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
Page: 109
[32] Fig. 6.A D G F B C
Page: 109
[33] Pag. 72.TAB. VII.Fig. 1.L B E N G F A K D C
Page: 116
[34] Fig. 2.A H L K M B E N Q P O C D
Page: 116
[35] Fig. 3.B F A K O N M E V L C H D
Page: 116
[36] Pag. 76.TAB. VIII.Fig. 1.O P E V D H C L M N A B F
Page: 123
[37] Fig. 2.A B C E H G F
Page: 123
[38] Fig. 3.D A B C E H G K F
Page: 123
[39] Fig. 4.A L C M B E G F
Page: 123
[40] Fig. 5.A B C D K F G
Page: 123
[41] Fig. 6.G E C K H F L D M N A O B Z
Page: 123
[42] Pag. 82.TAB. IX.Fig. 1.AMO FNP B G C H D K L
Page: 132
[43] Fig. 2.A C E F B D
Page: 132
[44] Fig. 3.C B e N L m E O M D f F A
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[45] Fig. 4.C B E G F D f H b A
Page: 132
[46] Fig. 5.C V B E S Δ M O Λ H Φ G Π T N P I
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[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
Page: 139
[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
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[Figure 49]
Page: 143
[50] Pag. 92.TAB. XIFig. 1.D C F E B L H I K A G
Page: 148
[51] Fig. 2.E D A B C
Page: 148
[52] Fig. 3.E H C A D F G B
Page: 148
[53] Pag. 96.TAB. XII.Fig. 1.C E H A G K D B
Page: 155
[54] Fig. 2.N O L K B C M P G D A E F H
Page: 155
[55] Fig. 3.N M H G K O F L C D B E P A Q
Page: 155
[56] Fig. 4.A D F E G B C
Page: 155
[57] Pag. 104.TAB. XIII.Fig. 1.H E M A F K G B D
Page: 166
[58] Fig. 2.A F N E G B D
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[59] Fig. 4.A G D C H E K F B
Page: 166
[60] Fig. 3.E B H X L D C A G D C
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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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