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

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            <s xml:id="echoid-s754" xml:space="preserve">
              <pb o="337" file="0043" n="46" rhead="GREGORII à S. VINCENTIO."/>
            ex æquo erit cylindrus parabolicus A V C E D B ad ungu-
              <lb/>
            lam A B C D ut 40 ad 16, hoc eſt, ut 5 ad 2; </s>
            <s xml:id="echoid-s755" xml:space="preserve">quod fuit
              <lb/>
            demonſtrandum.</s>
            <s xml:id="echoid-s756" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s757" xml:space="preserve">Quæ hîc dixi à Cl. </s>
            <s xml:id="echoid-s758" xml:space="preserve">Viro oſtenſa fuiſſe, veriſſima ſunt,
              <lb/>
            ac proinde non eſt quod de veritate hujus Theorematis du-
              <lb/>
            bitemus: </s>
            <s xml:id="echoid-s759" xml:space="preserve">Cujus aliam quoque demonſtr. </s>
            <s xml:id="echoid-s760" xml:space="preserve">adferre poſſem, lon-
              <lb/>
            ge ab iſta diverſam, niſi ad ſequentia properarem.</s>
            <s xml:id="echoid-s761" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s762" xml:space="preserve">Repetitâ igitur parte ultimâ ſchematis, quod ſuprà de-
              <lb/>
              <note position="right" xlink:label="note-0043-01" xlink:href="note-0043-01a" xml:space="preserve">TAB. XXXVII.
                <lb/>
              Fig. 2.</note>
            ſcripſimus, ſit oſtendendum, quod ſolidum Μ Ξ, id eſt,
              <lb/>
            quod oritur ex ductu plani E Ξ S in planum E M Λ S ad
              <lb/>
            ſolidum Λ Σ, id eſt, quod oritur ex ductu plani S Ξ Σ P
              <lb/>
            in planum S Λ Π P, eam habet rationem quam 53 ad 203.
              <lb/>
            </s>
            <s xml:id="echoid-s763" xml:space="preserve">Deſcribatur ſuper E F parabola E Π F, axem habens P Π,
              <lb/>
            quam conſtat eſſe quartam partem ipſius E F ſive M E. </s>
            <s xml:id="echoid-s764" xml:space="preserve">Erit
              <lb/>
            igitur parabola E Π F eadem quam V. </s>
            <s xml:id="echoid-s765" xml:space="preserve">Cl. </s>
            <s xml:id="echoid-s766" xml:space="preserve">in prop. </s>
            <s xml:id="echoid-s767" xml:space="preserve">41. </s>
            <s xml:id="echoid-s768" xml:space="preserve">& </s>
            <s xml:id="echoid-s769" xml:space="preserve">
              <lb/>
            42. </s>
            <s xml:id="echoid-s770" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s771" xml:space="preserve">10. </s>
            <s xml:id="echoid-s772" xml:space="preserve">notat literis A R B. </s>
            <s xml:id="echoid-s773" xml:space="preserve">Ait autem in dicta prop. </s>
            <s xml:id="echoid-s774" xml:space="preserve">
              <lb/>
            42. </s>
            <s xml:id="echoid-s775" xml:space="preserve">& </s>
            <s xml:id="echoid-s776" xml:space="preserve">veriſſimum eſt, ſolidum quod producitur ex ductu
              <lb/>
            plani E Σ L F in planum F Π M E æquari ſolido quod fit
              <lb/>
            ex parabola E Π F ducta in ſe ipſam: </s>
            <s xml:id="echoid-s777" xml:space="preserve">ſicut illud quoque
              <lb/>
            quod ſubjungit in Coroll. </s>
            <s xml:id="echoid-s778" xml:space="preserve">1. </s>
            <s xml:id="echoid-s779" xml:space="preserve">nimirum quod ſolidum ex pla-
              <lb/>
            no S Ξ Σ P in planum S Λ Π P, æquatur ſolido ex ductu
              <lb/>
            plani S Φ Π P in ſe ipſum; </s>
            <s xml:id="echoid-s780" xml:space="preserve">unde ſimiliter ſolidum ex pla-
              <lb/>
            no E Ξ S in planum E M Λ S æquabitur ſolido ex plano
              <lb/>
            E Φ S in ſe ipſum ducto.</s>
            <s xml:id="echoid-s781" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s782" xml:space="preserve">Oportet itaque oſtendere ſolidum ortum ex plano E Φ S
              <lb/>
            ad ſolidum ex plano S Φ Π P, utroque in ſe ipſum ducto,
              <lb/>
            eſſe ut 53 ad 203.</s>
            <s xml:id="echoid-s783" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s784" xml:space="preserve">Eſto ungula parabolica A E F Π, cujus baſis parabola
              <lb/>
              <note position="right" xlink:label="note-0043-02" xlink:href="note-0043-02a" xml:space="preserve">TAB. XXXVII.
                <lb/>
              Fig. 4.</note>
            E Π F repetita ſit ex figura præcedenti, eodemque modo
              <lb/>
            ut iſtic diviſa lineis Π P, Φ S. </s>
            <s xml:id="echoid-s785" xml:space="preserve">Sit autem altitudo ungulæ
              <lb/>
            A Π dupla diametri baſis Π P. </s>
            <s xml:id="echoid-s786" xml:space="preserve">Erit igitur hæc ea ungula,
              <lb/>
            quam intelligit in prop. </s>
            <s xml:id="echoid-s787" xml:space="preserve">dicta 42. </s>
            <s xml:id="echoid-s788" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s789" xml:space="preserve">10. </s>
            <s xml:id="echoid-s790" xml:space="preserve">ejuſdemque coroll.
              <lb/>
            </s>
            <s xml:id="echoid-s791" xml:space="preserve">2. </s>
            <s xml:id="echoid-s792" xml:space="preserve">fieri ex ductu parabolæ E Π F in ſe ipſam. </s>
            <s xml:id="echoid-s793" xml:space="preserve">Eâdem nimi-
              <lb/>
            rum conſideratione uſus quæ eſt in Scholio propoſ. </s>
            <s xml:id="echoid-s794" xml:space="preserve">19. </s>
            <s xml:id="echoid-s795" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s796" xml:space="preserve">
              <lb/>
            9. </s>
            <s xml:id="echoid-s797" xml:space="preserve">Nam alioqui ex ejuſmodi ductu potius dicendum eſſet ge-
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            minas ungulas produci, ſingulas altitudine æquales </s>
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