Slide Rule
Pocket calculators only came into common use in the 1970s. Digital computers first appeared in the 1940s, but were not in widespread use by the general public until the 1980s. Before pocket calculators, there were mechanical desktop calculators, but these could only add and subtract and at best do the most basic of multiplications.
A tool commonly used by engineers and scientists who dealt with math in their work was the slide rule. A slide rule is actually a simple form of what is called an analog computer, a device that does computation by measuring and operating on a continuously varying quantity, as opposed to the discreet units used by digital computers. While many analog computers work by measuring and adding voltages, the slide rule is based on adding distances.
A simple slide rule looks like two rulers that are attached to each other so that they can slide along one edge. In fact any two number lines that can be moved past each other make up a slide rule. To add two numbers on a slide rule, look at the above illustration, which shows how to add 3 and 4. Start by finding 3 on rule A. Then slide rule B so that the zero point of rule B lines up with 3 on rule A. Find 4 on rule B and it will be lined up with the sum on rule A, which is 7. Reverse these steps to subtract two numbers.
The slide rule was invented by William Oughtred (1574–1660), an English mathematician. Oughtred designed the common slide rule, which has a movable center rule between fixed upper and lower rules. Many different scales are printed on it, and a sliding cursor helps the user better view the alignment between scales. He also designed less common circular slide rules that worked on the same principles.
The previous example has already illustrated how to add and subtract using a slide rule. One can also multiply and divide with a slide rule using logarithms. In fact, slide rules were invented specifically for multiplying and dividing large numbers using logarithms shortly after John Napier invented logarithms.
To multiply 3,750 and 225 using a slide rule, first find log10 3,750 and log10 225. Use the slide rule to add these logarithms. Then find the antilog of the sum, which is the product of 3,750 and 225.
Division using a slide rule is the same as multiplication, except one subtracts the logarithms. Of course, one must have logarithm tables handy when multiplying or dividing with a slide rule, to look up the logarithms.
One can compute powers on a slide rule by taking the log of a log. Since Ax is the same as x times log A, one can do this multiplication by adding log x and log (log A). Special log-log scales on a slide rule make it possible to calculate powers. Roots, such as 
can be considered fractional powers, so the slide rule with a log-log scale could be used to compute roots as well. Additional scales were provided to look up trigonometric functions such as sine, cosine, and tangent.
The accuracy of a slide rule is limited by its size, the quality to which its scales are marked, and the ability of the user to read the scales. Typical engineering slide rules were accurate to within 0.1 percent. This degree of accuracy was considered sufficient for many engineering and scientific applications. However, the use of slide rules declined rapidly after the electronic calculator became inexpensive and widely used. This was due, in large part, to the fact that it is much easier and convenient to perform applications, such as multiplication, on a calculator than it is to look up logarithms.
Analog and Digital; Bases; Logarithms; Mathematical Devices, Early.
Bibliography
Hopp, Peter M. Slide Rules: Their History, Models, and Makers. Mendham, NJ: Astragal Press, 1999.
Sommers, Hobart H., Harry Drell, and T. W. Wallschleger. The Slide Rule and How to Use It. New York: Follett, 1964.
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