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
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[41] Fig. 6.G E C K H F L D M N A O B Z
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[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
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[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
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[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]
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[50] Pag. 92.TAB. XIFig. 1.D C F E B L H I K A G
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[51] Fig. 2.E D A B C
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[52] Fig. 3.E H C A D F G B
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[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
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[55] Fig. 3.N M H G K O F L C D B E P A Q
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[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
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[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
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[60] Fig. 3.E B H X L D C A G D C
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14187HOROLOG. OSCILLATOR.
PROPOSITIO XXV.
11De motu
IN CY-
CLOIDE.
IN Cycloide cujus axis ad perpendiculum erectus
eſt, vertice deorſum ſpectante, tempora deſcen-
ſus quibus mobile, à quocunque in ea puncto dimis-
ſum, ad punctum imum verticis pervenit, ſunt in-
ter ſe æqualia; habentque ad tempus caſus perpen-
dicularis per totum axem cycloidis eam rationem,
quam ſemicircumferentia circuli ad diametrum.
Eſto cyclois A B C cujus vertex A deorſum ſpectet, axis
22TAB. XI.
Fig. 1. vero A D ad perpendiculum erectus ſit, & à puncto quovis
in cycloide ſumpto, velut B; deſcendat mobile impetu na-
turali per arcum B A, ſive per ſuperficiem ita inflexam. Di-
co tempus deſcenſus hujus eſſe ad tempus caſus per axem
D A, ſicut ſemicircumferentia circuli ad diametrum. Quo
demonſtrato, etiam tempora deſcenſus, per quoslibet cy-
cloidis arcus ad A terminatos, inter ſe æqualia eſſe conſta-
bit.
Deſcribatur ſuper axe D A ſemicirculus, cujus circumfe-
rentiam ſecet recta B F, baſi D C parallela, in E; junctâ-
que E A, ducatur ei parallela B G, quæ quidem cycloidem
tanget in B. Eadem vero occurrat rectæ horizontali per A
ductæ in G: ſitque etiam ſuper F A deſcriptus ſemicirculus
F H A.
Eſt igitur, per præcedentem, tempus deſcenſus per ar-
cum cycloidis B A, ad tempus motus æquabilis per rectam
B G cum celeritate dimidia ex B G, ſicut arcus ſemicirculi
F H A ad rectam F A. Tempus vero dicti motus æquabilis
per B G, æquatur tempori deſcenſus naturaliter accelerati
per eandem B G, ſive per E A, quæ ipſi parallela eſt &
æqualis, hoc eſt, tempori deſcenſus accelerati per axem
D A. Itaque tempus per arcum B A, erit quoque ad 33Prop. 6.
Galil. de
motu Accel. pus deſcenſus per axem D A, ut ſemicirculi circumferentia
F H A ad diametrum F A. quod erat demonſtrandum.

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