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

Table of figures

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[71] Fig. 2.H A K B R P F L O M N D Q G E
Page: 185
[72] Fig. 3.Y H A S Z X T K B V L P F O C M N D G E
Page: 185
[Figure 73]
Page: 189
[74] Pag. 122TAB. XVII.Fig. 1.S A P B R M D I
Page: 196
[75] Fig. 2.H S Z K B C M D
Page: 196
[76] Fig. 3.P S Z M A B K D H
Page: 196
[77] Fig. 4.H C A E D F B G
Page: 196
[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
Page: 225
[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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12075HOROLOG. OSCILLATOR. traque parte centri Z, & ſit G H, earum quæ ſunt à parte
11De motu
IN Cy-
CLOIDE. B, centro proxima, vel per ipſum centrum tranſeat. Itaque
tangentes omnes inter G H & B O comprehenſæ, ut H K,
L M, N O, ſingulæ ſuis arcubus minores ſunt . 22Prop. 16.
huj. autem & tangens G F, arcu ſequente F D minor eſt , & 33Prop. 17.
huj. ſimiliter tangens E D arcu D A. Itaque tangentes omnes
inter B O & C D interjectæ, minores ſunt arcubus B H &
F A, ac proinde omnino minores arcubus B H, H A, ſive
arcu B A, quod erat primo oſtendendum.
Porro jam demonſtrabimus tangentes omnes inter B O & A
majores eſſe arcu A N. Enimvero parallela G H, vel pro-
pius centrum Z tranſit quam parallela E F, quam pono
proximam eſſe earum quæ à parte A tranſeunt, vel erit re-
motior, vel æque diſtabit.
Quod ſi E F longius à centro vel æque remota eſt ac G H,
erit tangens F G major arcu ſuo F H, & reliquæ tangen-
tes verſus A, nimirum E D, C A majores ſingulæ arcubus
44Prop. 15.
huj. ſuis ; adeo ut omnes ſimul G F, E D, C A majores ſint arcu H A. ſed & arcu H L major erit tangens L M , & 55Prop. 19.
huj. arcu L N tangens N O; itaque tangentes omnes, præter
H K, majores ſimul erunt arcu A N; multoque magis, ac-
cedente ipſa H K, tangentes omnes inter A & B compre-
henſæ arcu eodem A N majores erunt.
Si vero G H à centro longius diſtat quam E F, erit tan-
gens K H major arcu H F , & tangens M L ut ante 66Prop. 19.
huj. jor arcu L H, & tangens O N major arcu N L, & omnes
proinde tangentes O N, M L, K H majores arcu N F.
Sed & tangens E D major eſt arcu ſuo F D , & 77Prop. 11.
huj. C A major ſimiliter arcu ſuo D A. Itaque tangentes omnes
inter B O & A, præter G F, majores erunt arcu N A;
multoque magis tangentes eædem, accedente G F, hoc eſt,
omnes quæ inter B O & A interjiciuntur, eodem arcu N A
majores erunt.
Ex his vero etiam demonſtratio manifeſta eſt in caſibus
aliis, qualiscunque ſemicircumferentiæ arcus accipiatur,
quippe cum vel eadem ſit ubique, vel pars tantum præce-
dentis demonſtrationis.

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