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

Table of figures

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[61] Fig. 5.A D C G F E B H
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[62] Pag. 106.TAB. XIV.Fig. 2.T B M S O I C A F K E L Q P N
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[63] Fig. 1.E F K L A G H M C B D
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[64] Fig. 3.I G E B P R Q A K C D H F
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[65] Pag. 112.TAB. XV.Fig. 1.S D A B C E V
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[66] Fig. 2.F A E B K G H N L D M O C
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[67] Fig. 3.C D F A B K E G N H
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[68] Fig. 5.S M A N B K X T P L F V O C Y D E G H
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[69] Fig. 4.Y H A S B K T X F L V P O M N C D G E
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[70] Pag. 114.TAB. XVI.Fig. 1.M F E A K G N H B D C
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[71] Fig. 2.H A K B R P F L O M N D Q G E
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[72] Fig. 3.Y H A S Z X T K B V L P F O C M N D G E
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[Figure 73]
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[74] Pag. 122TAB. XVII.Fig. 1.S A P B R M D I
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[75] Fig. 2.H S Z K B C M D
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[76] Fig. 3.P S Z M A B K D H
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[77] Fig. 4.H C A E D F B G
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[78] Pag. 128.TAB. XVIII.Fig. 1.A G C B D E H F K I M
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[79] Fig. 2.A C G B E F D H M N O P
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[80] Fig. 3.D L Q A G Q M R E P. Q B F N H Q C Q K Q
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[81] Fig. 4.N Q K C Q D L R E P F A Q G M Q Q H B Q
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[82] Pag. 136.TAB. XIX.Fig. 1.D C X B Y E R I Q L S N K P A TF G Y M H O
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[83] Fig. 2.X C D A T E R I Q L S N K P B Y
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[84] Fig. 3.F G K C D I E M A B D
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[85] Fig. 4.D K E F L B A H G C E
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[86] Fig. 5.D C K L F E A G H D B
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[87] Fig. 6.C D K F L E H G A D B
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[88] Pag. 142.TAB. XX.Fig. 1.D L F K A E G H C L K F D B
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[89] Fig. 2.D F K L C H E G A K F L D B
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[90] Fig. 3.L D C A E H G B L D
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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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