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
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[Figure 144]
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[145] Pag. 262.TAB.XXIX.Fig. 1.P E O D C Q H M G N B S R T F
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[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
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[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
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[151] Pag. 276.TAB.XXXI.Fig. 2.a a m f k b e @ b a g a f b b h
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[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
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[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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15396CHRISTIANI HUGENII culus genitor A H D, cui occurrat B H, baſi parallela, in
11De linea-
RUM CUR-
VARUM
EVOLUTIO-
NE. H, & jungatur H A. Quia ergo B K tangit cycloidem in B,
conſtat eam parallelam eſſe rectæ H A . Itaque A H B K parallelogrammum eſt, ac proinde A K æqualis H B, hoc
22Propoſ. 15.
partis 2. eſt, arcui A H. Sit porro jam deſcriptus circulus K 33Propoſ. 14.
partis 2. genitori circulo, hoc eſt ipſi A H D, æqualis, qui tangat
baſin A G in K, rectam vero B K productam ſecet in pun-
cto E. Quia ergo ipſi A H parallela eſt B K E, ac proin-
de angulus E K A æqualis K A H, manifeſtum eſt B K
productam abſcindere à circulo K M arcum æqualem ei
quem à circulo A H D abſcindit recta A H. Itaque arcus
K E æqualis eſt arcui A H, hoc eſt rectæ H B, hoc eſt
rectæ K A. Hinc vero ſequitur, ex cycloidis proprietate,
cum circulus genitor M K tangebat regulam in K, punctum
deſcribens fuiſſe in E. Itaque recta K E occurrit cycloidi in
E ad angulos rectos . Eſt autem K E ipſa B K producta. 44Propoſ. 15.
partis 2. Ergo patet productam B K occurrere cycloidiad angulos re-
ctos. quod erat demonſtrandum.
PROPOSITIO VI.
SEmicycloidis evolutione, à vertice cœpta, alia
ſemicyclois deſcribitur evolutæ æqualis & ſimi-
lis, cujus baſis eſt in ea recta quæ cycloidem evolu-
tam in vertice contingit.
Sit ſemicyclois A B C, cui ſuperimpoſita ſit alia ſimilis
55TAB. XVI.
Fig. 1. A E F, quemadmodum in propoſitione præcedenti. Dico,
ſi linea flexilis, circa ſemicycloidem A B C applicata, evol-
vatur, incipiendo ab A, eam deſcribere extremitate ſua i-
pſam ſemicycloidem A E F. Quia enim ex puncto A egredi-
untur ſemicycloides A B C, A E F, in unam partem in-
flexæ, & ambæ in eandem cavæ, ac præterea ita comparatæ,
ut omnes tangentes ſemicycloidis A B C occurrant ſemicy-
cloidi A E F ad angulos rectos, ſequitur hanc evolutione
illius, à termino A incepta, deſcribi . quod erat 66Propoſ. 4.
huj.ſtrandum.

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