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

Table of figures

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[121] Pag. 170.TAB. XXVI.Fig. 1.Ω O Ω A Z R F R N E N R G S V P Φ Δ V B D K C
[122] Fig. 2.L O A V P Φ Δ V B E C S H D
[123] Fig. 3.F G E G P A P K K L B D B S
[Figure 124]
[Figure 125]
[126] Pag. 188.TAB.XXVII.Fig. 1.O V VA M N D N B O E CE A G B D C F
[127] Fig. 2.S Z G F H Y
[128] Fig. 3.D A D M T C
[129] Fig. 4.A E N D C
[130] Fig. 5.K D B G A F E H
[Figure 131]
[Figure 132]
[Figure 133]
[Figure 134]
[Figure 135]
[Figure 136]
[137] Pag. 248.TAB. XXVIII.Fig. 1.B A E D H F I G
[138] Fig. 2.M B A E D L N H F O I G
[139] Fig. 4.O P M I B G Q N L R H A F D
[140] Fig. 5.B A D L N H I
[141] Fig. 3.a B c A C
[142] Fig. 7.D A C B E G
[143] Fig. 6.D A G B
[Figure 144]
[145] Pag. 262.TAB.XXIX.Fig. 1.P E O D C Q H M G N B S R T F
[146] Fig. 4.C A H N E P B L K I
[147] Fig. 3.N Q O P T
[148] Fig. 2.F D I C A B H K E R S G
[149] Fig. 5.L M C M E H O D P I
[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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12880CHRISTIANI HUGENII quanta acquiritur deſcendendo per arcum Cycloi-
11De motu
IN Cy-
CLOIDE.
dis B G, fore ad tempus quo percurretur recta
O P, celeritate æquabili dimidia ejus quæ acqui-
ritur deſcendendo per totam tangentem B I, ſicut
eſt tangens S T ad partem axis Q R.
Deſcribatur enim ſuper axe A D ſemicirculus D V A ſe-
cans rectam B F in V, &
Σ G in Φ, & jungatur A V ſe-
cans rectas O Q, P R, G Σ in E K &
Λ. Jungantur item
H F, H A, H X &
A Φ; quæ poſtrema ſecet rectas O Q,
P R in punctis Δ &
Π.
Habet ergo dictum tempus per M N ad tempus per O P,
rationem eam quæ componitur ex ratione ipſarum linearum
M N ad O P, &
ex ratione celeritatum quibus ipſæ per-
curruntur, contrarie ſumpta , hoc eſt, &
ex ratione 22Prop. 5.
Galil. de
motu æ-
quab.
diæ celeritatis ex B I ſive ex F A, ad celeritatem ex B G, ſive
ex F Σ .
Atqui tota celeritas ex F A ad celeritatem ex F 33Prop. 8.
huj.
eſt in ſubduplicata ratione longitudinum F A ad F Σ , 44Prop. 3.
huj.
proinde eadem quæ F A ad F H Ergo dimidia celeritas ex
F A ad celeritatem ex F Σ erit ut F X ad F H.
Itaque tem-
pus dictum per M N ad tempus per O P habebit rationem
compoſitam ex rationibus M N ad O P, &
F X ad F H.
Harum vero prior ratio, nempe M N ad O P, eadem oſten-
detur quæ F H ad H Σ.
Eſt enim tangens Cycloidis B I parallela rectæ V A, ſi-
militerque tangens M G N parallela rectæ Φ A;
ac proinde
recta M N æqualis Δ Π, &
O P æqualis E K. Ergo dicta
ratio rectæ M N ad O P eadem eſt quæ Δ Π ad E K;
hoc
eſt, Δ A ad E A;
hoc eſt, Φ A ad Λ A; hoc eſt V A ad
Φ A .
Eſt autem ut V A ad A Φ ita F A ad A H; 55Lemma
@ræced,
quia quadratum V A æquale eſt rectangulo D A F, &
qua-
dratum A Φ æquale rectangulo D A Σ, quæ rectangula ſunt
inter ſe ut F A ad Σ A, hoc eſt ut quadratum F A ad qua-
dratum A H, erit proinde &
quadratum V A ad quadra-
tum Φ A ut quadratum F A ad quadratum A H;

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