The Equatorie Of The Planetis
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''The Equatorie of the Planetis'' is a 14th-century scientific work which describes the construction and use of an
equatorium An equatorium (plural, equatoria) is an astronomy, astronomical Mechanical calculator, calculating instrument. It can be used for finding the positions of the Moon, Sun, and planets without arithmetic operations, using a geometrical model to re ...
. It was first studied in the early 1950s by Derek J. Price, and was formerly attributed to
Geoffrey Chaucer Geoffrey Chaucer ( ; – 25 October 1400) was an English poet, author, and civil servant best known for ''The Canterbury Tales''. He has been called the "father of English literature", or, alternatively, the "father of English poetry". He w ...
. However, in 2014 it was shown to be written in the hand of the
St Albans St Albans () is a cathedral city in Hertfordshire, England, east of Hemel Hempstead and west of Hatfield, Hertfordshire, Hatfield, north-west of London, south-west of Welwyn Garden City and south-east of Luton. St Albans was the first major ...
monk John Westwyk. It is largely written in
Middle English Middle English (abbreviated to ME) is a form of the English language that was spoken after the Norman Conquest of 1066, until the late 15th century. The English language underwent distinct variations and developments following the Old English pe ...
, with some additions in
Latin Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...
. It is accompanied by extensive astronomical tables, with Latin headings and annotations.


Manuscript

Peterhouse MS 75 was a composite manuscript. In the early 1950s, after Price discovered the ''Equatorie'' in it, the manuscript was split into two parts (and both parts rebound): MS 75.I, containing the ''Equatorie'', and MS 75.II, containing works by
Nicholas Trivet Nicholas Trivet (or Trevet, as he himself wrote) (c. 1258 – c. 1328) was an English Anglo-Norman chronicler. Life Trivet was born in Somerset and was the son of Sir Thomas Trevet (died 1283), a judge who came of a Norfolk or Somerset family. ...
and
Vegetius Publius (or Flavius) Vegetius Renatus, known as Vegetius (), was a writer of the Later Roman Empire (late 4th century). Nothing is known of his life or station beyond what is contained in his two surviving works: ''Epitoma rei militaris'' (also r ...
. MS 75.I has two parts: fol. 1r-71r contains largely astronomical tables, and some astrological material, in two hands; 71v-78v contains the text of the Equatorie treatise.Cambridge, Peterhouse MS 75.I The parchment is of varying quality, with ten quires of pages measuring 365x260mm (except for the last quires). The ink is brown; there are signs of dampness on the upper edge, especially in the first quire, with some blurring in the fourth quire on the top of the pages. According to Rand Schmidt, the dampness and the wear and tear on some of the quires is evidence that the quires spent some time unbound. The text contains references to 31 December 1392, and this is used as a baseline date for many of the tables. John North showed that the text was written during the first nine months of 1393. How it came to Peterhouse is not known, but it probably happened during the 15th century; around 1538 it is entered in Peterhouse catalog, as ''Tab. aequ. planetarum autore Simon Bredon''. The ''Equatorie'' occupies eight leaves of the manuscript; the phrase ''Radix chaucer'' appears on fol. 5v. The manuscript has been digitised for the
Cambridge University The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...
Digital Library website, together with a virtual model of the equatorium.


"Radix chaucer"

On f. 5v, in a note on a page full of tables, the manuscript has the number "1392", followed by that number in
sexagesimal Sexagesimal, also known as base 60, is a numeral system with 60 (number), sixty as its radix, base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used—in a modified fo ...
notation, and the text "deffea xpi & Rxa chaucer". Price, and following him other scholars, expanded this as "differentia Christi et radix Chaucer"—or "the difference (in number of days) between (the year of Christ) and the (year of the) radix of Chaucer"—the radix in question then being the year 1392. F.N. Robinson was not convinced that this (third-person) reference indicated Chaucer's authorship. However, John North argued that the attachment of a name to a relatively "trivial" piece of data made it likely that this was a case of self-citation.


Discovery and authorship

The manuscript was in the library of
Peterhouse, Cambridge Peterhouse is the oldest Colleges of the University of Cambridge, constituent college of the University of Cambridge in England, founded in 1284 by Hugh de Balsham, Bishop of Ely. Peterhouse has around 300 undergraduate and 175 graduate stud ...
by 1538, and probably by 1472. It was discovered there by the historian
Derek de Solla Price Derek John de Solla Price (22 January 1922 – 3 September 1983) was a British physicist, historian of science, and information scientist. He was known for his investigation of the Antikythera mechanism, an ancient Greek planetary computer, and ...
in December 1951. Although the 19th-century manuscript catalogue stated that the manuscript contained "directions for making an astrolabe (?)", Price identified the instrument as a planetary
equatorium An equatorium (plural, equatoria) is an astronomy, astronomical Mechanical calculator, calculating instrument. It can be used for finding the positions of the Moon, Sun, and planets without arithmetic operations, using a geometrical model to re ...
. He argued that the manuscript was authored by, and written in the hand of, Geoffrey Chaucer. This was a controversial claim, and was treated with some scepticism by Chaucer scholars, though it received influential backing from the historian of astronomy John North. The manuscript was shown to be in the hand of John Westwyk by Kari Anne Rand in 2014. Further evidence for Westwyk's authorship was revealed by Seb Falk in a book published in 2020.


