SECT. IX. To Measure a Piece of Ground which is a perfect Circle.
THe proportion of the Circumference of any Circle, to its Diameter,* 1.1 is as 7 to 22. Example. In this Circle ABCD let the Diameter thereof be 56 Perches, Feet, or Inches, which multiplyed in it self giveth 4136.* 1.2 This Num∣ber multiplyed by 11, gives 45496, which being divided by 14,* 1.3 the Quotient will be 3249 10/14, that is the Area of the Circle.
How many Poles and Feet, or square Inches, is in any Cir∣cle whatsoever, you may know better by these Rules; First, If you know the Diameter, and would find the Circumference, say, as 7 to 22, so the Diame∣ter 56 to the Circumference 176; Or if you know the Cir∣cumference, and would find the Diameter, say, as 22 to 7, so is the Circumference 176, to the Diameter 56.
The Diameter and Circumference being thus known, the Rule to find the Content is this.
The Diameter being 56 Perch, and the Compass 176, the half of both these multi∣plyed together, and divided by 160, you have the quantity of Acres 15, Roods 1, Perch 24, which is the Contents of that Circle.
Extend the Compasses from O Center at (203 7/10 unto the Diameter AC 56, the same distance will reach again from 56 to the quantity of Acres 15 4/10.
I confess though the ordinary proportion of 7 to 22, is somewhat too much; yet it is but about 1 in 3000, which will breed no great difference in these Questions.