the “calculating clock,” was able to add
and subtract up to six-digit numbers
using a mechanism of gears and wheels.
But not all historians credit Schickard.
Some believe that there was an even earlier
attempt at mechanical computing by Leo-
nardo da Vinci, who also apparently
designed an adding machine. Some of his
notes were found in the National Museum
of Spain in 1967 and describe a machine
bearing a certain resemblance to Pascal’s
machine (see below).
How did Gottfried Wilhelm von Leibniz
advance calculating devices?
German mathematician and philosopher
Gottfried Wilhelm von Leibniz (1646–
1716) not only described the binary num-
ber system—a central concept of all mod-
ern computers—but also co-invented dif-
ferential calculus and designed a machine that would perform the four basic arithmetic
functions. By 1674 he had completed his design and commissioned the building of the
Leibniz Stepped Drum, or the Stepped Reckoner, as he called his machine.
The device used a special type of gear named the Leibniz wheel (or stepped drum),
a cylinder with nine bar-shaped teeth along a length parallel to the cylinder’s axis. As
the cylinder was rotated with a crank, a ten-toothed wheel would rotate from zero to
nine positions, depending on its position from the drum. The movements of the vari-
ous mechanisms would be translated into multiplication or division, depending on
what direction the stepped drum was rotated.
Although there were apparently only two prototypes of the device (both still exist),
Leibniz’s design—along with Pascal’s—were the basis for most mechanical calculators
in the 18th century. As with most such machines that could not be mass produced—
much less understood by the masses—they were more curiosities for display than
machines put to actual use.
How did Joseph-Marie Jacquard’s inventionbenefit calculating devices?
In the late 18th century, French weaver and inventor Joseph-Marie Jacquard (1752–
1834) developed a practical, automatic loom that wove patterns into fabric; it was con-
trolled by a linked sequence of punched cards. This in itself was a major advance in the
production of textiles, but it would also prove to be a boon to calculating devices. Bor- 353
MATH IN COMPUTING
Some people believe that the famous Renaissance
inventor and artist Leonardo da Vinci was also the
creator of an early type of mechanical computer.
Library of Congress.