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

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            <s xml:id="echoid-s493" xml:space="preserve">
              <pb o="331" file="0037" n="40" rhead="GREGORII à S. VINCENTIO."/>
            latera B G, A H. </s>
            <s xml:id="echoid-s494" xml:space="preserve">In duobus ſequentibus quadratis duean-
              <lb/>
            tur diagonii C I, D K. </s>
            <s xml:id="echoid-s495" xml:space="preserve">Sed in poſtremis rurſus ſemipara-
              <lb/>
            bolæ deſcribantur E Σ L, F Π M, quarum vertices E & </s>
            <s xml:id="echoid-s496" xml:space="preserve">
              <lb/>
            F, axes vero ſint quadratorum latera E Ψ, F Ω, & </s>
            <s xml:id="echoid-s497" xml:space="preserve">baſes
              <lb/>
            Ψ L, Ω M. </s>
            <s xml:id="echoid-s498" xml:space="preserve">Porro diviſis bifariam ſingulis lineis quæ ab
              <lb/>
            initio poſitæ fuerunt, in N, O, P, & </s>
            <s xml:id="echoid-s499" xml:space="preserve">medietatibus rurſus
              <lb/>
            bifariam in Q, R, S, ducantur per diviſionum puncta, qua-
              <lb/>
            dratorum lateribus parallelæ, T V, X Y; </s>
            <s xml:id="echoid-s500" xml:space="preserve">Ζ Γ, Δ Θ,
              <lb/>
            Π Σ, Λ Ξ.</s>
            <s xml:id="echoid-s501" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s502" xml:space="preserve">Oſtendit itaque Cl. </s>
            <s xml:id="echoid-s503" xml:space="preserve">V. </s>
            <s xml:id="echoid-s504" xml:space="preserve">in demonſtr. </s>
            <s xml:id="echoid-s505" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s506" xml:space="preserve">52. </s>
            <s xml:id="echoid-s507" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s508" xml:space="preserve">10.
              <lb/>
            </s>
            <s xml:id="echoid-s509" xml:space="preserve">Oper. </s>
            <s xml:id="echoid-s510" xml:space="preserve">Geom. </s>
            <s xml:id="echoid-s511" xml:space="preserve">& </s>
            <s xml:id="echoid-s512" xml:space="preserve">veriſſimum eſt, in circulo ſuperiori ſe-
              <lb/>
            gmentum C H G ad ſegmentum G H E F, eandem habere
              <lb/>
            rationem quam habet hîc ſolidum quod fit ex ductu plani
              <lb/>
            A Y Q in planum A H X Q, ad ſolidum ortum ex ductu
              <lb/>
            plani Q Y V N in planum Q X T N; </s>
            <s xml:id="echoid-s513" xml:space="preserve">ſicut enim ille in
              <lb/>
            ſuo ſchemate ſumit æquales lineas h i, k l, ita nobis æqua-
              <lb/>
            les ſunt ſumptæ in circulo, C G, G F, & </s>
            <s xml:id="echoid-s514" xml:space="preserve">hiſce pares A Q,
              <lb/>
            Q N.</s>
            <s xml:id="echoid-s515" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s516" xml:space="preserve">Atque ut ipſa demonſtrandi methodus quoque noſcatur,
              <lb/>
            ea hujuſmodi eſt. </s>
            <s xml:id="echoid-s517" xml:space="preserve">In prop. </s>
            <s xml:id="echoid-s518" xml:space="preserve">51. </s>
            <s xml:id="echoid-s519" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s520" xml:space="preserve">10. </s>
            <s xml:id="echoid-s521" xml:space="preserve">oſtenditur, ſolidum
              <lb/>
            quod fit ex ductu ſemiparabolæ A B G in ſemipar. </s>
            <s xml:id="echoid-s522" xml:space="preserve">A B H,
              <lb/>
            æquari ſemicylindro, baſin habenti ſemicirculum C E D & </s>
            <s xml:id="echoid-s523" xml:space="preserve">
              <lb/>
            altitudinem C D. </s>
            <s xml:id="echoid-s524" xml:space="preserve">Deinde in Corollario ejuſdem prop. </s>
            <s xml:id="echoid-s525" xml:space="preserve">idem
              <lb/>
            quoque ſingulis partibus quod totis ſolidis convenire doce-
              <lb/>
            tur. </s>
            <s xml:id="echoid-s526" xml:space="preserve">Nimirum id ſolidum quod fit ex ductu plani Q Y V N
              <lb/>
            in planum Q X T N, æquatur quoque parti dicti ſemicy-
              <lb/>
            lindri quæ inſiſtit ſegmento G H E F; </s>
            <s xml:id="echoid-s527" xml:space="preserve">Itemque ſolidum ex
              <lb/>
            ductu plani A Y Q in pl. </s>
            <s xml:id="echoid-s528" xml:space="preserve">A H X Q, æquatur ejuſdem ſemicy-
              <lb/>
            lindri parti quæ inſiſtit ſegmento C H G. </s>
            <s xml:id="echoid-s529" xml:space="preserve">Quorum hoc vel
              <lb/>
            ex eo conſtat, quod alioqui duo iſta ſolida ſimul ſumpta,
              <lb/>
            hoc eſt, ſolidum ex ductu plani A V N in pl. </s>
            <s xml:id="echoid-s530" xml:space="preserve">A H T N,
              <lb/>
            æquale non eſſet dimidio ejus quem diximus, ſemicylin-
              <lb/>
            dri; </s>
            <s xml:id="echoid-s531" xml:space="preserve">& </s>
            <s xml:id="echoid-s532" xml:space="preserve">conſequenter falſum quoque eſſet quod in confeſ-
              <lb/>
            ſo eſt, nimirum ſolidum ex ductu ſemiparab. </s>
            <s xml:id="echoid-s533" xml:space="preserve">A B G in ſe-
              <lb/>
            miparab. </s>
            <s xml:id="echoid-s534" xml:space="preserve">A B H æquari toti ſemicylindro. </s>
            <s xml:id="echoid-s535" xml:space="preserve">Apparet igitur,
              <lb/>
            quoniam dictæ ſemicylindri partes eandem inter ſe </s>
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