1 The Birth of Science - MSRI

3.3 Mechanics 63
documents — particularly works of military technology — that mention
machines actually built; and treatises written centuries later, above all
Pappus’ Collection and Heron’s works. Among these the most useful is
the Mechanics, 64 which describes the five simple machines (the winch, the
lever, the pulley, the wedge and the screw) as well as a number of composite
machines designed for various uses. The pseudo-Aristotelian Mechanics,
which share many features with Heron’s Mechanics, also contain
interesting information. We postpone until Chapter 10 a discussion of the
successive theoretical developments, and discuss here only the problem
that gave rise to the science of machines.
The main mechanical problem of the time can be described as follows.
Suppose we wish to raise a weight W to a height h. Instead of doing it directly,
one can use a machine that, upon application of a force F , raises the page 97
desired weight to the desired height, the point of application of F moving
in the process a distance l in the direction of F . In today’s language, the
principle of conservation of energy implies that the weight cannot be lifted
unless the product F l, now called the “work” performed by the force, exceeds
the product W h. If F l does exceed W h (and friction is sufficiently
small), the weight can be lifted, and moreover, by using appropriate devices,
one can choose the direction and the place where the force is applied,
as well as the decomposition of the work between the two factors:
one can apply a small force along a long distance or a large force along a
short distance. In particular, one can lift the weight W using a force F less
than W . The ratio W/F is the mechanical advantage of the machine.
The problem, given a maximum available force F and the need to lift
a weight W , is to design a machine having the appropriate mechanical
advantage and configuration, so the weight can be lifted by applying the
available force to a convenient point and in a convenient direction. All
devices of this type can ultimately be traced back to the simplest such device,
the lever, which Archimedes uses as the starting point of his scientific
theory of mechanics.
Of course problems of this type had always been around and had often
been solved practically, as far back as paleolithic times, when levers
and wedges were already in use. At the time of the ancient empires pliers
(pincers) were also known, and the pyramids could not have been built
without the help of many machines. Classical Greece certainly knew the
pulley and the winch, the latter having first been used, in all probability,
for shipbuilding or in the theater. This long evolution of empirical me-
64 This work was found in Arabic translation by Carra de Vaux and published in [Heron/Carra
de Vaux]. The standard critical edition, based on several manuscripts, is due to Nix and appears in
[Heron: OO], vol. 2.
Revision: 1.13 Date: 2002/10/16 19:04:00