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

Table of figures

< >
[41] Fig. 2.D B G H C E F
[42] Fig. 4.E C G A F B D
[43] Fig. 3.E C D F G H I
[44] Fig. 5.B F R C P L M O
[45] Fig. 6.Y S H E K B C G F R A L D N P M Z X V T
[46] Fig. 7.G F D M L E A K C B H
[47] Pag. 386.TAB. XL.Fig. 2.K B H F G E A I D L C
[48] Fig. 1.L K E D H C A G B
[49] Fig. 3.B Q N L M F G S H K A D C P
[50] Fig. 4.B G R A C D E H F
[51] Fig. 6.A C D M B
[52] Fig. 5.A E N F B L D M C G H I K O
[Figure 53]
[Figure 54]
[55] Pag. 398.TAB. XLI.Fig. 1.S T B R K H Q C N O M A E L D
[56] Fig. 2.D E F B G H C A
[57] Fig. 3.F D E G A B C
[58] Fig. 4.G N B H D K A E C F
[59] Fig. 8K A F c C E B h H G D d
[60] Fig. 6.C E D A F B R Q
[61] Fig. 5.G L B H D O A E C K
[62] Fig. 7.K F A C D B E H G
[63] Pag. 404.TAB. XLII.Fig. 1.K F M A C D B L E N G
[64] Fig. 3.G R D B H F E N A X C M P Q K
[65] Fig. 2.K A F c S C L E B T G D R d
[66] Fig. 4.K e G P E m B D f R F S H M C A N L Q n
[67] Fig. 5.B C R E G A F M Q D O
[68] Fig. 6.B C H G E A M Q P K D
[69] Fig. 7.B C E G A M P Q K H D
[Figure 70]
< >
page |< < (337) of 568 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div41" type="section" level="1" n="18">
          <p>
            <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-
              <lb/>
            minas ungulas produci, ſingulas altitudine æquales </s>
          </p>
        </div>
      </text>
    </echo>