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

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            <s xml:id="echoid-s535" xml:space="preserve">
              <pb o="332" file="0038" n="41" rhead="ΕΞΕΤΑΣΙΣ CYCLOM."/>
            habent quam baſes quibus inſiſtunt, certum eſſe quod dixi-
              <lb/>
            mus, ſegmentum circuli C H G ad G H E F, eſſe ut ſoli-
              <lb/>
            dum ex ductu plani A Y Q in pl. </s>
            <s xml:id="echoid-s536" xml:space="preserve">A H X Q ad ſolidum ex
              <lb/>
            ductu plani Q Y V N in pl. </s>
            <s xml:id="echoid-s537" xml:space="preserve">Q X T N.</s>
            <s xml:id="echoid-s538" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s539" xml:space="preserve">Hæc ita enucleatè ſcribere volui, ne cui ignaro fortaſſe na-
              <lb/>
            turæ demonſtrationum quibus Cl. </s>
            <s xml:id="echoid-s540" xml:space="preserve">V. </s>
            <s xml:id="echoid-s541" xml:space="preserve">utitur, ſcrupulus re-
              <lb/>
            ſtare poſſet, quod ubi ille in d. </s>
            <s xml:id="echoid-s542" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s543" xml:space="preserve">52, lib. </s>
            <s xml:id="echoid-s544" xml:space="preserve">10, duo cir-
              <lb/>
            culi ſegmenta conſiderat, quale ferè eſt G H E F, ego pro
              <lb/>
            altero eorum ſumpſerim ſegmentum C H G: </s>
            <s xml:id="echoid-s545" xml:space="preserve">Quodque in
              <lb/>
            linea A B ab ipſo termino A æquales partes capiam A Q,
              <lb/>
            Q N. </s>
            <s xml:id="echoid-s546" xml:space="preserve">Ipſum autem Cl. </s>
            <s xml:id="echoid-s547" xml:space="preserve">Virum hæc remorari non poſſunt,
              <lb/>
            neque hîc, neque in ſequentibus; </s>
            <s xml:id="echoid-s548" xml:space="preserve">quia cum in d. </s>
            <s xml:id="echoid-s549" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s550" xml:space="preserve">52.
              <lb/>
            </s>
            <s xml:id="echoid-s551" xml:space="preserve">& </s>
            <s xml:id="echoid-s552" xml:space="preserve">44, lib. </s>
            <s xml:id="echoid-s553" xml:space="preserve">10. </s>
            <s xml:id="echoid-s554" xml:space="preserve">præcipit in linea a b æquales inter ſe ſumi
              <lb/>
            h i, k l, ſcit hoc nullam limitationem admittere; </s>
            <s xml:id="echoid-s555" xml:space="preserve">ſicut & </s>
            <s xml:id="echoid-s556" xml:space="preserve">
              <lb/>
            in ſchemate communi prop. </s>
            <s xml:id="echoid-s557" xml:space="preserve">39, lib. </s>
            <s xml:id="echoid-s558" xml:space="preserve">10, ubivis in linea a b
              <lb/>
            ſumitur i k, quæ dividitur in duas æquales i m, m k. </s>
            <s xml:id="echoid-s559" xml:space="preserve">Idem
              <lb/>
            contingit in prop. </s>
            <s xml:id="echoid-s560" xml:space="preserve">ſequenti 40.</s>
            <s xml:id="echoid-s561" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s562" xml:space="preserve">Revertor autem ad propoſitum, & </s>
            <s xml:id="echoid-s563" xml:space="preserve">conſtat nunc quidem,
              <lb/>
            ſi detur Ratio ſolidi quod fit ex ductu plani A Y Q in pl.
              <lb/>
            </s>
            <s xml:id="echoid-s564" xml:space="preserve">A H X Q, ad ſolidum ex ductu plani Q Y V N in pl. </s>
            <s xml:id="echoid-s565" xml:space="preserve">
              <lb/>
            Q X T N, eo ipſo dari quoque rationem ſegmenti C H G
              <lb/>
            ad ſegmentum G H E F, ac proinde continuò tunc inveni-
              <lb/>
            ri poſſe quam rationem circulus habeat ad inſcriptum hexa-
              <lb/>
            gonum regulare.</s>
            <s xml:id="echoid-s566" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s567" xml:space="preserve">Vocemus autem brevitatis gratia, id quod fieri diximus
              <lb/>
            ex ductu plani A Y Q in planum A H X Q, ſolidum H Y.
              <lb/>
            </s>
            <s xml:id="echoid-s568" xml:space="preserve">Item quod ſit ex ductu plani Q Y V N in planum Q X T N,
              <lb/>
            ſolidum X V. </s>
            <s xml:id="echoid-s569" xml:space="preserve">Similiter quod oritur ex ductu plani C Θ R
              <lb/>
            in planum C K Δ R, vocemus ſolidum K Θ; </s>
            <s xml:id="echoid-s570" xml:space="preserve">eâdemque
              <lb/>
            brevitate dicamus ſolida Δ Γ, Μ Ξ, Λ Σ, quibus quæ de-
              <lb/>
            notentur jam ſatis intelligitur.</s>
            <s xml:id="echoid-s571" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s572" xml:space="preserve">His ſic conſtitutis, ſciendum eſt, omnem ſpem & </s>
            <s xml:id="echoid-s573" xml:space="preserve">fundamen-
              <lb/>
            tum perficiendæ Quadraturæ Cl. </s>
            <s xml:id="echoid-s574" xml:space="preserve">Viro in eo poſitum eſſe,
              <lb/>
            quod exiſtimet rationem ſolidi H Y ad ſolidum X V (quam
              <lb/>
            unicam tantum deſiderari jam admonui) facile inveniri poſ-
              <lb/>
            ſe, ſi cognitæ ſint duæ rationes hæ, nimirum ratio </s>
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