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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134	83
135	84
136	85
137	86
138
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141	87
142	88
143
144	90
145	91
146	92
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150	93
151	94
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153	96
154
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157	97
158	98
159	99
160	100

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

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