First Prince ... 518 1320 1418
Second Prince ... 280 2442 2458
Third Prince ... 231 2960 2969
Fourth Prince ... 111 6160 6161
The area in every case is 341,880 square furlongs. I must here refrain
from showing fully how I get these figures. I will explain, however, that
the first three triangles are obtained, in the manner shown, from the
numbers 3 and 4, which give the generators 37, 7; 37, 33; 37, 40. These
three pairs of numbers solve the indeterminate equation, _a_^3_b_
-_b_^3_a_ = 341,880. If we can find another pair of values, the thing is
done. These values are 56, 55, which generators give the last triangle.
The next best answer that I have found is derived from 5 and 6, which
give the generators 91, 11; 91, 85; 91, 96. The fourth pair of values is
63, 42.
The reader will understand from what I have written above that there is
no limit to the number of rational-sided R.A.T.'s of equal area that may
be found in whole numbers.