Schickard, Pascal, and Leibniz built the first mechanical calculators. These machines marked the beginning of automatic computation, as mechanical levers, gears, and wheels replaced the human mind, performing more quickly and, in many cases, more accurately.

In the seventeenth century, a great leap in methods of calculation occurred with the introduction of the first mechanical calculating machines and the beginning of automatic computation. Mechanical levers, gears, and wheels were built to perform the tedious, laborious calculations involved in mathematics, astronomy, surveying, financial transactions, and other areas. [kw]Earliest Calculators Appear (1623-1674)
[kw]Calculators Appear, Earliest (1623-1674)
Science and technology;1623-1674: Earliest Calculators Appear[0930]
Inventions;1623-1674: Earliest Calculators Appear[0930]
Mathematics;1623-1674: Earliest Calculators Appear[0930]
France;1623-1674: Earliest Calculators Appear[0930]
Germany;1623-1674: Earliest Calculators Appear[0930]
Calculating machines

The struggle to develop quicker and more accurate methods of calculations had been occurring for centuries. The earliest physical aids to calculation included the abacus, tally sticks, quadrants, sectors, compasses, and slide rules. In the early seventeenth century, John Napier Napier, John developed logarithms Calculus , an ingenious method for multiplying and dividing used in the early calculators. Napier’s Rabdologiae, seu Numerationis per Virgulas Libri Duo (1617; Study of Divining Rods, or Two Books of Numbering by Means of Rods
Study of Divining Rods, or Two Books of Numbering by Means of Rods (Napier) , 1667) described a device referred to as “Napier’s bones,” a precursor of the slide rule. Developments in clock making and the building of automata in the seventeenth century also aided the development of mechanical calculators to perform the four standard arithmetic functions, addition, subtraction, multiplication, and division.

The Lutheran minister Wilhelm Schickard Schickard, Wilhelm became a professor of biblical languages at the University of Tübingen, Württemberg in 1619. His research also encompassed astronomy and mathematics. Schickard worked with the astronomer Johannes Kepler, Kepler, Johannes and their discussions regarding Napier’s logarithms inspired Schickard to design a calculator to automate the process of multiplication. His research in astronomy had driven him to develop skills as a mechanic as he struggled to build his own astronomical instruments. Those skills enabled him to build a mechanical calculator in 1623.

Schickard’s machine used wheels with ten teeth, one for each of the digits 0-9. Each wheel represented a “place” in a numeral: There was a units wheel, a tens wheel, a hundreds wheel, and so forth. The machine’s carry mechanism carried from each wheel to the next higher wheel when the lower wheel turned from 9 to 0. However, the carry mechanism only worked for up to six digits. The force required to produce a carry from six to seven digits (that is, from 999,999 to 1,000,000) would have damaged gears on the unit wheel. To compensate for this limitation, the machine incorporated brass rings: Every time a carry was propagated past 6 digits, a bell would ring, and the operator could slip a brass ring on his finger to remind him how many times the carry had propagated past six digits. Thus, each ring on the operator’s finger stood for one million units.

Blaise Pascal, Pascal, Blaise a mathematician, Mathematics;Europe also struggled with the laborious methods of calculation. While Pascal was not aware of Schickard’s machine, he was inspired to design a calculator to relieve the boring routine of calculations his father needed for tax assessing and collecting in Rouen, France. Like Schickard, Pascal was dissatisfied with the skills of local craftspeople and taught himself the mechanical skills necessary to create a calculating device. Pascal also delved into blacksmithing to experiment with different materials for the gears.

Pascal built about fifty calculators. Most of these calculators had eight wheels, but one had as many as ten. The top of the machine contained toothed wheels and two series of windows above them to show results. The upper windows showed results for addition and the lower for subtraction. Subtraction was accomplished using a method called “nines complement addition,” because the wheels in the machine could not be turned backward.

Due to its use of the technical “nines complement” method, Pascal’s device required more mathematical knowledge by the operator than did Schickard’s machine. Pascal’s versatile machines operated in French monetary units (livres, sols, and deniers) as well as decimals, however. His machines, like Schickard’, performed multiplication and division, but the process was awkward and unwieldy, using repeated additions or subtractions. Unlike Schickard, Pascal did not rely on a single-tooth gear for the carry mechanism. Pascal’s solution used falling weights rather than gears. Thus, the strain on gears that limited Schickard’s machine did not limit Pascal’. His machines, however, were susceptible to producing inaccurate results by generating extra carries.

Another mathematician and philosopher, Gottfried Wilhelm Leibniz, Leibniz, Gottfried Wilhelm set out to improve upon Pascal’s work. Leibniz served as adviser to the elector of Mainz, and he needed to plan a way to distract the French from their focus on attacking German lands. He intended to draw France’s attention to Egypt by campaigning for a united European effort to conquer the non-Christian world. Leibniz traveled extensively during this campaign and became aware of Pascal’s work while in Paris. Leibniz designed a device to be attached to the top of a machine like Pascal’s and allow it to do multiplication more easily. However, Leibniz either did not have enough information on Pascal’s machine or did not understand it properly, and the device would not have worked.

