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

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11873HOROLOG. OSCILLATOR.

PROPOSITIO XVII.

11De motu
IN Cy-
CLOIDE.

IIsdem poſitis, ſi tertia recta prioribus parallela
22TAB. VIII.
Fig. 3. D K, circulum ſecuerit, quæ ab ea quæ centro
propior eſt A F, tantundem diſtet quantum hæc à
reliqua B G: dico partem tangentis in A, à pa-
rallela ultimo adjecta, & media interceptam, nem-
pe A D, arcu A C à primis duabus parallelis in-
tercepto minorem eſſe.

Hoc enim patet quum A D ipſi A B æqualis ſit, quam
antea oſtendimus arcu A C minorem eſſe.

PROPOSITIO XVIII.

SI circulum, cujus centrum E, duæ rectæ paral-
33TAB. VIII.
Fig. 4. lelæ ſecuerint A F, B G; & à puncto B, ubi
quæ à centro remotior eſt, vel tantundem atque
altera diſtat, circumferentiæ occurrit, ducatur
recta circumferentiam tangens: erit pars hujus
B A, à parallelis intercepta, major arcu ab iis-
dem parallelis intercepto B C.

Ducatur enim in puncto C, recta M C L circumferentiam
tangens, quæ occurrat tangenti B A in L. In triangulo igi-
tur A C L, angulus C æqualis eſt angulo M C F, hoc eſt,
ei quem capit portio circuli C B F. angulus autem A æqua-
tur angulo quem capit portio circuli B C G, quæ portio
quum ſit major vel æqualis portioni C B F, quippe quum
B G vel ulterius diſtet à centro quam C F, vel tantun-
dem: erit proinde trianguli A C L angulus A minor vel
æqualis angulo C: & conſequenter latus C L vel minus
vel æquale lateri A L. Atqui C L una cum L B majores
ſunt arcu C B. Ergo & A L una cum L B, hoc eſt,

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Scan	Original
111	69
112	70
113	71
114	72
115
116
117
118	73
119	74
120	75
121	76
122
123
124
125	77
126	78
127	79
128	80
129	81
130	82
131
132
133
134	83
135	84
136	85
137	86
138
139
140

Scan	Original
111	69
112	70
113	71
114	72
115
116
117
118	73
119	74
120	75
121	76
122
123
124
125	77
126	78
127	79
128	80
129	81
130	82
131
132
133
134	83
135	84
136	85
137	86
138
139
140