Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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HOROLOG. OSCILLATOR.
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<
s
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xml:space
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">Et apparet, ſi dimidiam cycloidem, ipſi A B C gemel-
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<
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lam, contrario ſitu ab altera parte lineæ C G diſponamus,
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velut C N, ejus evolutione, vel etiam dum filum, jam
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extenſum in C F, circa eam replicatur, alteram ſemicy-
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cloidem F N fili extremitate deſcriptum iri, quæ ſimul
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cum priore A E F integram conſtituat.</
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<
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">Atque ex his, & </
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<
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">propoſitione 25 de deſcenſu gravium, ma-
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nifeſtum jam eſt quod ſupra in Conſtructione Horologii de
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æquabili penduli motu dictum fuit. </
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<
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xml:space
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">Patet enim perpendicu-
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lum, inter laminas binas, ſecundum ſemicycloidem inflexas,
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ſuſpenſum agitatumque, motu ſuo cycloidis arcum deſcri-
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bere, ac proinde æqualibus temporibus quaſlibet ejus reci-
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procationes abſolvi. </
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<
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xml:space
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">Non refert enim utrum in ſuperficie,
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ſecundum cycloidem curvata, mobile feratur, an filo alliga-
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tum lineam ipſam in aëre percurrat, cum utrobique eandem
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libertatem, eandemque in omnibus curvæ punctis inclina-
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tionem ad motum habeat.</
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">Cyclois linea ſui axis, ſive diametri circuli ge-
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nitoris, quadrupla eſt.</
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<
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Fig. 1.</
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cycloidem A B C evolutam, filum occupet rectam C F,
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quæ dupla eſt A D, proptarea quod axes cycloidum A B C,
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A E F ſunt æquales; </
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">apparet ſemicycloidem ipſam A B C,
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filo ſibi circum applicito æqualem, duplam eſſe ſui axis A D,
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ac totam proinde cycloidem axis ſui quadruplam.</
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<
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">Apparet etiam tangentem B E, quæ refert partem fili ex-
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tenſam, antea curvæ parti B A applicatam, huic ipſi longi-
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tudine æquari. </
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<
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">Eſt autem B E dupla ipſius B K, ſive A H,
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quoniam in propoſitione quinta oſtenſum eſt K E ipſi A H
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æqualem eſſe. </
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<
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">Itaque pars cycloidis A B rectæ A H, ſive
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B K, dupla erit: </
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cycloidis: </
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rit.</
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