Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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CHRISTIANI HUGENII
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nempe rectangulum fit à diſtantia centri gravitatis
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figuræ ab eadem recta, & </
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">à ſubcentrica cunei, qui
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per illam ſuper figura abſcinditur.</
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<
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">Poſitis enim cæteris omnibus quæ in conſtructione præce-
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">TAB. XIX.
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Fig. 4.</
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denti, ſit L A cunei A B D ſubcentrica in rectam E E. </
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portet igitur oſtendere, ſummam quadratorum omnium à di-
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ſtantiis particularum figuræ A C B æquari rectangulo ab
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F A, L A, multiplici ſecundum particularum numerum.</
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<
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">Et conſtat quidem ex demonſtratione præcedenti, altitu-
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dines parallelepipedorum ſingulorum, ut G K, æquales eſ-
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ſe diſtantiis particularum, quæ ipſorum baſes ſunt, ut G,
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ab recta A E. </
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<
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">Quare, ſi jam parallelepipedum G K ducamus
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in diſtantiam G H, perinde eſt ac ſi particula G ducatur in
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quadratum diſtantiæ G H. </
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<
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">Eodemque modo ſe res habet in
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reliquis omnibus. </
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<
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">Atqui producta omnia parallelepipedorum
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in diſtantias ſuas ab recta A E, æquantur ſimul producto ex
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cuneo A B D in diſtantiam L A , quia cuneus gravitat
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xml:space
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">Prop. 1.
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huj.</
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per puncto L. </
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<
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">Ergo etiam ſumma productorum à particulis
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ſingulis G, in quadrata ſuarum diſtantiarum ab recta A E,
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æquabitur producto ex cuneo A B D in rectam L A, hoc
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eſt, producto ex figura A C B in rectangulum ab F A, L A.
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<
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">Nam cuneus A B D, æqualis eſt producto ex figura A C B
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in rectam F A . </
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<
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">Rurſus quia figura A C B æqualis eſt
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præced.</
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ducto ex particula una G, in numerum ipſarum particula-
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rum; </
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<
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">ſequitur, dictum productum ex figura A C B in re-
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ctangulum ab F A, L A, æquari producto ex particula G
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in rectangulum ab F A, L A, multiplici ſecundum nume-
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rum particularum G. </
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<
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">Cui proinde etiam æqualis erit dicta
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ſumma productorum, à particulis ſingulis G in quadrata
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ſuarum diſtantiarum ab recta A E, ſive à particula una G in
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ſummam omnium horum quadratorum. </
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<
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">Quare, omiſſa utrin-
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que multiplicatione in particulam G, neceſſe eſt ſummam
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@andem quadratorum æquari rectangulo ab F A, L A, mul-
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tiplici ſecundum numerum particularum in quas figura A C B
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diviſa intelligitur. </
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<
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">quod erat demonſtrandum.</
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