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

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13685HOROLOG. OSCILLATOR. quarum unaquæque minor ſit arcus cycloidis B N altitudine,
11De motu
IN CY-
CLOIDE. itemque minor altitudine arcus circumferentiæ F L; & ad-
ditâ ad F G unâ earum partium G ζ, ducantur à punctis di-
viſionum rectæ baſi D C parallelæ, & ad tangentem B Θ
terminatæ, P O, Q K, & c; itemque à puncto ζ recta ζ Ω
quæ ſecet cycloidem in V, circumferentiam in η; quibus-
que in punctis ductæ parallelæ ſecant circumferentiam F H,
ab iis tangentes deorſum ducantur usque ad proximam quæ-
que parallelam, velut θ Δ, Γ Σ: Quarum infima à puncto
Η ducta occurrat rectæ ζ Ω in X. Similiter vero & à pun-
ctis, in quibus dictæ parallelæ occurrunt cycloidi, ducan-
tur totidem tangentes deorſum, velut S Λ, T Ξ, & c. qua-
rum infima, tangens nempe à puncto E ducta, occurrat re-
ctæ ζ Ω in R.

Quia igitur P ζ æqualis eſt F G altitudini arcus B E,
cui æqualis eſt ex conſtructione altitudo arcus N M, erit &
P ζ æqualis altitudini arcus N M. Eſt autem recta P O ex
conſtructione ſuperior termino N. Ergo & ζ Ω, & in ea
punctum V, ſuperius termino M. Quare, cum arcus S V
æqualis ſit altitudinis cum arcu N M, ſed termino S ſubli-
miore quam N, erit tempus per S V brevius tempore per N M.

22Prop. 22.
huj.

Atqui tempus per tangentem S Λ, cum celeritate æqua-
bili ex B S, brevius eſt tempore deſcenſus accelerati per ar-
cum S T, incipientis in S. Nam celeritas ex B S, qua to-
ta S Λ transmiſſa ponitur, æqualis eſt celeritati ex S T 33Prop. 8.
huj. quæ motui per arcum S T in fine demum acquiritur; ipſa-
que S Λ minor eſt quam S T. Similiter tempus per tangen-
tem T Ξ, cum celeritate æquabili ex B T, brevius eſt tem-
pore deſcenſus accelerati per arcum T Y poſt S T; quum
celeritas ex B T, qua tota T Ξ transmiſſa ponitur, ſit æqua-
lis celeritati ex S Y, quæ in fine demum acquiritur motui
dicto per arcum T Y poſt S T; ipſaque T Ξ minor ſit arcu
T Y. Atque ita tempora omnia motuum æquabilium per
tangentes cycloidis, cum celeritatibus per ſingulas quantæ
acquiruntur deſcendendo ex B usque ad punctum ipſarum
contactus, breviora ſimul erunt tempore deſcenſus

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Scan	Original
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136	85
137	86
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141	87
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145	91
146	92
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153	96
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Scan	Original
131
132
133
134	83
135	84
136	85
137	86
138
139
140
141	87
142	88
143
144	90
145	91
146	92
147
148
149
150	93
151	94
152	95
153	96
154
155
156
157	97
158	98
159	99
160	100