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

Table of figures

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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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[91] Fig. 4.D L C E A X V G H L D B
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[92] Fig. 5.T F K A V Q Z D E O B X P C Y f I G M L R N S H
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[93] Fig. 6.K E A H C L D F G B
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[94] Pag. 154.TAB. XXI.Fig. 1.G E G O A K L Q Q M M H F R R N N B D L K C P S V X Z Y X V T
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[95] Fig. 3.F A D E B C G H
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[96] Fig. 2.G E Ω O Ω S A S Q Q M M R R N X F N V P Φ Δ V B C K D Z
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[97] Pag. 156.Fig. 2.S F Z V O V L A Q Q M M I R R N N X T X K E K Y H G P B C D
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[98] Fig. 1.F H A E G B C
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[99] Fig. 3.C B A E D
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[100] Fig. 4.E F E D D D V O B A N C K H
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[101] Fig. 5.D D D E F E B A C H K
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[102] Pag. 160.Fig. 1.F D D @ N A L C H K M
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[103] Fig. 2.D D D F B A L C H K
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[104] Fig. 3.C A B
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[105] Fig. 4.B A K C E D G
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[106] G D E C A K B
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[107] G D K C A B
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[108] Fig. 5.K B K A C E D F
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[109] Fig. 6.Q B Q O N A C E D R P F
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[110] Pag. 164.Fig. 1.G B O N C R P F
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12176CHRISTIANI HUGENII
PROPOSITIO XXI.
11De motu
IN Cy-
CLOIDE.
SI mobile deſcendat continuato motu per quælibet
plana inclinata contigua, ac rurſus ex pari al-
titudine deſcendat per plana totidem contigua, ita
comparata ut ſingula altitudine reſpondeant ſingu-
lis priorum planorum, ſed majori quam illa ſint
inclinatione. Dico tempus deſcenſus per minus in-
clinata, brevius eſſe tempore deſcenſus per magis
inclinata.
Sint ſeries duæ planorum inter easdem parallelas horizon-
22TAB. IX.
Fig. 1. tales comprehenſæ A B C D E, F G H K L, atque ita ut
bina quæque ſibi correſpondentia plana utriusque ſeriei iisdem
parallelis horizontalibus includantur; unumquodque vero ſeriei
F G H K L magis inclinatum ſit ad horizontem quam pla-
num ſibi altitudine reſpondens ſeriei A B C D E. Dico bre-
viori tempore abſolvi deſcenſum per A B C D E, quam
per F G H K L.
Nam primo quidem tempus deſcenſus per A B, brevius
eſſe conſtat tempore deſcenſus per F G, quum ſit eadem
ratio horum temporum quæ rectarum A B ad F G , 33Prop. 7.
huj. A B minor quam F G, propter minorem inclinationem.
Producantur jam ſurſum rectæ C B, H G, occurrantque
horizontali A F in M & N. Itaque tempus per B C poſt
A B, æquale eſt tempori per eandem B C poſt M B, cum
in puncto B eadem celeritas contingat, ſive per A B, ſive
per M B deſcendenti . ſimiliterque tempus per G H 44Prop. 6.
huj. F G, æquale erit tempori per eandem G H poſt N G. Eſt
autem tempus per B C poſt M B ad tempus per G H poſt
N G, ut B C ad G H longitudine, ſive ut C M ad H N,
cum hanc rationem habeant & tempora per totas M C, N H,
& per partes M B, N G , ideoque etiam tempora reliqua. 55Prop. 7.
huj. Eſtque B C, minor quam G H propter minorem inclina-
tionem. Patet igitur tempus per B C poſt M B ſive

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