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

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        <div xml:id="echoid-div49" type="section" level="1" n="21">
          <p>
            <s xml:id="echoid-s968" xml:space="preserve">
              <pb o="347" file="0055" n="59" rhead="EPISTOLA."/>
            nobis, circa has propoſitiones & </s>
            <s xml:id="echoid-s969" xml:space="preserve">ſignificationem verbi continere,
              <lb/>
            opinio fuit Incomparabili Carteſio, quem ſi minus inſignem
              <lb/>
            Geometram quam Algebriſtam fuiſſe arbitraris, parum ex ve-
              <lb/>
            ro judicas. </s>
            <s xml:id="echoid-s970" xml:space="preserve">Ejus ad amicum epiſtolæ copia mihi facta eſt, cum
              <lb/>
            jam diu exetaſis noſtra prodiiſſet, quâ quoniam non tantum id
              <lb/>
            quod dixi comprobatur, ſed & </s>
            <s xml:id="echoid-s971" xml:space="preserve">tota inſuper ad opus Geometri-
              <lb/>
            cum P. </s>
            <s xml:id="echoid-s972" xml:space="preserve">à S
              <emph style="super">to</emph>
            . </s>
            <s xml:id="echoid-s973" xml:space="preserve">Vincentio pertinet, integram hic adſcribere vi-
              <lb/>
            ſum eſt. </s>
            <s xml:id="echoid-s974" xml:space="preserve">Gallicè ſic habet.</s>
            <s xml:id="echoid-s975" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s976" xml:space="preserve">
              <emph style="sc">Monsieur</emph>
            .</s>
            <s xml:id="echoid-s977" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s978" xml:space="preserve">J’Aygardé vos livres un peulong temps, pource que je deſirois
              <lb/>
            en vous les renvoyant, vous rendre compte de la Quadrature
              <lb/>
            du cercle pretendue, & </s>
            <s xml:id="echoid-s979" xml:space="preserve">j’ avois bien de la peine à me reſoudre de
              <lb/>
            feuilleter tout le gros volume qui en traite. </s>
            <s xml:id="echoid-s980" xml:space="preserve">En fin j’ en ay veu
              <lb/>
            quelque choſe & </s>
            <s xml:id="echoid-s981" xml:space="preserve">aſſez ce me ſemble pour pouvoir dire qu’ilne conti-
              <lb/>
            ent rien de bon qui ne ſoit facile, & </s>
            <s xml:id="echoid-s982" xml:space="preserve">qu’on ne puſt eſcrire tout en
              <lb/>
            une ou deux pages. </s>
            <s xml:id="echoid-s983" xml:space="preserve">Lereſte n’ eſt qu’un paralogiſme touchant la
              <lb/>
            Quadrature du cercle, enveloppé en quantité de propoſitions qui
              <lb/>
            ne ſervent qu’ à embroüiller la matiere, & </s>
            <s xml:id="echoid-s984" xml:space="preserve">ſont tresſimples & </s>
            <s xml:id="echoid-s985" xml:space="preserve">
              <lb/>
            facilles pour la pluspart, bien que la façon dont il les traite, les
              <lb/>
            face paroiſtre un peu obſcures. </s>
            <s xml:id="echoid-s986" xml:space="preserve">Pour trouver ſon paralogiſme, j’ai
              <lb/>
            commencé par la 1134
              <emph style="super">e</emph>
            page, ou il dit: </s>
            <s xml:id="echoid-s987" xml:space="preserve">Nota autem eſt propor-
              <lb/>
            tio ſegmenti L M N K ad ſegmentum E G H F, ce qui eſt faux,
              <lb/>
            & </s>
            <s xml:id="echoid-s988" xml:space="preserve">la preuve qu’il en donne eſt fondée ſur la 39
              <emph style="super">e</emph>
            propoſition en la
              <lb/>
            page 1121. </s>
            <s xml:id="echoid-s989" xml:space="preserve">du meſme livre, ou ily a une erreur tresmanifeſte,
              <lb/>
            qui conſiſte en ce qu’il veut appliquer à pluſieurs quantitez conjo-
              <lb/>
            intes ce qu’il a prouvé auparavant des meſmes quantitez divisées.
              <lb/>
            </s>
            <s xml:id="echoid-s990" xml:space="preserve">Carpar exemple, ayant les 4. </s>
            <s xml:id="echoid-s991" xml:space="preserve">ordres de proportionelles
              <lb/>
              <note position="right" xlink:label="note-0055-01" xlink:href="note-0055-01a" xml:space="preserve">
                <lb/>
              2, # 4, # 8, # 2, # 8, # 32.
                <lb/>
              ###### &
                <lb/>
              2, # 6, # 18, # 2, # 10, # 50.
                <lb/>
              </note>
            bien qu’il ſoit vray que 8. </s>
            <s xml:id="echoid-s992" xml:space="preserve">eſt à 32. </s>
            <s xml:id="echoid-s993" xml:space="preserve">en raiſon duoblée de ce que 4.
              <lb/>
            </s>
            <s xml:id="echoid-s994" xml:space="preserve">eſt à 8. </s>
            <s xml:id="echoid-s995" xml:space="preserve">Et que 18. </s>
            <s xml:id="echoid-s996" xml:space="preserve">eſt auſſi à 50. </s>
            <s xml:id="echoid-s997" xml:space="preserve">en raiſon doublée de ce que 6. </s>
            <s xml:id="echoid-s998" xml:space="preserve">
              <lb/>
            eſt à 10. </s>
            <s xml:id="echoid-s999" xml:space="preserve">il n’ eſt pas vray pour cela que 8 + 18. </s>
            <s xml:id="echoid-s1000" xml:space="preserve">c’ eſt à dire 26. </s>
            <s xml:id="echoid-s1001" xml:space="preserve">ſo-
              <lb/>
            it à 32 + 50. </s>
            <s xml:id="echoid-s1002" xml:space="preserve">c’ eſt à dire 82. </s>
            <s xml:id="echoid-s1003" xml:space="preserve">en raiſon double de celle qui eſt entre
              <lb/>
            4 + 6. </s>
            <s xml:id="echoid-s1004" xml:space="preserve">c’ eſt à dire 10, & </s>
            <s xml:id="echoid-s1005" xml:space="preserve">8 + 10, c’ eſt à dire 18. </s>
            <s xml:id="echoid-s1006" xml:space="preserve">Tous ſesraiſon-
              <lb/>
            nements ne ſont fondez que ſur cettefaute, & </s>
            <s xml:id="echoid-s1007" xml:space="preserve">ce qu’il eſcrit </s>
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