Measure, Proportion and Mathematical Structure of Galleo’s Mechanics

Abstract

The subject of measure and proportion as an object of scientific analysis in Galileo’s works is closely connected with the broadest and most general problems of the history of the 17th-century science. When did the classical science arise? What concepts and notions designated its origin? In this respect the concepts of uniform motion of a body left to its own resources and of uniformly accelerated motion of a freely falling body, on the one hand, and methods of experimental and quantitative mathematical investigation of nature, on the other, are usually regarded as the most characteristic. The synthesis of the concepts mentioned is the most typical of the 17th century. These components of the new science existed earlier, but the synthesis changed the character of both. The concepts of uniform and uniform-difform motion were used by the Paris nominalists. In the 17th century and, first in the Discorsi (and partly in the Dialogo already) they became quantitative characteristics of motion and made the quantitative mathematical approach possible in principle. Bacon stressed the decisive role of experiment, success- fully used by Gilbert later in the 15th and 16th centuries. But only with Galileo did it become a quantitative experiment answering not only the questions “Is it so?”, and “What is the cause of this or that phenomenon?” but most often the question of “Is it equal or unequal?”, and “Equal to what?”, “How much is this?” With Galileo mathematics had not yet become scientific tool but had all the necessary prerequisites.