As a mathematical justification of Mach's principle, we present a system of cosmological equations that combines the parameters of the Universe and fundamental physical constants. The equations included in the system of cosmological equations were derived independently and at different times by famous scientists: Schrödinger, Blackley, Milne, Hoyle and existed in a scattered form. The system of cosmological equations, formed on the basis of Mach's principle, allows us to derive mathematically the parameters of the observable Universe with an accuracy close to the accuracy of the gravitational constant G. This translates Mach's philosophical principle about the connection between the Universe and the microworld onto a rigorous mathematical basis. The system of cosmological equations gives the following roots (parameters of the observable Universe): mass: Mu = 1.15348u2026 u202210^53 kg; radius: Ru = 0.856594u2026u202210^26 m; time: Tu = 2.85729u2026 u202210^17 s; acceleration: Ao = 10.4922u202210^-10 m/s^2, Hubble parameter H0 = 1.74991х 10^-18 s-1 (53.9967 km/s/Mpc). The derived values of the parameters of the observable Universe confirm with high accuracy the connection between the Universe and the microworld formulated by Mach. The mathematical substantiation of Mach's principle showed that the parameters of the Universe are directly related to the parameters of the fundamental object of the microworld - the ELECTRON. Mach's principle turned out to be much deeper: not only are the inertial properties of any body determined by its interaction with the entire Universe, but the parameters of the Universe themselves are directly related to the fundamental constants of the microworld.