PROBLEM.

Having any two fides of a cone, to find the other fide.

By the help of the foregoing problem, you'll find, that to fquare the flant height (which is the length of a line drawn from its vertical point to the circumference of its bafe) and from that fquare fubtract the fquare of the femidiameter of its bafe, then the fquare root of the remainder is the perpendicular height of

the cone.

Note. The fame rule ferves for a pyramid. EXAMPLE.

B

Given the flant height A B 60, and bafe diameter A C 36, to find the perpendicular height B D?

36

60

There is a tower whofe height is 45 yards, and is furrounded by a moat 30 yards broad; of what height muft a fcaling-ladder be that will reach from the outfide of the moat to the top of tower?

Yards.

Two men fet out together from one place; one went directly north 72 miles, and the other went directly weft 96 miles; I would know how far they are afunder

72

96

Suppofe a fhip fails 440 miles till her difference of latitude is 310 miles, I demand how far fhe is departed from the meridian?

N. B. In this question, the departure is the distance that the fhip is to the eaft or weft of the meridian, and is the bafe line; the diftance that the fhip has failed is the hypothenufe; and the difference of latitude is the perpendicular, and fhews how much the fhip is to the north or fouth of the place it fet fail from.

A

A ladder 52 feet long, being fo placed in a street, that it reach a window 29 feet from the ground on one fide, and by turning the ladder over (without removing the foot) it will touch a moulding 40 feet from the ground on the other fide; how broad is the street?

Alfo from the foregoing problem, there may be other examples very eafily constructed to exercise the learner therein, as the three cafes all depend upon one theorem.

PROBLEM. Having the three fides of an oblique angled triangle given, to find the point in the bafe where the perpendicular of a right angled triangle fall fall.

RULE. Square the two longeft fides, and from the fum of thefe fquares fubtract the fquare of the leffer fide, divide half the remainder by the longest fide, and the quotient will give the anfwer.

EXAMPLE. Given the longest fide A C 100, the next in length A B 80, and the leaft fide B C 40, to find the point D in the bafe where the perpendicular shall fall?