The Ancients’ Inferno: The Slow and Tortuous Development of ‘Newtonian’ Principles of Motion in the Eighteenth Century

Abstract

In his Introduction to the History of Structural Mechanics Edoardo Benvenuto provided us with the suggestive image of a science growing according to two laws. The first one is represented by the Apollo's arrow. ``The arrow hits the quarry and kills it{''}. This is a metaphor of science seen as an ever-growing machinery whose ultimate goal is to solve particular questions and make progress possible. The second law is represented by the Ancients' Inferno, ``where Danaides, Ixions and Sysiphes eternally labour, filling bottomless hogsheads and lifting weights which always fall again: in its theoretical development throughout the centuries, scientific work seems to be concerned with defining again and again a small list of basic words which give form to the foundations of theories{''}. Such a twofold vision of science applies surprisingly well to the way the so-called ``Newtonian{''} mechanics is today seen and taught and the way, in the eighteenth century, it grew out of the mist of confusion, detours, false starts, and repetitive definitions of ``a small list of basic words{''}, of which ``force{''} is probably the best example. The painstaking task of ancient mecaniciens, and in particular of those forming the so-called ``Basel school{''} has been told by Clifford A. Truesdell in his works, and especially in The Rational Mechanics of Flexible or Elastic Bodies 1638-1788 and in his celebrated Essays in the History of Mechanics. It is my purpose to recall, in Benvenuto's and Truesdell's own words, the complex and tortuous development of ideas eventually leading to the modern laws of `Newtonian' mechanics as opposed to the view of those laws - and of the additional concepts they imply, such as ``force{''}, or ``relativity{''}, or ``reference system{''} - we tend to have today, i.e., of a part of a mathematical machinery laid down at some point in time and since then restless acting as Apollo arrow.