**Reinher of Paderborn** was a German mathematician who worked on the mathematics of the calendar and in particular on the calculation of Easter.

- This is supported by fifteen documents testified by him and by copies of his treatise Computus emendatus Ⓣ(Calculation improved).
- In 1171 Reinher published his treatise Computus emendatus Ⓣ(Calculation improved), an improved calculation method for calculating the date of Easter.
- As Easter and the movable feasts stand in a special relation to the spring full moon, there existed a particular difficulty in calculating the date of Easter to match the solar year of about 365 days and the lunar year of about 354 days.
- There is no simple relation between the length of these two types of years hence they were to be calculated as exactly as possible.
- Reinher was very interested in raising the prestige of the church in the field of calendrical calculations.
- An innovation for this period was his introduction to the Jewish calendar knowledge, based on this knowledge he analyzed the mistakes of the previous calculation of the lunar year and he described in detail the steps for a correct approach.
- Reinher compared the lunar cycles of the Hebrews and of Dionysius Exiguus.
- Reinher used a lunar orbit of the Hebrews consisting of 29 days, 12 hours and 793 parts, each hour corresponds to 1080 parts.
- He calculated the lunar orbit of Dionysius by dividing every 19 years by 235; and he obtained 29 days, 12 hours and 174 parts, each hour corresponds to 235 parts.
- In the western world Reinher was the first who has used the Indian number system instead of the Roman numeral system for mathematical and astronomical work - because of the advantage of writing and arithmetic.
- Other western sources reported the Indian numerals and the Algorismus, such as the Salzburger Computus (1143), the note-book of Hugo von Lerchenfeld or the annals of Regensburg (1174-1197), the Computus of Master Chonrad (1200, in a revision of 1396), manuscripts (late 12th century) of the monastery Prüfening and the monastery Salem (liber algorizmi), the Massa compoti of Alexandre de Villedieu (c.
- 1200) or the arithmetic book Liber abaci of Leonardo Fibonacci (1202).
- But no one before Reinher used the new number system in a scientific treatise.
- He understood the new idea of the Indian number system, and earlier than many others of his time he recognized how the use of Indian numerals simplified the arithmetic.
- Reinher made his calculations with our familiar decimal system.
- But his mathematical vocabulary was that of Boethius (480-524) and not that of Plato Tiburtinus (c.
- Since both were not yet able to scan a text, they were unaware that Reinher had used more than once addere and subtrahere, e.g. addiderimus (lib.
- Reinher reported (lib.
- 1.19) about the special planetary alignment in the night of 13 September 1170, when Mars and Jupiter for a time appeared as only one star, a conjunction in the zodiac sign of Gemini, which is proved by the tables of Schoch (1873-1929) for the 13./14.9.1170.
- Incidentally, the same sample year (4930) also is used by Moses Maimonides (1138-1204) in his book of recognition (Mishneh Torah).
- This caused an error of 1 day in 310.028329 years.
- How exactly the 19-year lunar cycle was calculated by Reinher, shows a comparison with the values determined by him.
- Reinher calculated the 19-year lunar cycle - according to the Hebrew calendar - with 6939.68962 days.
- According to him, the mistake of Dionysius Exiguus is 1 day in 314.683706 years.
- The script Computus emendatus Ⓣ(Calculation improved) of Reinher of Paderborn is preserved in five manuscripts.
- The copies HANN and LEID begin with a praise for Reinher.
- Incipit praefatio magistri Reinheri decani Patherbornensis, perspicacissimi calculatoris, in compotum emendatum.
- In the 15th century the manuscript of Reinher is proven to have been known, although we do not know the handwriting used.
- At the Council of Basel 1431-1449, the treatise of Reinher was in many ways helpful.
- Cusanus and the Cistercian monk Hermann Zoestius of the convent of Marienfeld belonged to the calendar committee and pushed for a calendar reform.
- Both quoted in their tracts from the work of Reinher.
- Zoestius described Reinher as author, but Cusanus made Albertus Magnus the author.
- the former Cathedral School in Paderborn may be regarded as one of the most advanced of its time with respect to the mathematical teaching because no other can make it probable that there has been already calculated with Arabic numerals previously.
- Incidentally, the later mathematician Karl Theodor Wilhelm Weierstrass (1815-1897) was a student of the Akademisches Gymnasium (now Theodorianum), which in its tradition goes back to the cathedral school of 799.
- of an equally moving as forgotten brilliant achievement of medieval science.

Born about 1140, Paderborn, Roman Empire, now Germany. Died about 1190, Paderborn, Roman Empire, now Germany.

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Astronomy, Origin Germany

Epochs: 1

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive