
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.
