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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15093HOROLOG. OSCILLATOR. major erit ratio K B ad B N quam E F ad F G. Sed A B
11De linea-
RUM CUR-
VARUM
EVOLUTIO-
NE. major eſt quam K B, quoniam angulus K in triangulo A K B
eſt obtuſus, eſt enim major angulo H E F qui eſt obtuſus
ex conſtructione. Ergo ratio A B ad B N major erit ratio-
ne K B ad B N, ac proinde omnino major ratione E F ad
F G. Eodem modo & ratio B C ad C O, & C D ad D P,
major oſtendetur ratione E F ad F G. Itaque conſtat pro-
poſitum.
PROPOSITIO III.
DUæ curvæ in unam partem inflexæ & in eas-
dem partes cavæ ex eodem puncto egredi ne-
queunt, ita ad ſe invicem comparatæ, ut recta
omnis quæ alteri earum ad angulos rectos occurrit,
ſimiliter occurrat & reliquæ.
Sint enim, ſi fieri poteſt, hujuſmodi lineæ curvæ A C E,
22TAB. XII.
Fig. 3. A G K, communem terminum habentes A, & ſumpto in ex-
teriore illarum puncto quolibet K, ſit inde educta K E recta,
curvæ A G K occurrens ad angulos rectos, ac proinde
etiam curvæ A C E.
Poteſt jam recta quædam ſumi major curva K G A, quæ
ſit Q. Diviſa autem intelligatur ipſa K G A, ut in propo-
ſitione antecedenti dictum fuit, in tot partes punctis H G F,
ut ſubtenſæ ſingulæ K H, H G, G F, F A, ad perpen-
diculares curvæ ſibi contiguas H M, G N, F O, A P
majorem rationem habeant quam linea Q ad rectam K E.
Itaque & omnes ſimul dictæ ſubtenſæ ad omnes dictas per-
pendiculares majorem habebunt rationem quam Q ad K E.
Producantur autem perpendiculares eædem & occurrant cur-
væ A C E in D, C, B, nimirum ad angulos rectos ex
hypotheſi. Erit jam K E minor quam M D. Etenim, ducta
E L ipſi K E perpendiculari, quoniam K E occurrit lineæ
curvæ E C A ad angulos rectos, tanget E L curvam A C E,
occurretque neceſſario rectæ M D inter D & M.

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