Brachistochrone - BhraS + IST + (ah) + Kram + (e) -> BhraS-iST-ah-Kram-e -> BhraS-iST-ah-Chram-e -> Bharch-iST-o-ChraNe -> Bharch-ist-o-ChroNe
BhraS - To Fall with Cerebral S. English does not have this sound "S" sound, and it is sometimes heard in "Shutup", but here "sh" is actually written for Palatal Soft "S" sound as "Sh" and also becomes "ch" in spelling when pronounced as "sh".
IST - iiST - ist - The suffix for Superlatives - like - 'est' in English. "S" and "T" are Cerebral sounds. "S" becomes "s" in approximations and "I", Big 'i' becomes 'i'.
ah - Termination for Singular Nominative or Subjective - like Rama becomes Ramah. "ah" is the Hard "h" sound and is called 'visargha' in Sanskrit. When meeting the soft sound "sh", not as the Sibilants liked by Hard Consonants, can become 'o'. Sibilants are treated as Hard sounds but English "Sh" and Sanskrit "Sh" are also treated as "Soft" sounds.
Kram - To Progress, to follow order, sequence, progression, trace space-time events.
e - For Locative Case of "In" and " On".
So it means the "Fall + Best + Progress or Path of Succession Events + In" - which is what the word means in Greek and English!