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

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189117HOROLOG. OSCILLATOR. rum quæ ex paraboloidibus naſcuntur conſtructionem, du-
11De linea-
RUMCUR.
VARUM
EVOLUTIO-
NE. cendæ ſunt lineæ D B Z, quæ ad datum punctum B ſecent
curvas A B, ſive ipſarum tangentes B H, ad angulos re-
ctos; dicemus in univerſum quomodo hæ tangentes inve-
niantur. In æquatione itaque, quæ cujusque curvæ naturam
explicat, quales æquationes duabus tabellis præcedentibus
exponuntur, conſiderare oportet quæ ſint exponentes pote-
ſtatum x & y, & facere ut, ſicut exponens poteſtatis x ad
exponentem poteſtatis y, ita ſit S K ad K H. Juncta enim
H B curvam in B continget. Velut in tertia hyperboloide,
cujus æquatio eſt x y2 = a3: quia exponens poteſtatis x eſt
1, poteſtatis autem y exponens 2; oportet eſſe ut 1 ad 2 ita
S K ad K H. Horum autem demonſtrationem noverunt
analyticæ artis periti, qui jam pridem omnes has lineas con-
templari cœperunt; & non ſolum paraboloidum iſtarum,
ſed & ſpatiorum quorundam infinitorum, inter hyperboloi-
des & aſymptotos interjectorum, plana ſolidaque dimenſi
ſunt. Quod quidem & nos, facili atque univerſali metho-
do, expedire poſſemus, ex ſola tangentium proprietate ſum-
pta demonſtratione. Sed illa non ſunt hujus loci.

73[Figure 73]

HOROLOGII OSCILLATORII
PARS QUARTA.

De centro Oſcillationis.

CEntrorum Oſcillationis, ſeu Agitationis, inveſtigatio-
nem olim mihi, fere adhuc puero, aliiſque multis, do-
ctiſſimus Merſennus propoſuit, celebre admodum inter illius
temporis Geometras problema, prout ex litteris ejus ad me
datis colligo, nec non ex Carteſii haud pridem editis, qui-
bus ad Merſennianas ſuper his rebus reſponſum continetur.
Poſtulabat autem centra illa ut invenirem in circuli

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Scan	Original
101
102
103
104	65
105	66
106	67
107	68
108
109
110
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