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

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178112CHRISTIANI HUGENII niam curva, ad quam ſunt puncta T, V, geometrica eſt.
11De linea-
RUM CUR-
VARUM
EVOLUTIO-
NE. Ratio igitur Y K ad K T data erit, adeoque & V X ad
X T. ex qua etiam rationem L K ad N M dari oſtendimus.

Quænam vero ſit linea ad quam ſunt puncta T, V, in-
venitur ponendo certum punctum S in recta K L, & vocan-
do S K, x; K T, y. Nam quia data eſt curva A B F,
eique B M ad angulos rectos ducta, invenietur inde quanti-
tas lineæ K M, per methodum tangentium à Carteſio traditam,
quæ ipſi K T, ſive y æquabitur, & ex ea æquatione, natura
curvæ T V innoteſcet, ad quam deinde tangens ducenda
eſt. Sed clariora omnia fient ſequenti exemplo.

Sit A B F paraboloides illa, cui ſuperius rectam æqua-
22TAB. XVI.
Fig. 3. lem invenimus; in qua nempe cubi perpendicularium in
rectam S K, ſint inter ſe ſicut quadrata ex ipſa S K abſciſ-
ſarum. Et oporteat invenire curvam C D E cujus evolu-
tione paraboloides S B F deſcribatur.

Hic primum ratio B O ad B P facile invenitur, quia
tangentem paraboloidis in puncto B duci ſcimus, ſumpta S H
æquali {1/2} S K. Cui tangenti cum B M ad angulos rectos in-
ſiſtat, dantur jam lineæ M H, H K, ac proinde earum in-
ter ſe ratio, quæ eſt eadem quæ O B ad B P.

Ut autem ratio B P, ſive K L ad M N innoteſcat, po-
nantur ad K L perpendiculares rectæ K T, L V, æquales
ſingulis K M, L N, ſitque V X parallela L K. Jam quia
ex duabus ſimul K L, L N, auferendo K M, relinquitur
M N ; hoc eſt, auferendo ex duabus X V, V L, ſive

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Scan	Original
121	76
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125	77
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129	81
130	82
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134	83
135	84
136	85
137	86
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