The rectangulus was an astronomical instrument made by

Richard of Wallingford Richard of Wallingford (1292–1336) was an English mathematician, astronomer, horologist, and cleric who made major contributions to astronomy and horology while serving as abbot of St Albans Abbey in Hertfordshire. Biography Richard was bor ...

around 1326. Dissatisfied with the limitations of existing astrolabes, Richard developed the rectangulus as an instrument for

spherical trigonometry Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are grea ...

and to measure the angles between planets and other astronomical bodies. This was one of a number of instruments he created, including the '' Albion'', a form of

equatorium An equatorium (plural, equatoria) is an astronomical calculating instrument. It can be used for finding the positions of the Moon, Sun, and planets without arithmetic operations, using a geometrical model to represent the position of a given c ...

, and a famously complicated and expensive horologium (

astronomical clock An astronomical clock, horologium, or orloj is a clock with special mechanisms and dials to display astronomical information, such as the relative positions of the Sun, Moon, zodiacal constellations, and sometimes major planets. Definition ...

). His ''Tractus Rectanguli'', describing the rectangulus, was an influential text in medieval astronomy and at least thirty copies were known to survive. His ''Quadripartitum'' was the first text on spherical trigonometry to be published in Western Europe. The rectangulus was a form of skeleton

torquetum The ''torquetum'' or turquet is a medieval astronomical instrument designed to take and convert measurements made in three sets of coordinates: Horizon, equatorial, and ecliptic. It is said to be a combination of Ptolemy's astrolabon and the p ...

. 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 The ecliptic or ecliptic plane is the orbital plane of the Earth around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic agains ...

. 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 A plumb bob, plumb bob level, or plummet, is a weight, usually with a pointed tip on the bottom, suspended from a string and used as a vertical reference line, or plumb-line. It is a precursor to the spirit level and used to establish a verti ...

lines descended from the scales above and intersected with linear scales marked on the horizontal scales below. 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. This is now in the

Museum of the History of Science, Oxford The History of Science Museum in Broad Street, Oxford, England, holds a leading collection of scientific instruments from Middle Ages to the 19th century. The museum building is also known as the Old Ashmolean Building to distinguish it fro ...

References

{{Reflist, colwidth=35em, refs= {{Cite web , title=Model of the "Rectangulus" of Richard of Wallingford , id=10928 , publisher=

Museum of the History of Science The History of Science Museum in Broad Street, Oxford, England, holds a leading collection of scientific instruments from Middle Ages to the 19th century. The museum building is also known as the Old Ashmolean Building to distinguish it from th ...

, url=http://www.mhs.ox.ac.uk/collections/imu-search-page/record-details/?TitInventoryNo=10928&querytype=field&thumbnails=&irn=17054 {{Cite book , title=Cosmos: An Illustrated History of Astronomy and Cosmology , first=John , last=North , publisher=

University of Chicago Press The University of Chicago Press is the largest and one of the oldest university presses in the United States. It is operated by the University of Chicago and publishes a wide variety of academic titles, including ''The Chicago Manual of Style'', ...

, year=2008 , isbn=978-0226594415 , pages=259–261 {{Cite book , title=God's Clockmaker , first=John , last=North , year=2007 , publisher=A&C Black , isbn=978-1852855710 , url=https://books.google.com/books?id=XIytAwAAQBAJ&pg=PA349 , pages=348–350 {{Cite book , title=The Medieval Machine , first=Jean , last=Gimpel , authorlink=Jean Gimpel , year=1992 , origyear=1976 , edition=2nd , publisher=Pimlico , isbn=978-0-7126-5484-5 , pages=155–157 {{Cite web , title=Richard of Wallingford: Abbot of St. Albans, 1326-1335 , publisher=St. Albans and Herts Architectural and Archaeological Society. , url=https://www.stalbanshistory.org/wp-content/uploads/2019/05/1926_05_.pdf , pages=236–237, 239 {{Cite journal , title=Richard of Wallingford and his Rectangulus , first=R.T. , last=Gunther , journal=

Nature Nature, in the broadest sense, is the physical world or universe. "Nature" can refer to the phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. Although humans are ...

, volume=118 , issue=2978 , pages=773–774 , date=27 November 1926 , doi=10.1038/118773a0 , bibcode = 1926Natur.118..773G , doi-access=free {{Cite journal , last=Michel , first=H. , title=Le Rectangulus de Wallingford , year=1944 , journal=Ciel et Terre , volume=60 , pages=11–12 , bibcode=1944C&T....60..196M Astronomical instruments Historical scientific instruments Mechanical calculators