æquationem ex iis, qua-
              <lb/>
            rum radices dari nequeunt; </s>
            <s xml:id="echoid-s4215" xml:space="preserve">& </s>
            <s xml:id="echoid-s4216" xml:space="preserve">contrarium probari per
              <emph style="sc">XI</emph>
            e-
              <lb/>
            jus Propoſitionem, neque per Supplementum, non poterit, ni-
              <lb/>
            hilominus ſi illa terminatio reducta ſit ad quandam æquatio-
              <lb/>
            nem ejus naturæ, crederem Quadraturam Geometricè eſſe in-
              <lb/>
            ventam per interſectionem quarundam linearum curvarum,
              <lb/>
            quæ in Geometriâ admittuntur.</s>
            <s xml:id="echoid-s4217" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4218" xml:space="preserve">Non inhærebo in aliis objectionibus, quas propoſui; </s>
            <s xml:id="echoid-s4219" xml:space="preserve">Di-
              <lb/>
            cam tantum, has, ſicuti locum amplius non habent poſt cor-
              <lb/>
            rectionem Dn. </s>
            <s xml:id="echoid-s4220" xml:space="preserve">Gregorii, ita antea firmo fundamento nixas
              <lb/>
            fuiſſe; </s>
            <s xml:id="echoid-s4221" xml:space="preserve">quoniam omiſſa diviſione neceſſariâ per a@ b in tot
              <lb/>
            locis propoſitionis
              <emph style="sc">VII</emph>
            . </s>
            <s xml:id="echoid-s4222" xml:space="preserve">poterat præſumi illum non noviſſe
              <lb/>
            talem diviſionem eſſe poſſibilem, & </s>
            <s xml:id="echoid-s4223" xml:space="preserve">conſequenter illum
              <lb/>
            credidiſſe, in compoſitione de qua agitur indefinitas ad-
              <lb/>
            mitti debere quantitates.</s>
            <s xml:id="echoid-s4224" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4225" xml:space="preserve">Tranſeo igitur ad comparationem noſtrarum methodorum
              <lb/>
            pro dimenſione Circuli proxima: </s>
            <s xml:id="echoid-s4226" xml:space="preserve">Certum eſt, primas ejus
              <lb/>
            approximationes quarum fundamentum ſunt ipſius propo-
              <lb/>
            fitiones
              <emph style="sc">XX</emph>
            , & </s>
            <s xml:id="echoid-s4227" xml:space="preserve">
              <emph style="sc">XXI</emph>
            . </s>
            <s xml:id="echoid-s4228" xml:space="preserve">eaſdem eſſe cum iis, quas dedi in tra-
              <lb/>
            ctatu de Circuli magnitudine; </s>
            <s xml:id="echoid-s4229" xml:space="preserve">ubi demonſtravi eadem illa
              <lb/>
            Theoremata, ſcil. </s>
            <s xml:id="echoid-s4230" xml:space="preserve">ſi Polygonum in Circulo inſcriptum ſit
              <lb/>
            a; </s>
            <s xml:id="echoid-s4231" xml:space="preserve">& </s>
            <s xml:id="echoid-s4232" xml:space="preserve">Polygonum ſimul circumſcriptum ſit d: </s>
            <s xml:id="echoid-s4233" xml:space="preserve">contentum
              <lb/>
            Circuli minus eſſe quam {1/3}a + {2/3} d , ſed majus quam {4/3}
              <note symbol="* it" position="right" xlink:label="note-0193-01" xlink:href="note-0193-01a" xml:space="preserve">Vide ſupræ
                <lb/>
              pag. 361.
                <lb/>
              pr.
                <emph style="sc">VI</emph>
              .</note>
            {1/3} a , poſito c pro Polygono inſcripto quod duplo
              <note symbol="* it" position="right" xlink:label="note-0193-02" xlink:href="note-0193-02a" xml:space="preserve">Vide ibid.
                <lb/>
              prop.
                <emph style="sc">V</emph>
              .</note>
            habeat laterum numerum quam a vel d. </s>
            <s xml:id="echoid-s4234" xml:space="preserve">Quidquid hic </s>
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