Problem 5

Given the diameter of one circle to make another circle which
shall be any number of times greater or less than the given circle.

Rule

Square the
given diameter and if the required circle be greater multiply the square of the
diameter by the proportion and the root of the product will be the required
diameter. But if the required circle be less, divide the square of the diameter
by the proportion and the root of the quotient will be the diameter required.

Comment: No
results in geometry are covered in the notebook. Given the statement of the
rule no knowledge of geometry is necessary.

Example

There is a
circle whose diameter is 4 inches. I want to know the diameter of a circle 3
times as big.

Solution

Square the
diameter: . Multiply by the
increase in size: . The solution is , which can be found longhand
by the algorithm given earlier in Macdonald’s
notes, which was taken from Nicholas Pike’s *A
New and Complete System of Arithmetick*.