...water strikes the wheel ; and if we take h, a fourth proportional to g', (c — t;)1 and \g, h will be the height from which a body must fall to acquire the velocity c — v, and will be equal to - — - — - • Wherefore, by a prop, well known in Hydraulics, the...

...the triangles BAI, K AI, being similar, BA is equal to -r^— Since, then, AB is equal to four timca the height from which a body must fall to acquire the velocity with which it is AE9 AI9 to be thrown ; ^ (or -r^- its equal) is the same. Consequently (by this Prop.)...

...water strikes the wheel; and if we take h, afourth proportional T2 tog * , (c—v) % and \g, h will be the height from which a body must fall to acquire the velocity C—v, and will be— fc ~ v} * • Wherefore, by a 2 § proposition, well known in Hydraulics, the...

...waterstrikes the wheel ; and if we take h, a fourth proportional % (c— • v) * and 4*7, h will be the height from which a body must fall to acquire the velocity <N — v, and will be— (c~ v) * • Wherefore, by a 2g proposition, well known in Hydraulics, the...

...4. Tlit velocity and elevation being given, to fnd the range. ,,* Take; AD =: -, or equal four times the height from which a body must fall to acquire the velocity v ; from o, draw DC, making the angle ADC = ABC; from c, draw BC, parallel to AD, meeting the plane...

...is required, these formulas would become v 3 - = l 3 tv 64 1 2s 32 4 v 2s v — 8^/1 — - = 32 t t The value of this force varies in different latitudes,...from which a body must fall to acquire the velocity. 161. In order that a body projected directly upwards, shall rise to a given height, it must receive...

...reasoning of the demonstration conducting to the solution and not following it synthetically. A is the height from which a body must fall to acquire the velocity at any point D, which the given body moving in the trajectory VIK (sought by the investigation) has...

...numbers appear to have been computed for any velocity, », is p = Ibs. for each square foot ; a being the height from which a body must fall to acquire the velocity r. There is certainly a trifling difference between the numbers thus computed and those in the table,...

...reasoning of the demonstration conducting to the solution and not following it synthetically. A is the height from which a body must fall to acquire the velocity at any point D, which the given body moving in the trajectory VIK (sought by the investigation) has...

...of w when Dw would be equal to the force of gravity, and DK = Bl = 2y, we have D =- -jfi or H being the height from which a body must fall to acquire the velocity V/i' since K = 4^77, D = ~ , and27>>= -. Sc/wlium 3. It is natural to imagine that we might obtain...