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

Table of figures

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[121] Pag. 170.TAB. XXVI.Fig. 1.Ω O Ω A Z R F R N E N R G S V P Φ Δ V B D K C
[122] Fig. 2.L O A V P Φ Δ V B E C S H D
[123] Fig. 3.F G E G P A P K K L B D B S
[Figure 124]
[Figure 125]
[126] Pag. 188.TAB.XXVII.Fig. 1.O V VA M N D N B O E CE A G B D C F
[127] Fig. 2.S Z G F H Y
[128] Fig. 3.D A D M T C
[129] Fig. 4.A E N D C
[130] Fig. 5.K D B G A F E H
[Figure 131]
[Figure 132]
[Figure 133]
[Figure 134]
[Figure 135]
[Figure 136]
[137] Pag. 248.TAB. XXVIII.Fig. 1.B A E D H F I G
[138] Fig. 2.M B A E D L N H F O I G
[139] Fig. 4.O P M I B G Q N L R H A F D
[140] Fig. 5.B A D L N H I
[141] Fig. 3.a B c A C
[142] Fig. 7.D A C B E G
[143] Fig. 6.D A G B
[Figure 144]
[145] Pag. 262.TAB.XXIX.Fig. 1.P E O D C Q H M G N B S R T F
[146] Fig. 4.C A H N E P B L K I
[147] Fig. 3.N Q O P T
[148] Fig. 2.F D I C A B H K E R S G
[149] Fig. 5.L M C M E H O D P I
[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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12678CHRISTIANI HUGENII tiones B D & E F, æqualis altitudinis, hoc eſt, ejusmodi
11De motu
IN Cy-
CLOIDE.
ut parallelæ horizontales B C, D H, quæ ſuperiorem por-
tionem B D includunt, æque inter ſe diſtent ac E G,
F K, inferiorem partionem E F includentes.
Dico tempus
deſcenſus per curvam B D brevius fore tempore per E F.
Sumatur enim in B D punctum quodlibet L, & in E F
punctum M, ita ut eadem ſit altitudo E ſupra M quæ B
ſupra L.
Et deſcripto ſuper axe A C ſemicirculo, occurrant
ei rectæ horizontales L N, M O, in N &
O, & jungan-
tur N A, O A.
Itaque quum punctum N ſit altius puncto
O, manifeſtum eſt rectam N A minus ad horizontem incli-
nari quam O A.
Eſt autem ipſi N A parallela tangens curvæ
in L puncto , &
ipſi O A parallela tangens curvæ in M. 22Prop. 15.
huj.
Ergo curva B D in puncto L minus inclinata eſt quam curva
E F in puncto M.
Quod ſi igitur portio E F, invariata in-
clinatione, altius extolli intelligatur velut in e f, ita ut in-
ter eaſdem parallelas cum portione B D comprehendatur,
invenietur punctum M in m, æquali altitudine cum puncto
L.
eritque etiam inclinatio curvæ e f in puncto m, quæ ea-
dem eſt inclinationi curvæ E F in M, major inclinatione
curvæ B D in L.
Similiter vero, & in quolibet alio puncto
curvæ e f, major oſtendetur inclinatio quam curv æ B D
in puncto æque alto.
Itaque tempus deſcenſus per B D bre-
vius erit tempore per e f, ſive, quod idem eſt, per E F.
33Prop.
præced.
quod erat demonſtrandum.
LEMMA.
ESto circulus diametro A C, quem ſecet ad an-
44TAB. IX.
Fig. 4.
gulos rectos D E, &
à termino diametri A e-
ducta recta A B occurrat circumferentiæ in B, ipſi
vero D E in F.
Dico tres haſce, A B, A D, A F,
proportionales eſſe.
Sit enim primo interſectio F intra circulum; & arcui B D
recta ſubtenſa ducatur.
Quia igitur arcus æquales ſunt A

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