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
Page: 271
[122] Fig. 2.L O A V P Φ Δ V B E C S H D
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[123] Fig. 3.F G E G P A P K K L B D B S
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[Figure 124]
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[Figure 125]
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[126] Pag. 188.TAB.XXVII.Fig. 1.O V VA M N D N B O E CE A G B D C F
Page: 292
[127] Fig. 2.S Z G F H Y
Page: 292
[128] Fig. 3.D A D M T C
Page: 292
[129] Fig. 4.A E N D C
Page: 292
[130] Fig. 5.K D B G A F E H
Page: 292
[Figure 131]
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[Figure 132]
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[Figure 133]
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[Figure 134]
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[Figure 135]
Page: 336
[Figure 136]
Page: 353
[137] Pag. 248.TAB. XXVIII.Fig. 1.B A E D H F I G
Page: 355
[138] Fig. 2.M B A E D L N H F O I G
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[139] Fig. 4.O P M I B G Q N L R H A F D
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[140] Fig. 5.B A D L N H I
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[141] Fig. 3.a B c A C
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[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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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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