I ovde se vidi genijalnost ovog graditelja.
Assuming the radii of the three circles in the diagram are successively R0, R1, R2 we have(1) 1/√R2 = 1/√R1 - 1/√R0.
By induction, then(2) 1/√Rn = 1/√R1 - (n - 1)/√R0.
Denoting 1/√Rn = un, we convert (2) to a simple linear relation(3) un = u1 - (n-1)u0, n > 1.
Since, for all n, un > 0, (3) shows that the process may continue as long as u1 - (n-1)u0 > 0, o, in other words, while(4) n < 1 + u1 / u0, i.e, n ≤ u1 / u0
For R0 = 106mm and R1 = 1 mm, u1 / u0 = 103. Which means that it is impossible to construct circle C1001 and C1000 is the last one, thus solving the problem. (The solution from [Morsels] shows also that R1000 = R0, giving another reason why the process can't continue beyond n = 1000.)
Iz svega gore napisanog vidi se da je projektant znao da izračuna tačno rastojanje između zemlje i meseca, kao i između korisnika njegovog proizvoda i centra zemlje. Kako je to genijalno otkriće.