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

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              <pb o="339" file="0045" n="48" rhead="GREGORII à S. VINCENTIO."/>
            A D C B eſt 8, talium erit dimid. </s>
            <s xml:id="echoid-s840" xml:space="preserve">ungula E A P Π 256,
              <lb/>
            quoniam ut 1 ad 32, ita eſt 8 ad 256. </s>
            <s xml:id="echoid-s841" xml:space="preserve">Diximus autem par-
              <lb/>
            tem ſol. </s>
            <s xml:id="echoid-s842" xml:space="preserve">A Π S D eſſe talium 203. </s>
            <s xml:id="echoid-s843" xml:space="preserve">Igitur dim. </s>
            <s xml:id="echoid-s844" xml:space="preserve">ungula
              <lb/>
            E A P Π eſt ad partem A Π S D ut 256 ad 203; </s>
            <s xml:id="echoid-s845" xml:space="preserve">& </s>
            <s xml:id="echoid-s846" xml:space="preserve">divi-
              <lb/>
            dendo pars reliqua E D S Φ ad partem A Π S D, ut 53 ad
              <lb/>
            203; </s>
            <s xml:id="echoid-s847" xml:space="preserve">quod erat demonſtr. </s>
            <s xml:id="echoid-s848" xml:space="preserve">Oſtendimus igitur illud quoque
              <lb/>
            ſolidum, quod ſuprà diximus fieri ex ductu plani E Ξ S in
              <lb/>
            planum E M Λ S, eam habere rationem ad ſolidum ortum ex
              <lb/>
            ductu plani S Ξ Σ P in planum S Λ Π P, quam 53 ad 203.</s>
            <s xml:id="echoid-s849" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s850" xml:space="preserve">Tandem ad alterum eorum quæ demonſtrare promiſimus
              <lb/>
              <note position="right" xlink:label="note-0045-01" xlink:href="note-0045-01a" xml:space="preserve">TAB. XXXVII.
                <lb/>
              Fig. 2.</note>
            accedamus, repetitâque parte mediâ ſchematis triplicis
              <lb/>
            quod ſuprà deſcriptum fuit, oſtendendum ſit; </s>
            <s xml:id="echoid-s851" xml:space="preserve">ſolidum or-
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            tum ex ductu plani C Θ R in planum C K Δ R, ad ſoli-
              <lb/>
            dum ex ductu plani R Θ Γ O in planum R Δ Z O eam ha-
              <lb/>
              <note position="right" xlink:label="note-0045-02" xlink:href="note-0045-02a" xml:space="preserve">Fig. 5.</note>
            bere rationem, quam 5 ad 11. </s>
            <s xml:id="echoid-s852" xml:space="preserve">Supra latus C D trianguli
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            C D I, erigatur ad perpendiculum triangulum C K D, & </s>
            <s xml:id="echoid-s853" xml:space="preserve">
              <lb/>
            jungatur K I. </s>
            <s xml:id="echoid-s854" xml:space="preserve">Erit jam pyramis C D I K illud ſolidum quod
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            intelligitur fieri ex ductu trianguli C D I in triangulum C D K.
              <lb/>
            </s>
            <s xml:id="echoid-s855" xml:space="preserve">Etenim ſectâ pyramide plano A Z O Γ ſecundum O Γ,
              <lb/>
            quod rectum ſit ad baſin C D I, erit ſectio quadratum, id
              <lb/>
            eſt, rectangul. </s>
            <s xml:id="echoid-s856" xml:space="preserve">quod fit ex lineis Γ O, O Z; </s>
            <s xml:id="echoid-s857" xml:space="preserve">eademque ſe-
              <lb/>
            ctio dividet pyramidem bifariam. </s>
            <s xml:id="echoid-s858" xml:space="preserve">Secta item plano E Δ R Θ
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            priori parallelo, ſecundùm lineam R Θ, exiſtet inde re-
              <lb/>
            ctangulum E R, quale continetur lineis Θ R, R Δ. </s>
            <s xml:id="echoid-s859" xml:space="preserve">Opor-
              <lb/>
            tet itaque oſtendere, quòd ſolidum K C R E Δ eſt ad ſo-
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            lidum Δ Λ Ο Θ Δ, ut 5 ad 11.</s>
            <s xml:id="echoid-s860" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s861" xml:space="preserve">Ducatur ſecundùm E Δ planum Δ E B parallelum baſi
              <lb/>
            C D I; </s>
            <s xml:id="echoid-s862" xml:space="preserve">abſcindet illud pyramidem B E Δ K ſimilem toti
              <lb/>
            pyramidi C I D K, quæque proinde erit ad hanc in tripli-
              <lb/>
            cata ratione laterum homologorum B Δ ad C D. </s>
            <s xml:id="echoid-s863" xml:space="preserve">Sed B Δ,
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            cum ſit æqualis ipſi C R, quarta pars eſt lateris C D. </s>
            <s xml:id="echoid-s864" xml:space="preserve">Ita-
              <lb/>
            que qualium partium pyramis B E Δ K eſt unius, talium
              <lb/>
            pyramis C I D K erit 64: </s>
            <s xml:id="echoid-s865" xml:space="preserve">& </s>
            <s xml:id="echoid-s866" xml:space="preserve">dimidium hujus, hoc eſt, ſo-
              <lb/>
            lidum K A O C erit 32. </s>
            <s xml:id="echoid-s867" xml:space="preserve">Qualium autem pyramis B E Δ K
              <lb/>
            eſt unius talium quoque priſma B E R eſt 9; </s>
            <s xml:id="echoid-s868" xml:space="preserve">quoniam ba-
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            ſin habent communem B E Δ, & </s>
            <s xml:id="echoid-s869" xml:space="preserve">priſmatis altitudo B C </s>
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