Discorsi e dimostrazioni matematiche, intorno a due nuove scienze
Galileo Galilei(1564-1642)
 In the early 17th century, all natural science was profoundly affected by Galileo. Mechanics in particular, was decisively innovated. Galileo did this mainly through his two famous workers, “Dialogo Sopra I due Massimi Sistemi del Mondo Tolemaico e Copernicano, 1632” and the work above. The former is his most famous, and was especially important because the authority of the church was shaken by human reason through the heated controversy caused by his book. However, the work above is more important by far in the history of science because of its direct contributions and comprehensive influence on that field.
 In this work, Galileo founded a new domain of mechanics called dynamics. He confuted Aristotele’s thesis of the falling body, in which falling velocity is in proportion to its weight and the void which is based on this thesis does not exist. He admitted the validity of the void and conjectured that all bodies fall with the same velocity in a vacuum, and verified that experimentally in approximation. He could not make a vacuum where he could observe the motion of two pendulums of equal lengths but different weights, and confirmed that the oscillation period was the same on condition that the air resistance was ignored.
 Subsequently, he surmised that the falling body is accelerated uniformly. Therefore its velocity is in proportion to its falling time. He demonstrated that mathematically and deducted that the falling distance is in proportion to the square root of falling time. Galileo verified this through his famous experiment which entailed the measurement of passing time and distance of a rolling ball on an inclined plane. He dealt with the motion of the projectile and explained this as a composition consisting of horizontal uniform motion and natural accelerated motion (free falling), and demonstrated that the locus of the projectile is a parabola using Apollonios’s (c. 262-c. 200 b. c.) theorems of the parabola.
 In addition to this, Galileo studied various other subjects such as hydrostatics and pneumatics. Galileo altered Aristotele’s theory of motion and founded modern mechanics by establishing a new domain in dynamics.
 It should be emphasized that Galileo’s importance stems not only from his direct achievements, but also more vitally from his methodology. Galileo proposed a hypothesis for a certain phenomenon, drew conclusions from it by mathematical deduction, then verified these conclusions through induction my experiments. This methodology came to be known as hypothetical deduction. It consisted of a combination of experiments that became the germ of the mechanistic nature in the modern world. Galileo maintained through this that in mathematics lies the structure of nature itself."