button to main menu  Greenwood and Hodgson 20.9.1823
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  An acre of grazing
Westmorland Gazette, 20 September 1823:-
TO THE EDITOR OF THE CHRONICLE.
SIR,
Your correspondent asks in what manner a horse must be tethered in a circular field of four acres, so as to eat only one acre of the same, also bounded by a circle, the tether pin not being fixed in the centre of the field, in other words he is to eat but one fourth of the field. Now as circles are as the squares of their diameters by the second Proposition of the 12th Book of Euclid, these diameters are as the square roots of their areas, therefore one is to one half, so is the diameter of the whole field of four acres to that of the circle of one acre. Now if the diameter of the larger area be taken equal 156.62 yards that of the less circular area will be 78.31 yards; consequently if the pin be fixed at the distance of 39.155 yards from the centre the horse will be able to eat an acre in a circle passing through the centre of the field and touching the fence of the same. Should your Correspondent be desirous of seeing the figure of the field represented upon paper, he may describe the circle of which AB. is any diameter and O. its centre; bisect OA. in P. from P. as a centre with distance OP. or PA. describe the circle OCAD.; which will represent the space to which the horse is to be confined by the tether fixed to the point P. and equal in length to OP.
RURICOLA.

Summary

from - Ruricola
to - the Editor, replying to JNC
AN ACRE OF GRAZING an answer
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