JF Ptak Science Books Post 20*30*

With "all" of the recent talk about prime numbers I thought to post this elegant and small summary of the different ways of writing numbers.

Above is a lovely detail of a collection of "ancient arithmetical characters", including notations for the numbers 1 through 9 by "Boethius, Plenudes, al Sephadi, Sacro Bosco, Indian, Roger Bacon, and AL Sephadi".

*Boethius*: Anicius Manlius Severinus Boëthius,^{ }and commonly called Boethius (c. 480–524 or 525 ACE), whose *Arithmetic* (based upon the work of Nicomachus, 60-120 ACE) was one of the great classic works of Medieval mathematics. He credits the "Pythagorians" with the introduction of his numerical notation, though it is not clear what exactly he meant, and that the term may have applied to anything Eastern. That said his 1,8 and 9 are what we know today, and 2 and 5 are the same but inverted; his 3,4,6,7 are not very recognizable. (His *Consolation of Philosophy*, written while he was in prison and awaiting execution for treason, is another Medieval classic, this in philosophy.) Works by Anicius Manlius Severinus Boethius at Project Gutenberg and the entry for Boethius at the wonderful Standford University encyclopedia of philosophy, here.

[The full segment (still only 4x5 inches) of the engraving from Abraham Rees (1743–1825) massive encyclopedia, *The Cyclopædia; or, Universal Dictionary of Arts, Sciences, and Literature* and printed in London in 1820, though it was "adapted" from a table created by the J.E. Montucla in his *Histoire de la Mathematique*, which was published in 1757]:

*Plenudes:* Maximus Penudes, (born 1260, Nicomedia, Byzantium, [now İzmit, Turkey]—died *c.* 1310, at Constantinople; a theologian, scholar, and translator who brough Arabic mathematics to life in Greek.

*al Sephadi*: 13th century Arabian philosopher and scholar. I've seen his name in reference to some number problems and the development of chess.

*Sacro Bosco*: Sacro Busto, or Sacrobosco (also called John or Johannes Halifax,
Holyfax, Holywalde, Sacroboscus, Sacrobuschus, de Sacro Bosco, or de
Sacro Busto) was a member of the Order of St. Augustine and a professor
of mathematics and astronomy/astrology at Paris ca. 1230. (There are many
places attributed to be his birthplace, but it seems fairly certain
that he at least was educated at Oxford.) He became a celebrated member
of the intelligensia, with his fame in the later centuries coming via
three of his surviving works, each an elementary textbook on mathematics
and astronomy: *De algorismo*, the *De computo*, and *De sphaera*. I think it is accurate to say that the *Sphaera* was the most
famous of his works--it is a very long-lived fundamental textbook on
astronomy (and the second astronomical text ever printed, in 1472) and
went through 24 editions to 1500, and then another 40 editions from 1500
to 1547. The book was still in use in the mid-17th century but far
less so, until it finally fell away into the
antiquarian dust. It was a short work--basically about 35 pages--and
concisely written, even elementary, but it did receive some close
attention by some of the great early thinkers in astronomy and
mathematics who contributed commentaries, including Michael Scot (between
1230 and 1235), John Pecham (prior to 1279), and by Campanus of Novara
between (1265 to 1292).

*Indian*: Well. Very very quickly put, the use of a decimal system in the Indian subcontinent has been in place for at least 2,500 years, though it is called in the West the Hindu-Arabic or Arabic number system, as the numbers came to Europe via the Arabs who had incorporated it in conquest of the Persians who in turn had adopted the Indian system. The use of the arithmetical notations spread across Europe relatively slowly in Medieval times, taking perhaps two hundred years to finally reach into England in the 11th century.

*Roger Bacon*: The English *Doctor Mirabilis*, who studied/taught at Oxford and then at University of Paris, made major steps towards the establishment of the scientific method, and in the 13th century was using a fairly-modern numerical notation save for the 2,4, and 5. (Bacon contributes one of the standard "great" quotes in the history of quotable quotes of math: "Mathematics is the gate and key of the sciences...neglect of mathematics works injury to all knowledge,
since he who is ignorant of it cannot know the other sciences or the
things of this world. And what is worse, men who are thus Ignorant are
unable to perceive their own ignorance and so do not seek a remedy." Roger Bacon, *Opus Majus*, as cited in: Morris Kline (1969) *Mathematics and the physical world*. p.1)

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