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

Table of figures

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[141] Fig. 3.a B c A C
Page: 355
[142] Fig. 7.D A C B E G
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[143] Fig. 6.D A G B
Page: 355
[Figure 144]
Page: 359
[145] Pag. 262.TAB.XXIX.Fig. 1.P E O D C Q H M G N B S R T F
Page: 370
[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
Page: 370
[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
Page: 379
[151] Pag. 276.TAB.XXXI.Fig. 2.a a m f k b e @ b a g a f b b h
Page: 390
[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
Page: 403
[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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[161] Fig. 8.R G M K N D B V C A
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[162] Fig. 7.R d D G g B h H E V C u A c
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[163] Fig. 2.B F G C H A K D E
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[164] Fig. 4.A B G F E C D
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[165] Fig. 6.T G D H B E M L N C K I S P F V R Q O A
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[166] Fig. 3.A E G B D F C
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[167] Fig. 5.N K F E C B A H L V W R G
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[168] Fig. 9.Z R A X H C B D M K S Q G
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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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