Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

Table of figures

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[31] Fig. 5.A B F E D G C
[32] Fig. 6.A D G F B C
[33] Pag. 72.TAB. VII.Fig. 1.L B E N G F A K D C
[34] Fig. 2.A H L K M B E N Q P O C D
[35] Fig. 3.B F A K O N M E V L C H D
[36] Pag. 76.TAB. VIII.Fig. 1.O P E V D H C L M N A B F
[37] Fig. 2.A B C E H G F
[38] Fig. 3.D A B C E H G K F
[39] Fig. 4.A L C M B E G F
[40] Fig. 5.A B C D K F G
[41] Fig. 6.G E C K H F L D M N A O B Z
[42] Pag. 82.TAB. IX.Fig. 1.AMO FNP B G C H D K L
[43] Fig. 2.A C E F B D
[44] Fig. 3.C B e N L m E O M D f F A
[45] Fig. 4.C B E G F D f H b A
[46] Fig. 5.C V B E S Δ M O Λ H Φ G Π T N P I
[47] Pag. 86.TAB. X.Fig. 1.D C N F X B V P Δ Σ S M Λ Q Γ T Π Ξ Y G H E I R Φ O A Θ
[48] Fig. 2.D C F B P Θ S O N Q L Δ K Γ T Λ Π Σ Y Ψ Ξ G H E I ζ η X V R Ω A M Θ
[Figure 49]
[50] Pag. 92.TAB. XIFig. 1.D C F E B L H I K A G
[51] Fig. 2.E D A B C
[52] Fig. 3.E H C A D F G B
[53] Pag. 96.TAB. XII.Fig. 1.C E H A G K D B
[54] Fig. 2.N O L K B C M P G D A E F H
[55] Fig. 3.N M H G K O F L C D B E P A Q
[56] Fig. 4.A D F E G B C
[57] Pag. 104.TAB. XIII.Fig. 1.H E M A F K G B D
[58] Fig. 2.A F N E G B D
[59] Fig. 4.A G D C H E K F B
[60] Fig. 3.E B H X L D C A G D C
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            <s xml:id="echoid-s1887" xml:space="preserve">
              <pb o="85" file="0127" n="136" rhead="HOROLOG. OSCILLATOR."/>
            quarum unaquæque minor ſit arcus cycloidis B N altitudine,
              <lb/>
              <note position="right" xlink:label="note-0127-01" xlink:href="note-0127-01a" xml:space="preserve">
                <emph style="sc">De motu</emph>
                <lb/>
                <emph style="sc">IN CY-</emph>
                <lb/>
                <emph style="sc">CLOIDE</emph>
              .</note>
            itemque minor altitudine arcus circumferentiæ F L; </s>
            <s xml:id="echoid-s1888" xml:space="preserve">& </s>
            <s xml:id="echoid-s1889" xml:space="preserve">ad-
              <lb/>
            ditâ ad F G unâ earum partium G ζ, ducantur à punctis di-
              <lb/>
            viſionum rectæ baſi D C parallelæ, & </s>
            <s xml:id="echoid-s1890" xml:space="preserve">ad tangentem B Θ
              <lb/>
            terminatæ, P O, Q K, &</s>
            <s xml:id="echoid-s1891" xml:space="preserve">c; </s>
            <s xml:id="echoid-s1892" xml:space="preserve">itemque à puncto ζ recta ζ Ω
              <lb/>
            quæ ſecet cycloidem in V, circumferentiam in η; </s>
            <s xml:id="echoid-s1893" xml:space="preserve">quibus-
              <lb/>
            que in punctis ductæ parallelæ ſecant circumferentiam F H,
              <lb/>
            ab iis tangentes deorſum ducantur usque ad proximam quæ-
              <lb/>
            que parallelam, velut θ Δ, Γ Σ: </s>
            <s xml:id="echoid-s1894" xml:space="preserve">Quarum infima à puncto
              <lb/>
            Η ducta occurrat rectæ ζ Ω in X. </s>
            <s xml:id="echoid-s1895" xml:space="preserve">Similiter vero & </s>
            <s xml:id="echoid-s1896" xml:space="preserve">à pun-
              <lb/>
            ctis, in quibus dictæ parallelæ occurrunt cycloidi, ducan-
              <lb/>
            tur totidem tangentes deorſum, velut S Λ, T Ξ, &</s>