Debate

Price published an abstract in 1953, and the whole text (facsimile, transcription, and studies of the manuscript) in 1955. He maintained the possibility that Chaucer authored the ''Equatorie'', possibly as the missing part of his ''
A Treatise on the Astrolabe ''A Treatise on the Astrolabe'' is a medieval instruction manual on the astrolabe by Geoffrey Chaucer. It was completed in 1391. It describes both the form and the proper use of the instrument, and stands out as a prose technical work from a wr ...
'', which describes the
astrolabe An astrolabe (; ; ) is an astronomy, astronomical list of astronomical instruments, instrument dating to ancient times. It serves as a star chart and Model#Physical model, physical model of the visible celestial sphere, half-dome of the sky. It ...
; the ''Equatorie'' makes direct reference to it. He argued that the manuscript was a
holograph An autograph or holograph is a manuscript or document written in its author's or composer's hand. The meaning of " autograph" as a document penned entirely by the author of its content (as opposed to a typeset document or one written by a copy ...
draft, written in the hand of its author, as shown by the many additions and corrections in the manuscript. Price offered five points as indicators of Chaucer's authorship: #Style and scientific treatment of the material are similar to ''
A Treatise on the Astrolabe ''A Treatise on the Astrolabe'' is a medieval instruction manual on the astrolabe by Geoffrey Chaucer. It was completed in 1391. It describes both the form and the proper use of the instrument, and stands out as a prose technical work from a wr ...
''; #The text mentions that the year 1392 is the "Radix" (or "root") of Chaucer; #The main hand (including that of the "Radix" note) resembled, Price thought, a document likely written in Chaucer's hand; #Linguistic similarities between the ''Equatorie'' and Chaucer's work, including "verbal echoes of the ''Astrolabe''; #The author is influenced by Merton's school of astronomy but lives in London, and the writing is that of an amateur, not a professional astronomer; in addition, the writer is familiar with "the diplomatic cipher methods of his time"—all elements that correspond with Chaucer's biography. Following the publication of the facsimile and transcription, G. Herdan published an article in which he concluded, based upon the percentage of words in the ''Equatorie'' of "Romance vocabulary" (which includes words from
Old French Old French (, , ; ) was the language spoken in most of the northern half of France approximately between the late 8th -4; we might wonder whether there's a point at which it's appropriate to talk of the beginnings of French, that is, when it wa ...
, Anglo-Norman French, and
Latin Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...
), that Chaucer was indeed the author: "The agreement between observation and expectation, or between fact and theory, is so striking that without going further into the question of statistical significance we may conclude that by the token of Romance vocabulary the ''Equatorie'' is to be regarded as a work by Chaucer". However, Price's arguments were challenged in various ways. His claim that the manuscript was a draft in the hand of its author was disputed, though ultimately the evidence does seem to support it. More significantly, Price's claim that the handwriting was that of Geoffrey Chaucer was disproved by analysis by Kari Anne Rand Schmidt. In 2014 Kari Anne Rand identified the hand as belonging to John Westwyk.


Content

The text describes the construction of an
equatorium An equatorium (plural, equatoria) is an astronomy, astronomical Mechanical calculator, calculating instrument. It can be used for finding the positions of the Moon, Sun, and planets without arithmetic operations, using a geometrical model to re ...
, an instrument comparable to the
astrolabe An astrolabe (; ; ) is an astronomy, astronomical list of astronomical instruments, instrument dating to ancient times. It serves as a star chart and Model#Physical model, physical model of the visible celestial sphere, half-dome of the sky. It ...
– but where an astrolabe shows the positions of the stars, an equatorium computes them for the planets, according to the
Geocentric model In astronomy, the geocentric model (also known as geocentrism, often exemplified specifically by the Ptolemaic system) is a superseded scientific theories, superseded description of the Universe with Earth at the center. Under most geocentric m ...
of
Ptolemy Claudius Ptolemy (; , ; ; – 160s/170s AD) was a Greco-Roman mathematician, astronomer, astrologer, geographer, and music theorist who wrote about a dozen scientific treatises, three of which were important to later Byzantine science, Byzant ...
. The instrument is constructed from two discs, six feet in diameter. One of them is solid, and is marked with characteristics of the orbits of the various planets: their
apogee An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values. Apsides perta ...
, their
equant Equant (or punctum aequans) is a mathematical concept developed by Claudius Ptolemy in the 2nd century AD to account for the observed motion of the planets. The equant is used to explain the observed speed change in different stages of the plane ...
s, and other centres. The other disc consists of "a ring, a diametral bar, and a rule pivoted at the centre of the bar". The two discs are joined and simulate the motions of each of the planets. A divided circle around the rims of the two discs allow for the transferral of information from sets of tables (the
Alfonsine tables The ''Alfonsine Tables'' (, ), sometimes spelled ''Alphonsine Tables'', provided data for computing the position of the Sun, Moon and planets relative to the fixed stars. The tables were named after Alfonso X of Castile, who sponsored their cr ...
, from a Parisian document) that contain the data for each planet. The design was based on earlier equatoria, but refined for greater ease of manufacture and use. It permits the user to find the longitudes of any classical planet (including the Sun and Moon, as well as the lunar latitude).


Cipher

A
cipher In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is ''encipherment''. To encipher or encode i ...
is used for some comments on the tables, and Price gave the key. He could not, however, discern what the rationale of or the ordering behind the key was – whether it was perhaps based on some medieval version of the Greek alphabet, or whether there was "some key-phrase or sentence such as a name or family motto" behind it.


References


Notes


Bibliography

* * * * * *


External links


Cambridge Digital Library: ''Equatorie of the Planetis''
Digitised images, transcription, translation & virtual model of Peterhouse MS 75.I.
Seb Falk: ''What's the difference between an astrolabe and an equatorium''
Blog post. {{DEFAULTSORT:equatorie of the planetis, The 14th-century books Works by Geoffrey Chaucer Astronomy books Middle English literature