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

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

Table of contents

[11.] CHRISTIANI HUGENII A ZULICHEM, Const, F. HOROLOGIUM.

[12.] ILLUSTRISSIMIS AC POTENTISSIMIS HOLLANDIAE Et WESTFRISIAE ORDINIBUS Dominis ſuis, Christianus Hugenius à Zulighem Felicitatem omnem.

[13.] CHRISTIANI HUGENII A ZULICHEM, Const. F. HOROLOGIUM.

[14.] FINIS.

[15.] CHRISTIANI HUGENII ZULICHEMII, CONST. F. HOROLOGIUM OSCILLATORIUM. SIVE DE MOTU PENDULORUM AD HOROLOGIA APTATO DEMONSTRATIONES GEOMETRICÆ

[16.] Dividitur liber hic in partes quinque, quarum

[17.] LUDOVICO XIV, FRANCIÆ ET NAVARRÆ REGI INCLYTO.

[18.] HADRIANI VALLII DAPHNIS, ECLOGA.

[19.] CHRISTIANI HUGENII ZULICHEMII, CONST. F. HOROLOGIUM OSCILLATORIUM, SIVE DE MOTU PENDULORUM AD HOROLOGIA APTATO Demonſtrationes Geometricæ.

[20.] HOROLOGII OSCILLATORII PARS PRIMA, Deſcriptionem ejus continens.

[21.] HOROLOGII OSCILLATORII PARS SECUNDA. De deſcenſu Gravium & motu eorum in Cycloide. HYPOTHESES. I.

[22.] II.

[23.] III.

[24.] PROPOSITIO I.

[25.] PROPOSITIO II.

[26.] PROPOSITIO III.

[27.] PROPOSITIO IV.

[28.] PROPOSITIO V.

[29.] PROPOSITIO VI.

[30.] PROPOSITIO VII.

[31.] PROPOSITIO VIII.

[32.] PROPOSITIO IX.

[33.] PROPOSITIO X.

[34.] PROPOSITIO XI.

[35.] PROPOSITIO XII.

[36.] PROPOSITIO XIII.

[37.] PROPOSITIO XIV.

[38.] PROPOSITIO XV.

[39.] PROPOSITIO XVI.

[40.] PROPOSITIO XVII.

15396CHRISTIANI HUGENII culus genitor A H D, cui occurrat B H, baſi parallela, in
11De linea-
RUM CUR-
VARUM
EVOLUTIO-
NE. H, & jungatur H A. Quia ergo B K tangit cycloidem in B,
conſtat eam parallelam eſſe rectæ H A . Itaque A H B K parallelogrammum eſt, ac proinde A K æqualis H B, hoc
22Propoſ. 15.
partis 2. eſt, arcui A H. Sit porro jam deſcriptus circulus K 33Propoſ. 14.
partis 2. genitori circulo, hoc eſt ipſi A H D, æqualis, qui tangat
baſin A G in K, rectam vero B K productam ſecet in pun-
cto E. Quia ergo ipſi A H parallela eſt B K E, ac proin-
de angulus E K A æqualis K A H, manifeſtum eſt B K
productam abſcindere à circulo K M arcum æqualem ei
quem à circulo A H D abſcindit recta A H. Itaque arcus
K E æqualis eſt arcui A H, hoc eſt rectæ H B, hoc eſt
rectæ K A. Hinc vero ſequitur, ex cycloidis proprietate,
cum circulus genitor M K tangebat regulam in K, punctum
deſcribens fuiſſe in E. Itaque recta K E occurrit cycloidi in
E ad angulos rectos . Eſt autem K E ipſa B K producta. 44Propoſ. 15.
partis 2. Ergo patet productam B K occurrere cycloidiad angulos re-
ctos. quod erat demonſtrandum.

SEmicycloidis evolutione, à vertice cœpta, alia
ſemicyclois deſcribitur evolutæ æqualis & ſimi-
lis, cujus baſis eſt in ea recta quæ cycloidem evolu-
tam in vertice contingit.

Sit ſemicyclois A B C, cui ſuperimpoſita ſit alia ſimilis
55TAB. XVI.
Fig. 1. A E F, quemadmodum in propoſitione præcedenti. Dico,
ſi linea flexilis, circa ſemicycloidem A B C applicata, evol-
vatur, incipiendo ab A, eam deſcribere extremitate ſua i-
pſam ſemicycloidem A E F. Quia enim ex puncto A egredi-
untur ſemicycloides A B C, A E F, in unam partem in-
flexæ, & ambæ in eandem cavæ, ac præterea ita comparatæ,
ut omnes tangentes ſemicycloidis A B C occurrant ſemicy-
cloidi A E F ad angulos rectos, ſequitur hanc evolutione
illius, à termino A incepta, deſcribi . quod erat 66Propoſ. 4.
huj.ſtrandum.

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