# The invention of the Slide Rule

### Edmund Gunter (1581--1626)

Edmund Gunter's most important book entitled Description and use of the Sector, was first published in English in 1623. This has been described as ``the most important work on the science of navigation to be published in the seventeenth century." A sector is a mathematical instrument consisting of two hinged arms on which there are engraved scales which can be used to help with calculations. This is not a slide-rule; the single scale is used in conjunction with a pair of compasses. What makes Gunter's sector special is that it is the first mathematical instrument to be inscribed with a logarithmic scale to help solve numerical problems. In practice the points of the compass tend to damage the scales which reduces the accuracy of the instrument.

### William Oughtred (1574--1660)

William Oughtred was a clergyman and keen mathematician. He is believed to have introduced the x symbol for multiplication in his book Clavis Mathematicae (Key to Mathematics), written about 1628 and published in London in 1631. This was a very important maths text book at the time. Newton read and was influenced by it for example. He is now generally though to be the inventer of the slide rule. Both straight and circular rules are described in a book with the title ``The Circles of Proportion and the Horizontal Instrument" London 1632. There is, however, good evidence to suggest that Oughtred had made his invention a number of years earlier and failed to publish it.
[Tell me more]

### Richard Delamain (1600--1644)

Richard Delamain, a teacher of mathematics, was originally William Oughtred's student. He taught Charles I for example and the first published account of a slide rule as we would recognize it was given in his book Grammelogia. This was a 30 page pamphlet which described a circular slide rule. The instrument consisted of two metal disks held together at the centre with a small pin.

### The dispute

Both Oughtred and Delamain argued over who invented the circular slide rule in their various books over the years. Their friends also got involved and things became heated. Delamain was a big slide rule fan, arguing that mechanical aids helped people understand how to calculate. Oughtred was not. He didn't publish his notes earlier because,
the true way of Art is not by Instruments, but by Demonstration: and that it is a preposterous course of Artists, to make their Schollers only doers of tricks, as it were Juglers: to the despite of Art, losse of precious time, and betraying of willing and industrious wits, unto ignorance, and idlenesse. That the use of Instruments is indeed excellent, if a man be an Artist but contemptible, being set and opposed to Art.
Circles of Proportion (1632)
Each accuses the other of stealing the invention. In one copy of circles Oughtred writes,
I borrowed and perused that worthless Pamphlet [Grammelogia], and in reading it (I beshrew him for making me cast away so much of that little time is remayning to my declined years) I met with such a patchery and confusion of disjoynted stuffe, that I was striken with a new wonder, that any man should be so simple as to shame himselfe to the world with such a hotch-potch.
Circles of Proportion (1632)
It is generally believed that Oughtred and Delamain were independent inventors. Oughtred got there first but Delamain was the first to publish. Certainly Oughtred's circle of proportion is more detailed and versatile than Delamain's Mathematical Ring.

There is little, if any, dispute that William Oughtred invented the rectilinear (straight) slide rule.

### References

[1] Florian Cajori.
A History of the Logarithmic Slide Rule, J.F. Tapley Co. New York, (1909). See also this online version of the book.
[2] Peter M. Hopp.
Slide Rules: Their History, Models, and Makers, Astragal Press, (1998).
[3] A. J. Turner
William Oughtred, Richard Delamain and the Horizontal Instrument in the Seventeenth Century, Annali Dell Intituto E Museo Di Storia Della Scienze Firenze (1981) 6, pg 99-125.
[4] Charles H. Cotter.
Edmund Gunter (1581-1626). Journal of Navigation, 34(3):363--367, (1981).
[5] D. J. Bryden
A Patchery and Confusion of Disjointed Stuffe: Richard Delamain's Grammelogia of 1631/3, Trans. Camb. Bibliog Soc. (1978) VI, pg 158-66.
[6] Florian Cajori.
Willaim Oughtred: A Great Seventeenth-Century Teacher of Mathematics Open Court, (1916).

[Slide rule page] [Chris Sangwin]