Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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MECHANICAM.
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K C. </
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<
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xml:space
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">Similiter verò duobus his, filo G K tracto à potentia
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quæ ſit ut tripla G K, & </
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<
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ut ſimplex longitudo D K, æquipollet filum H K tractum
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à potentia quæ ſit ut quadrupla H K. </
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<
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xml:space
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">Ergo hoc æquipollet
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filis onmibus K A, K B, K C, K D, punctum K uti di-
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ctum eſt trahentibus. </
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<
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">Atqui filo K H in directum opponitur
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filum K E tractum à potentia quæ eſt ut longitudo K E, id
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eſt ut quadrupla K H. </
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<
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">Ergo cum filis K E, K H, in partes
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directè oppoſitas trahentibus cum potentiis æqualibus, pun-
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ctum K neceſſario in locum ſuum ſervatum ſit, ſequitur & </
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<
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K A, K B, K C, K D, uti dictum eſt trahentibus & </
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<
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alia parte filo K E nodum reſtare immotum. </
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<
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">Quod erat de-
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monſtrandum.</
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<
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">Poſſunt autem & </
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<
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">binorum quorumque punctorum centra
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gravitatis primò deſignari, & </
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<
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vitatis quaternorum, & </
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<
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</
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<
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">qua ratione ſimplicior plerumque efficitur demonſtratio, ac
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præſertim ſi datorum punctorum numerus fuerit pariter
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par.</
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<
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">Ut ſi quatuor data fuerint A, B, C, D; </
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<
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Fig. 3.</
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plano, ſive non: </
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<
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E & </
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G; </
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<
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D. </
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">Quod ſi jam nodus G trahatur filis G A, G B, G C,
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G D, à potentiis quæ ſint inter ſe ut hæ ipſæ filorum longi-
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tudines; </
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<
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">dico fieri æquilibrium.</
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<
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<
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">Conſtat enim filis G A, G B, æquipollere filum G E
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tractum à potentia quæ ſit ut dupla G E; </
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<
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xml:space
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">filis verò G C,
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G D, æquipollere filum G F tractum à potentia quæ ſit ut
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dupla G F. </
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<
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">Cum ergo G E, G F æquales ſint, unamque
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lineam rectam efficiant, eodem modo nodus G trahitur, ac
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ſi traheretur à potentiis æqualibus per fila G E, G F. </
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de immotum manere neceſſe eſt.</
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<
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">Conſtat verò ſi puncta A, B, C, D non ſint in eodem
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plano, fore G centrum gravitatis pyramidis cujus anguli hæc
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ipſa quatuor puncta; </
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