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Gunter’s Line calculating ruler

Made c. 1867

In 1620 English mathematician Edmund Gunter invented the first analogue device that used Napier’s logarithms to perform calculations. Called Gunter’s Line of Proportion, or Gunter’s Rule, it is inscribed with a line marked at intervals such that the distance of a number from 1 represented its logarithm. Distances on the scale could be added using a pair of dividers to multiply two numbers, or subtracted to divide one number by another. This example was made around 1860 from boxwood, which, cruci...


Calculating rule, Gunter's Line of Proportion, duplex, boxwood, maker unknown, 1850-1867

Calculating rule, duplex, boxwood, top edge is a 24 inch ruler (reading right to left), bottom edge bevelled. Scales are engraved into wood in colour black.

The scales on this rule are specifically designed for navigation.

Left half:
24 inch ruler (reading right to left),
a grid of lines at ½ inch spacing with nomographs at either end.
Right half:
LEA - Leagues
RUM - Rhumb
M.L - Miles of Longitude
CHO - Chord - in degrees of Latitude
SIN - Sines
TAN - Tangents

S.R - Sines of Rhumbs
T.R - Tangents of Rhumbs
NUM - Line of Numbers -
SIN - the Sine of the angle on this line is read off on the NUM scale
V.S - Versed Sines
TAN - the Tangent of the angle on this line is read off on the NUM scale
MER - Meridian line - the distance along a meridian line of degrees of latitude.
E.P - Line of Equal Parts


4 mm
44 mm


This Gunter's Rule has inscribed on the reverse the name of a previous owner: "William Potts The Craigs Moor School July 12th 1867".

Maker unkown.
c. 1867


The slide rule is a mechanical representation of the way logarithms can be used for multiplication, division and the taking of squares and square roots as well as other mathematical functions. Logarithms, which were invented by the Scottish mathematician and landowner John Napier in 1614, can be added together to perform multiplication and subtracted one from another to perform division of two numbers, thus allowing multiplication and division to be carried out with ease.

The development of the slide rule went through several stages. The first significant device was Gunter's Line of Proportion (also known as the Gunter's Rule or Gunter's Scale) invented by the English astronomer and mathematician Edmund Gunter in 1624. He engraved a two foot long (60cm) straight-edge rule with lines marking the numbers placed at distances proportional to the logarithms of the numbers.

By using a Gunter's Rule multiplication or division can be carried out simply through the addition or subtraction of distances on the rule using a pair of pointers or compasses. In order to multiply two numbers, one pointer of the compass is set down on the scale at the index marker (the number 1) on the line of Numbers and opened so that the other pointer of the compass extends to the multiplicand (the number to be multiplied). The compass is then re-placed with one leg at the multiplier, and its other leg now points to the product of the two numbers.

The earliest Gunter's Rules had few scales on them, simply the line of numbers in logarithmic proportion, a line of squares and a line of cubes of the numbers plus the trigonometric scales which are useful for gunnery and navigation. [Hopp, p.9] They became the primary tool for navigation over the 18th century and were considered accurate enough for them to be still in use for navigation in the mid-19th century. [Cajori, p.21]

Peter Hopp, "Slide Rules, their History, Models and Makers", Mendham, New Jersey: Astragal Press, 1999.

Florian Cajori, "A history of the logarithmic slide rule and allied instruments", Mendham, N.J.: Astragal Press, c1994.
Bromley, Allan 1978-2002


Donated through the Australian Government Cultural Gifts Program in memory of Associate Professor Allan Bromley, 2010
20 January, 2010

Cite this Object

Gunter's Line calculating ruler 2016, Museum of Applied Arts & Sciences, accessed 24 November 2017, <>
{{cite web |url= |title=Gunter's Line calculating ruler |author=Museum of Applied Arts & Sciences |access-date=24 November 2017 |publisher=Museum of Applied Arts & Sciences, Australia}}

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