Accession No

1143


Brief Description

6-inch gunter sector, by Jesse Ramsden, English, 1760-1800 (c)


Origin

England; London


Maker

Ramsden, Jesse


Class

calculating; mathematics


Earliest Date

1760


Latest Date

1800


Inscription Date


Material

metal (brass); ivory


Dimensions

length 161mm; breadth 36mm; thickness 3mm


Special Collection

Robert Whipple collection


Provenance

Donated by Robert S. Whipple to the University of Cambridge in 11/1944 as part of the Whipple Museum of the History of Science’s founding collection.


Inscription

‘Ramsden,
London.’ (obverse)


Description Notes

6-inch gunter sector, by Jesse Ramsden, c. 1760 - c. 1800

6-inch ivory sector with brass hinge and shoulders.
Obverse has double scales of: ‘S’ (sines) divided [0] - 90˚, numbered by 10˚, 0 - 70˚ subdivided to 30´, 70˚ - 80˚ subdivided to 1˚, 80˚ - 85˚ subdivided to 2˚; ‘t’ (tangents) divided 45˚ - [75˚ 45´] numbered by 10˚ (and for 75˚), 45˚ - 50˚ subdivided to 30´, remainder subdivided to 15´; ‘T’ divided [0] - 45˚, numbered by 10˚, subdivided to 15´. On fully opened limbs single scales of ‘num’ (log numbers) divided 1 - 20[0], numbered ‘1, 2...9, 1, 2...10, 20’, 1 - 1[0] subdivided to 0.1, 1[0] - 3[0] subdivided to 0.5, 3[0] - 10[0] subdivided to 1, 10[0] - 20[0] subdivided to 2; ‘sin’ (log sinces) divided [50´] - [90˚], numbered 1, 2, 3...10, 20...70, 50´ - 6˚ subdivided to 5´, 6˚ - 10˚ subdivided to 10´, 10˚ - 20˚ subdivided to 15´, 20˚ - 30˚ subdivided to 30´, 30˚ - 70˚ subdivided to 1˚, 70˚ - 80˚ subdivided to 2˚; ‘tan’ (log tangents) divided [1˚ 25´] - 45˚ and back to 70˚], numbered 1, 2...10, 20, 30, 40, 45, 50, 60, 70, 1˚ 25´ - 6˚ subdivided to 5´, 6˚ - 10˚ subdivided to 10´, 10˚ - 30˚ subdivided to 15´, 30˚ - 45˚ subdivided to 30´.
Reverse carries double scales of: ‘L’ (lines or equal parts) divided [0] - 10, numbered by 1, subdivided to 0.05; ‘S’ (secants) divided [10˚] - 75˚, numbered by 10˚, 20˚ - 50˚ subdivided to 1˚, 50˚ - 60˚ subdivided to 30´, 60˚ - end subdivided to 15´; ‘C’ (chords) divided [0] - 60˚, numbered by 10˚, subdivided to 0.5; ‘Pol’ divided 12 - 4, numbered by 1. On upper limb single scales of: ‘I M’ (inclined meridian) divided [0] - 90˚, numbered by 10˚, subdivided to 1˚; ‘C’ (chords) divided [0] - 90˚, numbered by 10˚, subdivided to 1˚. On lower limb single scales of ‘L’ (latitude) divided [0] - [90˚], numbered by 10˚ (except 80), 0 - 70˚ subdivided to 1˚; ‘H’ (hours) divided [0] - VI, numbered by I, subdivided to 5 minutes. On the fully opened limbs single scale of inches, divided [0] - 12, numbered by 1, subdivided to 0.1.
Two brass pins to secure limbs together.

Condition good; complete


References


Events

Description
Sectors were used for calculation by navigators, surveyors, gunners and draftsmen (and, famously, by Galileo) from about the mid-16th Century to the mid-19th Century. During the 16th Century, they were used as general mathematical tools, but the introduction of logarithms drastically expanded their application. Usually made of brass, wood or ivory, they look like a jointed rule with scales engraved on either side.

Sectors use the principle of similar triangles (that the ratio of lengths of two sides of similar triangles will always be the same) with scales of proportion for calculating mathematical functions such as finding the line of equal parts, inscribing a rectangular polygon inside a circle of a given radius and protracting angles. This made them useful for similar calculations to a slide rule.

18/10/2002
Created by: Saffron Clackson on 18/10/2002


FM:39550

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