            <s xml:id="echoid-s1897" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1898" xml:space="preserve">qua-
              <lb/>
            rum infima, tangens nempe à puncto E ducta, occurrat re-
              <lb/>
            ctæ ζ Ω in R.</s>
            <s xml:id="echoid-s1899" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1900" xml:space="preserve">Quia igitur P ζ æqualis eſt F G altitudini arcus B E,
              <lb/>
            cui æqualis eſt ex conſtructione altitudo arcus N M, erit & </s>
            <s xml:id="echoid-s1901" xml:space="preserve">
              <lb/>
            P ζ æqualis altitudini arcus N M. </s>
            <s xml:id="echoid-s1902" xml:space="preserve">Eſt autem recta P O ex
              <lb/>
            conſtructione ſuperior termino N. </s>
            <s xml:id="echoid-s1903" xml:space="preserve">Ergo & </s>
            <s xml:id="echoid-s1904" xml:space="preserve">ζ Ω, & </s>
            <s xml:id="echoid-s1905" xml:space="preserve">in ea
              <lb/>
            punctum V, ſuperius termino M. </s>
            <s xml:id="echoid-s1906" xml:space="preserve">Quare, cum arcus S V
              <lb/>
            æqualis ſit altitudinis cum arcu N M, ſed termino S ſubli-
              <lb/>
            miore quam N, erit tempus per S V brevius tempore per N M.</s>
            <s xml:id="echoid-s1907" xml:space="preserve"/>
          </p>
          <note symbol="*" position="right" xml:space="preserve">Prop. 22.
            <lb/>
          huj.</note>
          <p>
            <s xml:id="echoid-s1908" xml:space="preserve">Atqui tempus per tangentem S Λ, cum celeritate æqua-
              <lb/>
            bili ex B S, brevius eſt tempore deſcenſus accelerati per ar-
              <lb/>
            cum S T, incipientis in S. </s>
            <s xml:id="echoid-s1909" xml:space="preserve">Nam celeritas ex B S, qua to-
              <lb/>
            ta S Λ transmiſſa ponitur, æqualis eſt celeritati ex S T
              <note symbol="*" position="right" xlink:label="note-0127-03" xlink:href="note-0127-03a" xml:space="preserve">Prop. 8.
                <lb/>
              huj.</note>
            quæ motui per arcum S T in fine demum acquiritur; </s>
            <s xml:id="echoid-s1910" xml:space="preserve">ipſa-
              <lb/>
            que S Λ minor eſt quam S T. </s>
            <s xml:id="echoid-s1911" xml:space="preserve">Similiter tempus per tangen-
              <lb/>
            tem T Ξ, cum celeritate æquabili ex B T, brevius eſt tem-
              <lb/>
            pore deſcenſus accelerati per arcum T Y poſt S T; </s>
            <s xml:id="echoid-s1912" xml:space="preserve">quum
              <lb/>
            celeritas ex B T, qua tota T Ξ transmiſſa ponitur, ſit æqua-
              <lb/>
            lis celeritati ex S Y, quæ in fine demum acquiritur motui
              <lb/>
            dicto per arcum T Y poſt S T; </s>
            <s xml:id="echoid-s1913" xml:space="preserve">ipſaque T Ξ minor ſit arcu
              <lb/>
            T Y. </s>
            <s xml:id="echoid-s1914" xml:space="preserve">Atque ita tempora omnia motuum æquabilium per
              <lb/>
            tangentes cycloidis, cum celeritatibus per ſingulas quantæ
              <lb/>
            acquiruntur deſcendendo ex B usque ad punctum ipſarum
              <lb/>
            contactus, breviora ſimul erunt tempore deſcenſus </s>
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