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

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15999HOROLOG. OSCILLATOR. penitiùs quam cyclois cognita ſit. Methodum vero noſtram,
11De linea-
RUM CUR-
VARUM
EVOLUT@@-
NE. qua in hac metienda uſi ſumus, in aliis quoque experiri li-
buit, de quibus porro nunc agemus.

PROPOSITIO VIII.

CUjus lineæ evolutione parabola deſcribatur os-
tendere.

Sit paraboloides A B, cujus axis A D; vertex A; pro-
22TAB. XIII,
Fig. 1. prietas autem iſta, ut ordinatim ad axem applicatâ B D,
cubus abſciſſæ ad verticem D A æquetur ſolido, baſin ha-
benti quadratum D B, altitudinem vero æqualem lineæ cui-
dam datæ M; quæ quidem curva pridem geometris nota
fuit; & ponatur axi D E juncta in directum A E, quæ ha-
beat {8/27} ipſius M. Jam ſi filum continuum circa E A B ap-
plicetur, idque ab E evolvi incipiat, dico deſcriptam ex
evolutione eſſe parabolam E F, cujus axis E A G, vertex
E, latus rectum æquale duplæ E A.

Sumpto enim in curva A B puncto quolibet B, ducatur
quæ in ipſo tangat curvam recta B G, occurrens axi E A
in G. & ex G ducatur porro G F, quæ ad rectos angulos
occurrat parabolæ E F in F; & ſit ipſi G F perpendicula-
ris F H, quæ parabolam in F continget; & denique F K
ordinatim ad axem E G applicetur.

Eſt igitur K G æqualis dimidio lateri recto, hoc eſt, ipſi
E A; ac proinde, additâ vel ablatâ utrimque A K, erit
E K æqualis A G. Eſt autem A G triens ipſius A D, quo-
niam B G tangit paraboloidem in B: illud enim ex natura
curvæ hujus facile demonſtrari poteſt. Ergo & E K æqualis
eſt trienti A D: & K H, quæ ex natura parabolæ dupla eſt
K E, æquabitur duabus tertiis A D. Itaque cubus ex K H
æqualis eſt {8/27} cubi ex A D, hoc eſt, ſolido baſin habenti
quadratum D B, altitudinem vero æqualem {8/27} M, hoc eſt,
ipſi A E. Quamobrem ut quadratum D B ad quadratum
K H, ita erit K H longitudine ad A E, hoc eſt ad K G.
Erat autem K H æqualis {@/3} A D, hoc eſt ipſi G D.

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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
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149
150	93
151	94
152	95
153	96
154
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157	97
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160	100