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

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[Figure 131]
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[Figure 132]
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[Figure 133]
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[Figure 134]
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[Figure 135]
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[Figure 136]
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[137] Pag. 248.TAB. XXVIII.Fig. 1.B A E D H F I G
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[138] Fig. 2.M B A E D L N H F O I G
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[139] Fig. 4.O P M I B G Q N L R H A F D
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[140] Fig. 5.B A D L N H I
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[141] Fig. 3.a B c A C
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[142] Fig. 7.D A C B E G
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[143] Fig. 6.D A G B
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[Figure 144]
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[145] Pag. 262.TAB.XXIX.Fig. 1.P E O D C Q H M G N B S R T F
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[146] Fig. 4.C A H N E P B L K I
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[147] Fig. 3.N Q O P T
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[148] Fig. 2.F D I C A B H K E R S G
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[149] Fig. 5.L M C M E H O D P I
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[150] Pag. 268.TAB. XXX.a a I L K M g N l O c k P Q T S Q V T S R f f e n l d h g b
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[151] Pag. 276.TAB.XXXI.Fig. 2.a a m f k b e @ b a g a f b b h
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[152] Fig. 1.h g k h d a b c f e l
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[153] Pag. 286.TAB.XXXII.Fig. 1.A E C E E D B G
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[154] Fig. 2.H N K M
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[155] Fig. 4.B A D C
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[156] Fig. 5.A E E C H D G B
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[157] Fig. 6.A C C C C H G K E F D D D D
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[158] Fig. 3.G F F B D D C D A F A E E H
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[159] Fig. 7.K L R Z Y H V N S P A C E B X T M G Q O
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[160] Pag. 308.TAB.XXXIII.Fig. 1.P F Q K H L R G B E C N O 3 A 2
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13685HOROLOG. OSCILLATOR. quarum unaquæque minor ſit arcus cycloidis B N altitudine,
11De motu
IN CY-
CLOIDE. itemque minor altitudine arcus circumferentiæ F L; & ad-
ditâ ad F G unâ earum partium G ζ, ducantur à punctis di-
viſionum rectæ baſi D C parallelæ, & ad tangentem B Θ
terminatæ, P O, Q K, & c; itemque à puncto ζ recta ζ Ω
quæ ſecet cycloidem in V, circumferentiam in η; quibus-
que in punctis ductæ parallelæ ſecant circumferentiam F H,
ab iis tangentes deorſum ducantur usque ad proximam quæ-
que parallelam, velut θ Δ, Γ Σ: Quarum infima à puncto
Η ducta occurrat rectæ ζ Ω in X. Similiter vero & à pun-
ctis, in quibus dictæ parallelæ occurrunt cycloidi, ducan-
tur totidem tangentes deorſum, velut S Λ, T Ξ, & c. qua-
rum infima, tangens nempe à puncto E ducta, occurrat re-
ctæ ζ Ω in R.
Quia igitur P ζ æqualis eſt F G altitudini arcus B E,
cui æqualis eſt ex conſtructione altitudo arcus N M, erit &
P ζ æqualis altitudini arcus N M. Eſt autem recta P O ex
conſtructione ſuperior termino N. Ergo & ζ Ω, & in ea
punctum V, ſuperius termino M. Quare, cum arcus S V
æqualis ſit altitudinis cum arcu N M, ſed termino S ſubli-
miore quam N, erit tempus per S V brevius tempore per N M.
22Prop. 22.
huj.
Atqui tempus per tangentem S Λ, cum celeritate æqua-
bili ex B S, brevius eſt tempore deſcenſus accelerati per ar-
cum S T, incipientis in S. Nam celeritas ex B S, qua to-
ta S Λ transmiſſa ponitur, æqualis eſt celeritati ex S T 33Prop. 8.
huj. quæ motui per arcum S T in fine demum acquiritur; ipſa-
que S Λ minor eſt quam S T. Similiter tempus per tangen-
tem T Ξ, cum celeritate æquabili ex B T, brevius eſt tem-
pore deſcenſus accelerati per arcum T Y poſt S T; quum
celeritas ex B T, qua tota T Ξ transmiſſa ponitur, ſit æqua-
lis celeritati ex S Y, quæ in fine demum acquiritur motui
dicto per arcum T Y poſt S T; ipſaque T Ξ minor ſit arcu
T Y. Atque ita tempora omnia motuum æquabilium per
tangentes cycloidis, cum celeritatibus per ſingulas quantæ
acquiruntur deſcendendo ex B usque ad punctum ipſarum
contactus, breviora ſimul erunt tempore deſcenſus

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