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Inventory no. 54619 - Epact entry

Epact number: 68586

Protractor

Signed by Erasmus Habermel
circa 1580; German
Gilt copper; 132 mm in diameter

Main text

This beautifully and carefully made protractor was intended for specialist applications by a military engineer. The central scales give the successive positions of the tangential rule for drawing the sides of regular polygons with different numbers of sides between 3 and 16. Such polygons were the basis of the plans for contemporary fortifications.

The outer degree scale is divided by diagonals so that it can be read to 2 minutes of arc. That idea that angles could be, or would need to be, drawn to this level of accuracy seems extravagant.



Source museum: Museum of the History of Science, Oxford
Museum number: Inventory no. 54,619



Detailed text

The outer degree scale 0 to 360 is divided to 10, subdivided to 5 and to 1, numbered by 10. An inner diagonal scale carried the single degree divisions to 10 minutes by concentric circles and a radial arm with a scale 0 to 60, divided to 10, subdivided to 5 and separately subdivided to 2, taking the degree division to 2 minutes, numbered by 10.

The radial arm and two shaped and decorated arms on either side support a tangential ruler. Within the diagonal scale are 6 concentric scales each with a sets of numbered lines indicating the positions of the radial arm when the tangential arm coincides with the sides of the regular polygon having that number of sides. These numbers are distributed between the circles according to common factors, since the positions will coincide for figures where the numbers of sides are multiples. Thus 4, 6, 8 are in the outermost circle, followed by 5,10, 15; 7, 14; 13; 3, 6, 9, 12; 11.

Within the central ring supporting the rotatable arms and signed 'Erasmus Habermel fec:', is a raised glazed magnetic compass, with a blued steel needle. A silvered plate has lines for the cardinal directions marked 'Septentrio', 'Oriens', 'Meridies', 'Occidens' and a target line offset to the east for magnetic variation. An outer degree scale 0 to 90 to 0 to 90 to 0 is divided to 10, subdivided to 5 and separately subdivided to 2, numbered by 10.

The verso has a central star decoration, surrounded by foliate and other decoration in the style of Habermel, as well as four points for anchoring the protractor.

J. Bennett and S. Johnston, The Geometry of War 1500-1750 (Oxford, 1996)

Jim Bennett

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