A mathematical method for obtaining the value of the cosmological constant Ʌ from the cosmological equations of the Universe has been found. The method is based on the revealed connection of the cosmological constant Ʌ with fundamental physical constants. The new large scale numbers 10^140, 10^160 and 10^180 obtained from the scaling law allowed us to obtain cosmological equations linking the cosmological constant Ʌ with the fine structure constant "alpha", Planck's constant, the speed of light and the electron constants. The approximate Eddington equation Ʌ≈[(me/αћ)^4][(2Gmp/π)^2] is refined to an exact equation. A large number of new cosmological equations are derived, which include the cosmological constant Ʌ. The value of the constant Ʌ is obtained by different methods: from the finalized Eddington equations; from the coincidence of large numbers; from the cosmological equations of the universe and the speed of light; from the cosmological equations of the universe and Planck's constant; from the experimental value of the Pioneer anomaly; from the Kepler relation for the universe. All methods give the same value of the cosmological constant Ʌ (Ʌ = 1.36285...x 10^(-52) m^(-2) ). The theory based on the law of scaling of large numbers predicts a value of the constant Ʌ close to the experimental one. The accuracy of the calculated value of Ʌ is close to the accuracy of the Newtonian constant of gravitation G. The reason for the large number of equivalent equations that include the cosmological constant Ʌ remains a mystery.