Leibniz developed his own mechanical multiplier around 1671. The key component of this machine was the stepped drum, or reckoner, which had cogs of varying lengths. The problem of a correct propagation of a carry plagued Leibniz, as it had Schickard and Pascal. The carry mechanism Leibniz designed did not properly handle the calculation if a carry from one digit to the next then produced another carry to the next higher digit. Leibniz handled this problem by designing the mechanism so that a point from a disk in the mechanism would protrude if a propagating carry occurred. The operator would then notice the point and push the disk to propagate the carry manually. Thus, Leibniz’s machine was not fully automatic.

Leibniz demonstrated his machine in 1672 at the Royal Society in London. Because of comments on his machine, Leibniz began work on improvements and alterations. However, the same problems that Schickard and Pascal had encountered, inadequate workmen and materials, also hindered Leibniz. After tracking down a highly skilled clockmaker to assist in the construction, Leibniz built a new machine in 1674. This machine design incorporated a mechanical version of the shift-and-add procedure used on digital electronic computers in the twentieth century. Leibniz’s stepped drum remained the only practical means to build a workable calculator until the development of variable-toothed gears in the late nineteenth century.

Leibniz never achieved his goal of building a larger machine to mechanize all human reasoning processes by assigning a number to all possible thoughts and thus end fruitless arguing. However, he did develop binary arithmetic. While he never connected this system with his mechanical calculator, binary arithmetic would provide a system particularly suited to the electronics used in twentieth century computers.

While there had been attempts to mechanize calculations before 1623, they had required substantial human intervention. The machines invented in the seventeenth century differed significantly from their predecessors, because they attempted to automate the entire process, including the carry mechanism. The appearance of these earliest automatic calculators influenced intellectual and mathematical development, since the designers needed to develop calculation techniques to get levers, gears, and wheels to move in the ways required to do simple arithmetic.

The early calculators responded to a growing need for more, and more precise, calculations resulting from a significant increase in astronomical data, financial bureaucracies, colonial land acquisition, and other forms of numerical data generated by new technologies of measurement, such as the barometer. In addition, they both responded and contributed to a scientific culture that was developing precise scientific laws, such as Robert Boyle’s law, Johannes Kepler’s laws of planetary motion, and Sir Isaac Newton’s laws of motion and gravitation, which understood the physical world in terms of mathematical formulas.

The computers of the twentieth century owe the most to the work of Leibniz, his stepped reckoner, his development of binary arithmetic, and the shift-and-add procedure for multiplication. However, one of the earliest programming languages used on the electronic computers was named after Pascal in recognition of his accomplishments. Pascal built his machine at the age of nineteen and produced the first mechanical calculator available for sale to the public.

Seventeenth century calculators constituted a significant step in the efforts to automate human reasoning that would follow in the next three centuries. The work of Schickard, Pascal, and Leibniz inspired and influenced the work of later inventors in the seventeenth, eighteenth, and nineteenth centuries who would achieve the goal of fully automating (and accurately performing) the standard arithmetic functions of addition, subtraction, multiplication, and division. This work provided the foundation for the electronic computers of the twentieth century, which automated far more than these functions but continued using basic techniques developed in the seventeenth century.

• Adamson, Donald. Blaise Pascal: Mathematician, Physicist, and Thinker About God. New York: St. Martin’s Press, 1995. Biography of Pascal that includes information on Pascal’s calculator and minor information on Schickard and Leibniz.
• Aspray, William, ed. Computing Before Computers. Ames: Iowa State University Press, 1990. A series of essays describing developments in computational technology before the modern computer. The first essay in particular provides coverage of pre-nineteenth century developments.
• Spencer, Donald D. Great Men and Women of Computing. Ormond Beach, Fla.: Camelot, 1996. Accessible essays on individual contributors to the history of computing, including Pascal and Leibniz.
• Spencer, Donald D. The Timetable of Computers: A Chronology of the Most Important People and Events in the History of Computers. 2d ed. Ormond Beach, Fla.: Camelot, 1999. Illustrated chronology of events in the development of computing from the earliest days to the twentieth century. Includes comprehensive index.
• Williams, Michael R. A History of Computing Technology. 2d ed. Los Alamitos, Calif.: IEEE Computer Society Press, 1997. A survey of the development of calculating and computing machines and technology from earliest times to the twentieth century.

Robert Boyle; Galileo; Johannes Kepler; Gottfried Wilhelm Leibniz; Sir Isaac Newton; Blaise Pascal; Wilhelm Schickard. Calculating machines