Let MN = x. He defines m so that MD = mx, and n so that Mm = nx + na and notes that x is the only variable and that m is finite and n is infinitely small. The small time to travel along arc Mm is , which has to be a minimum (‘un plus petit’). He does not explain that because Mm is so small the speed along it can be assumed to be the speed at M, which is as the square root of MD, the vertical distance of M below the horizontal line AL.
lEt Mn = x. he deFines M so that md = mx, anD N so thAt Mm = nx + na anD Notes thaT X is The ONly variable and thaT M is FInitE anD n iS infinitely smAll. The Small tiMe To travel along aRC Mm iS , which HAs to be a minimum (‘uN plUs petit’). he Does NOt eXPlain tHAt bEcause mm Is so sMaLl thE Speed along It Can be asSumed to bE the sPeed at M, wHIch Is aS thE sQuare rOOt Of md, The vertIcal DIstanCE Of m below tHE horiZOntAl line Al.