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

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14692CHRISTIANI HUGENII

PROPOSITIO II.

11De linea-
RUM CUR-
VARUM
EVOLUTIO-
NE.
TAB. XII.
Fig. 2.

OMnis curva linea terminata, in unam partem
cava, ut A B D, ut poteſt in tot partes dividi, ut
ſi ſingulis partibus ſubtenſæ rectæ ducantur, velut
A B, B C, C D; & à ſingulis item diviſionis
punctis, ipſaque curvæ extremitate rectæ ducan-
tur curvam tangentes, ut A N, B O, C P, quæ
occurrant iis, quæ in proxime ſequentibus diviſionis
punctis curvæ ad angulos rectos inſiſtunt, quales
ſunt lineæ B N, C O, D P; ut inquam ſubtenſa
quæque habeat ad ſibi adjacentem curvæ perpendi-
cularem, velut A B ad B N, B C ad C O, C D
ad D P, rationem majorem quavis ratione propo-
ſita.

Sit enim data ratio lineæ E F ad F G, quæ recto angulo
ad F jungantur, & ducatur recta G E H.

Intelligatur primo curva A B D in partes tam exiguas ſe-
cta punctis B, C, ut tangentes quæ ad bina quæque inter
ſe proxima puncta curvam contingunt, occurrant ſibi mutuo
ſecundum angulos qui ſinguli majores ſint angulo F E H;
quales ſunt anguli A K B, B L C, C M D. quod quidem
fieri poſſe evidentius eſt quam ut demonſtratione indigeat.
Ductis jam ſubtenſis A B, B C, C D, & erectis curvæ
perpendicularibus B N, C O, D P, quæ occurrant pro-
ductis A K, B L, C M, in N, O, P: dico rationes ſin-
gulas rectarum, A B ad B N, B C ad C O, C D ad D P,
majores eſſe ratione E F ad F G.

Quia enim angulus A K B major eſt angulo H E F, erit
reſiduus illius ad duos rectos, nimirum angulus N K B,
minor angulo G E F. Angulus autem B trianguli K B N
eſt rectus, ſicut & angulus F in triangulo E F G.

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91	55
92	56
93	57
94	58
95	59
96	60
97	61
98	62
99	63
100	64
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

Scan	Original
91	55
92	56
93	57
94	58
95	59
96	60
97	61
98	62
99	63
100	64
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

Scan	Original
91	55
92	56
93	57
94	58
95	59
96	60
97	61
98	62
99	63
100	64
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