Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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HOROLOG. OSCILLATOR.
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eſt a, multiplici ſecundum ſemiſſem numeri particularum
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quas continet. </
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<
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xml:space
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">Et diſtantiæ omnes particularum ponderis C,
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ab eodem puncto A, ſunt a c. </
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xml:space
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">Ita ut ſumma utrarumque di-
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ſtantiarum ſit {1/2} a b + a c. </
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<
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xml:space
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quadratorum prius inventam, {1/3} a a b + a a c, fit
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{{1/3} a a b + a a c/{1/2} a b + a c} ſive {{1/3} a b + a c/{1/2} b + c}, longitudo penduli iſochroni. </
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<
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">Quæ
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itaque habebitur, ſi fiat, ut dimidia gravitas virgæ, una
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cum gravitate appenſi ponderis, ad trientem gravitatis virgæ,
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una cum gravitate ejuſdem appenſi ponderis, ita longitudo
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A C ad aliam. </
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<
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">Oportet autem ſumere longitudinem A C,
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à puncto ſuſpenſionis A ad centrum gravitatis ponderis C;
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</
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<
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">cum magnitudinis ejus ratio hic non habeatur, ac veluti
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minimum conſideretur.</
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">Quod ſi jam, præter pondus C, alterum inſuper D virgæ
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">TAB. XXVII@
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Fig. 4.</
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inhærere intelligatur, cujus gravitas, ſeu particularum nume-
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rus ſit d: </
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<
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">Ut pendulum ſimplex
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huic ita compoſito iſochronum inveniatur, addenda ſunt ad
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ſummam ſuperiorem quadratorum, quadrata diſtantiarum
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particularum ponderis D à puncto A, quæ quadrata apparet
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eſſe d f f. </
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<
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xml:space
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">Adeo ut ſumma omnium jam ſit futura {1/3} a a b +
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a a c + f f d. </
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">Item, ad ſummam diſtantiarum, addendæ
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diſtantiæ particularum ponderis D, quæ faciunt d f. </
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<
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ma proinde diſtantiarum omnium erit {1/2} b a + c a + d f;
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</
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<
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">per quam dividenda eſt iſta quadratorum ſumma, & </
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{{1/3} a a b + a a c + f f d/{1/2} a b + a c + f d}, longitudo penduli iſochroni.</
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<
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">Quod ſi vero, hæc longitudo penduli iſochroni, datæ æqualis
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poſtuletur, quæ ſit p, & </
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præter diſtantiam A D ſeu f, quæ determinat locum pon-
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deris D: </
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<
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">Nempe, cum poſtuletur {{1/3} a a b + a a c + f f d/{1/2} a b + a c + f d} æquale p, orietur ex
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hac æquatione f f = p f + {{1/2} a b p + c a p - {1/3} a a b - a a c/d}. </
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<
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xml:space
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">Et f = {1/2} </
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