On the Determination of the Solar Rotation Elements i, {\Omega} and Period using Sunspot Observations by Ru{\dj}er Bo\v{s}kovi\'c in 1777

In September 1777, Ru{\dj}er Bo\v{s}kovi\'c observed sunspots for six days. Based on these measurements, he used his own methods to calculate the elements of the solar rotation, the longitude of the node, the inclination of the solar equator and the period. He published a description of the methods, the method of observation and detailed instructions for calculations in the second chapter of the fifth part of the Opera in 1785. In this paper, Bo\v{s}kovi\'c original calculations and repeated calculations by his procedure are published. By analysing the input quantities, procedures, and results, the input quantities of the error, and the calculation results are discussed. The reproduction of Bo\v{s}kovi\'c calculations is successfully reproduced and we obtained very similar results. The conclusion proposes a relationship of Bo\v{s}kovi\'c research with modern astronomy.