Computus chirometralis
Computus chirometralis is a late medieval textbook in Medieval Latin , in which knowledge of the time about calendar calculations and astronomy is conveyed. As the title section chirometralis ( Gr. Χείρὠν = hand, μἔτρον = measure) expresses, the hand is used to learn the relevant data by counting the phalanges of the fingers.
The author
The author of the font cannot be determined with certainty. Several manuscripts of the work present him as Magister Johannes de Erfordia and give 1330 as the year of creation. Possibly he can be equated with Johannes Eligerus (Algeri) de Gondersleuen , who is praised by Johannes Trithemius in De scriptoribus ecclesiasticis as an important mathematician and astronomer from Saxony . However, this work does not appear under the titles mentioned by Trithemius. It seems certain that the work was created in the 1st third of the 14th century in the vicinity of the teaching company in Erfurt .
content
Since the text is poorly structured, it is cited according to the page number from 1r to 21v in Karl Mütz's edition.
Computus
Johannes Eligerus divided his work into the computus minoris and the computus maioris . In the computus minoris , topics of calendar calculation are briefly explained and then the determination and memorization of the associated values are discussed. So follows (1r / 23-2v / 3) a short definition of the 28-year solar cycle and the solar circle (position of a year in this cycle) verses for memorizing the corresponding century values and finally determining the solar circle for any year. Likewise, the Sunday letters (2v / 4-3r / 16), the 19-year Meton cycle (4r / 5-5r / 13), the determination of the Easter date (5r / 14-7v / 21) and the non-movable Christian holidays (7v / 2-8v / 7) treated.
In computus maioris , astronomically demanding explanations follow on the interaction of the lunar and solar cycle (10r / 1-16v / 6), the signs of the zodiac (16v / 7-17v / 13) and world models of the spheres (17r / 13-19r / 2).
chirometralis
A special feature of the book is the use of finger math . Different ways of counting and calculating with the fingers of the hand as the first "calculating machine" were already common in ancient times in many cultures. Pictorial as well as written references (e.g. Seneca in his Epistulae , Pliny the Elder in the Naturalis historia , Tertullian in the Apologeticum ) are found again and again. However, there are no systematic representations, possibly because they would not be meaningful without practical demonstration. The most comprehensive description can be found in Beda Venerabilis De temporum ratione, chap. 1 and 55. Beda's work was extremely widespread in Europe; over 250 manuscripts have survived. But here too, as in all of the literature that has survived, it is not about real arithmetic, but about counting and memory aids. Beda Venerabilis states in chap. 55 shows how the epacts of the moon in the 19-year Meton cycle are examined on the phalanges of a hand. Similarly, Johannes Eligerus encourages his students to use the limbs of one hand, including the front and back thumb and fingertips, when memorizing. In addition, they are offered a memory verse, a rhythmic sequence of syllables. A similar procedure can be found about 200 years earlier with the Guidonic hand for orientation in sound systems. The simplest example is the month names (13r, starting with March). The student learns the syllable sequence Mar ap ma iun iul au sep oc no de ia feb . When asked about the 7th month, he counts the syllables, pointing to the phalanx, comes to sep and then has to know that sep = September. The knowledge presented is of course much more complex, the more so as numbers are largely transmitted, which are initially converted into letters with an obvious conversion (1 = a, 2 = b, ...). In the example above, the following verse em Mar ap phil ... gives the dates of the 1st new moon for each month for a certain year.
Critical attitude and accuracy
The subject matter presented has been part of European science and school operations for centuries and has been spread out in many preserved manuscripts. Nevertheless, there has been a change over time. The author can now deal completely impartially with the errors that result from the inaccuracy of the calendar models used. This is how he states the inaccuracy of the Meton cycle (4r / 17):
et quando have regula vulgaris luna prima in libro, est quarta vel quinta in celo
and if, according to the general rule in the book, the moon is on the first day, it is on the fourth or fifth in the sky
The calendar year with its 365 days and a leap day every 4 years is also incorrect. Therefore, after several thousand years, Christmas would be celebrated in summer (7v). Johannes Eligerus adds somewhat vaguely: id tamen teoloice non conceditur (but this is not admitted theologically).
Astronomy made much more precise observations possible than in previous centuries. With astronomical instruments, especially the astrolabe , more exact series of numbers of the rising and setting of various celestial bodies were provided. In this document, too, time series from the entry of the full moon and new moon with day, hour and hourly part (= 3 minutes) are offered for memorizing (12r). The author is aware of the fact that it is location-dependent (Erfurt) information. For a trip of 12 miles to the east or west, an hourly part must be added or subtracted (16r).
Living on and tradition
The work quickly spread and entered the canon of those texts that played a role in the teaching of the medieval faculties of the 15th century. Around 100 manuscripts have been preserved. Famous scholars such as Johann von Glogau and Christian von Prachatitz wrote adaptations or commentaries, and it was finally printed in 1480/85 in the workshop of Johann Koehlhoff the Elder . The art of printing, and with it easier access to information, led to a decline in interest in such memorable memory performances. In 2003 Karl Mütz edited the original Latin text based on this cradle print by Johann Koehlhoff the Elder, together with a translation into German and extensive commentary.
Text editing and translation
- Karl Mütz: Computus chirometralis . Late medieval textbook for calendar calculation, Tübingen 2003
literature
- Siegmund Günther : History of mathematical teaching in the German Middle Ages up to 1525 , Berlin 1887
- Georges Ifrah: Universal History of Numbers , Frankfurt / New York 1981
- Sönke Lorenz : Studium generale Erfordense , Stuttgart 1989
Individual evidence
- ^ Sönke Lorenz: Studium generale Erfordense , p. 257
- ^ Sönke Lorenz: Studium generale Erfordense , p. 244
- ↑ Karl Mütz: Computus chirometralis . Late medieval textbook for calendar calculation, pp. 93–128
- ↑ Karl Mütz: Computus chirometralis . Late medieval textbook for calendar calculation, pp. 151–157
- ↑ Georges Ifrah: Universal History of Numbers , p. 79
- ↑ Georges Ifrah: Universal History of Numbers , p. 81f
- ^ Siegmund Günther: History of mathematical teaching in the German Middle Ages up to the year 1525 , p. 9
- ^ Charles W. Jones: Beda Venerabilis Opera , Pars VI, opera didascalica p. 241ff
- ↑ Siegmund Günther: History of mathematical teaching in the German Middle Ages up to the year 1525 , p. 13
- ↑ Karl Mütz: Computus chirometralis . Late medieval textbook for calendar calculation, introduction
- ^ Sönke Lorenz: Johannes Algeri (Eligerus), author of the Computus chirometralis , in Karl Mütz: Computus chirometralis , p. 186
- ↑ Sönke Lorenz: Studium generale Erfordense , pp. 250-255
- ^ Sönke Lorenz: Johannes Algeri (Eligerus), author of the Computus chirometralis , in Karl Mütz: Computus chirometralis , p. 186