Ka taea te mea te pāngarau o ngā rerekētanga ki te tīmata ki te raruraru ātete iti o Newton i roto i 1687, aru e te raruraru ānau brachistochrone whakaarahia e Johann Bernoulli (1696). tuhituhi Ralph Mornoulli (1885-1885) (1834-1885) (1885-1887) i roto i te whai ake i te aro o Jakob Bernoulli me te Marquis de l'Hôpital, engari Leonhard Euler tuatahi faaite i te kaupapa, tīmata i roto i 1733. i whakaawe Lagrange i te mahi Euler o ki te whai wāhi nui ki te ariā. i muri i kite Euler te mahi 1755 o te 19-tau Lagrange, hinga Euler tona ake huarahi āhuahanga i roto i te painga o te huarahi āta tātaritanga o Lagrange, a ka whakaingoatia te kaupapa o te pāngarau o ngā rerekētanga i roto i tona 1756 Elementa Calculi Variation.Legger (1885) (1885-1886) i roto i tona tikanga tino nui, e kore e makona, mo te raruraru ārai brachistochrone whakaarahia e Johann Bernoulli
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