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

Table of figures

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[111] Fig. 2.G B R F
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[112] Fig. 3.A E C F B
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[113] Fig. 4.A C E D F B
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[114] Fig. 6.A B C G D L
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[115] Fig. 5.H A O M R L N
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[116] Pag. 166.TAB.XXV.Fig. 1.A O C G D L N
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[117] Fig. 2.A B C G D L N
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[118] Fig. 3.O C D A K B N E F C D L M
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[119] Fig. 4.O A C D F E K B N C L D M
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[120] Fig. 5.E A G F H K B D C
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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
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[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
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[127] Fig. 2.S Z G F H Y
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[128] Fig. 3.D A D M T C
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[129] Fig. 4.A E N D C
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[130] Fig. 5.K D B G A F E H
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[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]
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[Figure 136]
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[137] Pag. 248.TAB. XXVIII.Fig. 1.B A E D H F I G
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[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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11169HOROLOG. OSCILLATOR.
PROPOSITIO XV.
11De de-
SCENSU
GRAVIUM.
DAto in Cycloide puncto, rectam per illud du-
cere quæ Cycloidem tangat.
Sit cyclois A B C, & punctum in ea datum B, per quod
22TAB. VII.
Fig. 2. tangentem ducere oporteat.
Circa axem cycloidis A D deſcribatur circulus genitor
A E D, & ducatur B E parallela baſi cycloidis, quæ dicto
circulo occurrat in E, & jungatur A E, cui denique paral-
lela per B agatur H B N. Dico hanc cycloidem in B con-
tingere.
Sumatur enim in ea punctum quodlibet, à B diverſum,
ac primo verſus ſuperiora velut H, & per H ducantur re-
cta baſi cycloidis parallela, quæ occurrat cycloidi in L, cir-
culo A E D in K, rectæ A E in M. Quia ergo K L eſt
æqualis arcui K A, recta autem K M minor arcu K E, erit
recta M L minor arcu A E, hoc eſt, rectâ E B, ſive M H;
unde apparet punctum H eſſe extra cycloidem.
Deinde in recta H N ſumatur punctum N inferius B, &
per N agatur, ut ante, baſi parallela, quæ occurrat cycloi-
di in Q, circulo A E D in O, rectæ A E productæ in P.
Quia ergo O Q, æqualis eſt arcui O A; O P autem major
arcu O E; erit P Q minor arcu E A, hoc eſt, rectâ E B,
ſive P N. Unde apparet rurſus punctum N eſſe extra cycloi-
dem. Cum igitur quodlibet punctum præter B, in recta
H B N ſumptum, ſit extra cycloidem, conſtat illam in
puncto B cycloidem contingere; quod erat demonſtrandum.
Huic demonſtrationi an locum ſuum hic relinquerem dubi-
tavi, quod non multum ei abſimilem à clariſſimo Wrennio
editam inveniam in libro Walliſii de Cycloide. Poteſt autem
& univerſali conſtructione propoſitum abſolvi, quæ non cy-
cloidi tantum ſed & aliis curvis, ex cujuſlibet figuræ circum-
volutione genitis, conveniat; dummodo ſit figura in ean-
dem partem cava, & ex iis quæ geometricæ vocantur.
Sit enim curva N A B, orta ex circumvolutione figuræ
33TAB. VII.
Fig. 3.

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