Rectangulus
The rectangulus was an
His Tractus Rectanguli, describing the rectangulus, was an influential text in medieval astronomy and at least thirty copies were known to survive.[1][2] His Quadripartitum was the first text on spherical trigonometry to be published in Western Europe.[3]
The rectangulus was a form of skeleton torquetum.[4] This was a series of nested angular scales, so that measurements in azimuth and elevation could be made directly in polar coordinates, relative to the ecliptic. Conversion from these coordinates though was difficult, involving what was the leading mathematics of the day. The rectangulus was an analogue computing device to simplify this: instead of measuring in angular measurements it could resolve the angles to Cartesian components directly. This then simplified the further calculations.
The rectangulus was constructed as a brass pillar with a number of linear scales hinged above it. Pinhole sights on the upper arm allowed it to be pointed accurately at the astronomical target. Plumb bob lines descended from the scales above and intersected with linear scales marked on the horizontal scales below.[5] These allowed measures to be read, not as angles, but as trigonometric ratios.
To celebrate the 600th anniversary of the Rectangulus in 1926 a replica was constructed.[2][6] This is now in the History of Science Museum, Oxford.[7]
References
- ^ ISBN 978-0-7126-5484-5.
- ^ a b c "Richard of Wallingford: Abbot of St. Albans, 1326-1335" (PDF). St. Albans and Herts Architectural and Archaeological Society. pp. 236–237, 239.
- ISBN 978-0226594415.
- Bibcode:1944C&T....60..196M.
- ISBN 978-1852855710.
- doi:10.1038/118773a0.
- Museum of the History of Science. 10928.