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

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          <p>
            <s xml:id="echoid-s574" xml:space="preserve">
              <pb o="333" file="0039" n="42" rhead="GREGORII à S. VINCENTIO."/>
            Μ Ξ ad ſol. </s>
            <s xml:id="echoid-s575" xml:space="preserve">Λ Σ, & </s>
            <s xml:id="echoid-s576" xml:space="preserve">ratio ſolidi Κ Θ ad ſol. </s>
            <s xml:id="echoid-s577" xml:space="preserve">Δ Γ. </s>
            <s xml:id="echoid-s578" xml:space="preserve">Sic enim
              <lb/>
            tunc argumentabitur; </s>
            <s xml:id="echoid-s579" xml:space="preserve">Nota eſt ratio ſolidi Μ Ξ ad ſol. </s>
            <s xml:id="echoid-s580" xml:space="preserve">Λ Σ,
              <lb/>
            item ratio ſolidi Κ Θ ad ſol. </s>
            <s xml:id="echoid-s581" xml:space="preserve">Δ Γ, ergo notum quoque quo-
              <lb/>
            ties illa ratio hanc contineat; </s>
            <s xml:id="echoid-s582" xml:space="preserve">Quoties autem illa hanc con-
              <lb/>
            tinet toties hæc ipſa, ſcilicet ratio ſolidi Κ Θ ad ſol. </s>
            <s xml:id="echoid-s583" xml:space="preserve">Δ Γ,
              <lb/>
            continet rationem ſolidi H Y ad X V; </s>
            <s xml:id="echoid-s584" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s585" xml:space="preserve">hæc ratio
              <lb/>
            nota erit. </s>
            <s xml:id="echoid-s586" xml:space="preserve">Quomodo hæc intelligenda ſint paulò inferiùs me-
              <lb/>
            lius patebit, ubi eandem argumentationem repetemus. </s>
            <s xml:id="echoid-s587" xml:space="preserve">Inter-
              <lb/>
            ea certo ſcio, nihil horum quæ dixi mihi à Cl. </s>
            <s xml:id="echoid-s588" xml:space="preserve">V. </s>
            <s xml:id="echoid-s589" xml:space="preserve">nega-
              <lb/>
            tum iri, modò conſideret in linea A B, ſumptas eſſe æqua-
              <lb/>
            les inter ſe partes A Q, Q N, & </s>
            <s xml:id="echoid-s590" xml:space="preserve">hiſce pares C R, R O;
              <lb/>
            </s>
            <s xml:id="echoid-s591" xml:space="preserve">E S, S P.</s>
            <s xml:id="echoid-s592" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s593" xml:space="preserve">Si igitur indicavero ipſi quæ ſit ratio ſolidi Μ Ξ ad ſol.
              <lb/>
            </s>
            <s xml:id="echoid-s594" xml:space="preserve">Λ Σ, item quæ ſit ratio ſolidi Κ Θ ad ſol. </s>
            <s xml:id="echoid-s595" xml:space="preserve">Δ Γ, & </s>
            <s xml:id="echoid-s596" xml:space="preserve">ne tum
              <lb/>
            quidem dicere poſſit quam rationem habeat ſolidum H Y
              <lb/>
            ad ſol. </s>
            <s xml:id="echoid-s597" xml:space="preserve">X V, fateatur ſane ſe fruſtra utramque Quadraturam
              <lb/>
            tentaſſe, tam Circuli quam Hyperboles. </s>
            <s xml:id="echoid-s598" xml:space="preserve">Circuli; </s>
            <s xml:id="echoid-s599" xml:space="preserve">quoniam
              <lb/>
            tunc videbit nequaquam procedere Propoſitionem 44. </s>
            <s xml:id="echoid-s600" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s601" xml:space="preserve">
              <lb/>
            10. </s>
            <s xml:id="echoid-s602" xml:space="preserve">Oper. </s>
            <s xml:id="echoid-s603" xml:space="preserve">Geom. </s>
            <s xml:id="echoid-s604" xml:space="preserve">quæ vana & </s>
            <s xml:id="echoid-s605" xml:space="preserve">inanis erit, niſi ex notis ra-
              <lb/>
            tionibus ſolidi Μ Ξ ad ſol. </s>
            <s xml:id="echoid-s606" xml:space="preserve">Λ Σ, & </s>
            <s xml:id="echoid-s607" xml:space="preserve">ſolidi Κ Θ ad ſol. </s>
            <s xml:id="echoid-s608" xml:space="preserve">Δ Γ,
              <lb/>
            innoteſcat ratio ſolidi H Y ad ſol. </s>
            <s xml:id="echoid-s609" xml:space="preserve">X V. </s>
            <s xml:id="echoid-s610" xml:space="preserve">Hyperboles ve-
              <lb/>
            ro; </s>
            <s xml:id="echoid-s611" xml:space="preserve">quoniam prop. </s>
            <s xml:id="echoid-s612" xml:space="preserve">146. </s>
            <s xml:id="echoid-s613" xml:space="preserve">ejusd. </s>
            <s xml:id="echoid-s614" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s615" xml:space="preserve">10. </s>
            <s xml:id="echoid-s616" xml:space="preserve">cui hæc quadratura
              <lb/>
            innititur, eadem eſt cum dicta prop. </s>
            <s xml:id="echoid-s617" xml:space="preserve">44. </s>
            <s xml:id="echoid-s618" xml:space="preserve">& </s>
            <s xml:id="echoid-s619" xml:space="preserve">iiſdem verbis
              <lb/>
            Hyperbolæ applicatur.</s>
            <s xml:id="echoid-s620" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s621" xml:space="preserve">Sin vero datis iſtis duabus rationibus invenire poſthac po-
              <lb/>
            tuerit rationem ſolidi H Y ad ſol. </s>
            <s xml:id="echoid-s622" xml:space="preserve">X V, tum ſe credat Cir-
              <lb/>
            culum reverâ quadraviſſe. </s>
            <s xml:id="echoid-s623" xml:space="preserve">Nota enim ſic erit ratio ſegmenti
              <lb/>
            C H G in circulo ad ſegmentum G H E F, & </s>
            <s xml:id="echoid-s624" xml:space="preserve">reliqua facile
              <lb/>
            perficientur.</s>
            <s xml:id="echoid-s625" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s626" xml:space="preserve">Dicam autem nunc ipſas Rationes. </s>
            <s xml:id="echoid-s627" xml:space="preserve">Et primam quidem,
              <lb/>
            hoc eſt rationem ſolidi Μ Ξ ad ſol. </s>
            <s xml:id="echoid-s628" xml:space="preserve">Λ Σ, ajo eſſe eandem
              <lb/>
            quæ numeri 53 ad 203. </s>
            <s xml:id="echoid-s629" xml:space="preserve">Alteram vero, rationem ſolidi Κ Θ
              <lb/>
            ad ſol. </s>
            <s xml:id="echoid-s630" xml:space="preserve">Δ Γ, eam quæ 5 ad 11. </s>
            <s xml:id="echoid-s631" xml:space="preserve">atque horum utrumque in-
              <lb/>
            frà ſum demonſtraturus.</s>
            <s xml:id="echoid-s632" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s633" xml:space="preserve">Priùs autem quod ab initio promiſi etiam oſtendam, hiſce
              <lb/>
            Rationibus cognitis, tamen rationem ſol. </s>
            <s xml:id="echoid-s634" xml:space="preserve">H Y ad ſol. </s>
            <s xml:id="echoid-s635" xml:space="preserve">X </s>
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