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

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            <s xml:id="echoid-s681" xml:space="preserve">
              <pb o="335" file="0041" n="44" rhead="GREGORII à S. VINCENTIO."/>
            5075 ad 6413. </s>
            <s xml:id="echoid-s682" xml:space="preserve">Quare qualium partium ſegmentum C H G
              <lb/>
            eſſet 5075, talium ſegmentum G H E F eſſet 6413; </s>
            <s xml:id="echoid-s683" xml:space="preserve">& </s>
            <s xml:id="echoid-s684" xml:space="preserve">pro-
              <lb/>
            inde quadrans F C E 11488; </s>
            <s xml:id="echoid-s685" xml:space="preserve">& </s>
            <s xml:id="echoid-s686" xml:space="preserve">ſector F H E (qui qua-
              <lb/>
            drantis tertia pars eſt) 3829 {1/3}: </s>
            <s xml:id="echoid-s687" xml:space="preserve">& </s>
            <s xml:id="echoid-s688" xml:space="preserve">triangulum G H F 2583 {@/3}.
              <lb/>
            </s>
            <s xml:id="echoid-s689" xml:space="preserve">Sicut autem ſector F H E ad triang. </s>
            <s xml:id="echoid-s690" xml:space="preserve">G H F, ita eſt ſector
              <lb/>
            F H C ad triangul. </s>
            <s xml:id="echoid-s691" xml:space="preserve">F C H, & </s>
            <s xml:id="echoid-s692" xml:space="preserve">ita circulus C D ad in-
              <lb/>
            ſcriptum ſibi hexagonum regulare. </s>
            <s xml:id="echoid-s693" xml:space="preserve">Ergo quoque qualium par-
              <lb/>
            tium circulus C D eſſet 3829 {1/3} talium hexagonum inſcri-
              <lb/>
            ptum foret 2583 {2/3}. </s>
            <s xml:id="echoid-s694" xml:space="preserve">Qualium autem hexagonum inſcriptum eſt
              <lb/>
            2583 {2/3}, talium hexagonum regulare circumſcriptum eſt 3444 {8/9}; </s>
            <s xml:id="echoid-s695" xml:space="preserve">
              <lb/>
            quoniam hoc inſcripti eſt ſeſquitertium: </s>
            <s xml:id="echoid-s696" xml:space="preserve">Ergo qualium
              <lb/>
            partium circulus C D eſſet 3829 {1/3}, talium hexagonum cir-
              <lb/>
            cumſcriptum eſſet 3444 {8/9}, atque ita eſſet ipſo circulo mi-
              <lb/>
            nus, quod eſt abſurdum.</s>
            <s xml:id="echoid-s697" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s698" xml:space="preserve">Manifeſtum igitur fecimus, ex duabus interpretationibus
              <lb/>
            verbi Continere, neutram caſui noſtro accommodari poſſe.
              <lb/>
            </s>
            <s xml:id="echoid-s699" xml:space="preserve">Aliam autem præter illas nullam in ſuo opere attulit; </s>
            <s xml:id="echoid-s700" xml:space="preserve">non
              <lb/>
            docuit igitur modum determinandi, quoties ratio ſol. </s>
            <s xml:id="echoid-s701" xml:space="preserve">Μ Ξ
              <lb/>
            ad ſol. </s>
            <s xml:id="echoid-s702" xml:space="preserve">Λ Σ contineat rationem ſol. </s>
            <s xml:id="echoid-s703" xml:space="preserve">Κ Θ ad ſolid. </s>
            <s xml:id="echoid-s704" xml:space="preserve">Δ Γ, ac
              <lb/>
            proinde nec determinari poterit quoties hæc ratio contineat
              <lb/>
            rationem ſolidi H Y ad ſolid. </s>
            <s xml:id="echoid-s705" xml:space="preserve">X V. </s>
            <s xml:id="echoid-s706" xml:space="preserve">Quare liquet, hanc
              <lb/>
            rationem, ne duabus quidem prioribus iſtis datis, per in-
              <lb/>
            venta Clariſſ. </s>
            <s xml:id="echoid-s707" xml:space="preserve">Viri cognoſci poſſe: </s>
            <s xml:id="echoid-s708" xml:space="preserve">ideoque fruſtra ipſum
              <lb/>
            ſperaſſe hoc modo perficere Circuli quadraturam.</s>
            <s xml:id="echoid-s709" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s710" xml:space="preserve">Reſtat nunc tantùm ut manifeſta faciam quæ in præce-
              <lb/>
            dentibus poſita fuere, dixi enim me demonſtraturm, quod
              <lb/>
            ſolidum Μ Ξ eſſet ad ſolid. </s>
            <s xml:id="echoid-s711" xml:space="preserve">Λ Σ, ut 53 ad 203: </s>
            <s xml:id="echoid-s712" xml:space="preserve">item quod
              <lb/>
            ſolidum Κ Θ rationem haberet ad ſolidum Δ Γ, quam 5 ad
              <lb/>
            11.</s>
            <s xml:id="echoid-s713" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s714" xml:space="preserve">Quoniam autem ad horum primi demonſtrationem neceſſa-
              <lb/>
            rium eſt, ut notum habeamus, quæ ſit Ratio ungulæ Paraboli-
              <lb/>
            cæ ad Cylindrum ſuum, qui baſi inſiſtit eidem, & </s>
            <s xml:id="echoid-s715" xml:space="preserve">eandem
              <lb/>
            habet altitudinem; </s>
            <s xml:id="echoid-s716" xml:space="preserve">idcirco hanc Rationem declarantes, Tra-
              <lb/>
            ctatum Clariſſ. </s>
            <s xml:id="echoid-s717" xml:space="preserve">Viri, quem de eadem Ungula, Parte 5. </s>
            <s xml:id="echoid-s718" xml:space="preserve">lib.
              <lb/>
            </s>
            <s xml:id="echoid-s719" xml:space="preserve">9. </s>
            <s xml:id="echoid-s720" xml:space="preserve">propoſuit, uno egregrio Theoremate auctiorem reddemus,
              <lb/>
            quod miror ipſum non inveniſſe, quum ex iis quæ </s>
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