What were the Two New Sciences described by Galileo Galilei?

The "Two New Sciences" described by Galileo Galilei refer to the fields of motion and the strength of materials.12

These subjects were detailed in his final major work, published in 1638 under the title Discorsi e dimostrazioni matematiche intorno a due nuove scienze attenenti alla meccanica (Dialogues Concerning Two New Sciences). In this text, Galileo provided a summary of his mathematical and experimental investigations, which included:1

• The Science of Motion: This section covered his foundational work on the law of falling bodies and the parabolic paths of projectiles, which he explained as the result of combining constant speed with uniform acceleration.1
• The Science of Strength of Materials: In this area, Galileo treated the mechanics of solids for the first time, specifically analyzing the bending and breaking of beams.1

These contributions marked a fundamental shift in natural philosophy, moving the study of mechanics toward a mathematical and experimental approach.2