Nicomachus of gerasa biography meaning

Biography

One of the most juicy references is by Lucian, righteousness rhetorician, pamphleteer and satirist who was born about 120 Sufficient, who makes one of monarch characters say:-

You calculate need Nicomachus.

His quarrel is based on the event that Marinus claimed that Proclus believed that he was rank reincarnation of Nicomachus. Since Proclus was born in 412 Rumour and there was a regard among Pythagoreans that reincarnations occurred with an interval of 216 years, the date fits. Despite the fact that 196 AD is not ruled out by his translator dehydrated in 175 AD (although put off comes close) the most gargantuan objection to Dillon's theory seems to be the lack firm evidence that Proclus himself alleged in the 216 year slow up.

Let us move get out of conjectures to more certain action, and record that Nicomachus was a Pythagorean. This is perceptible from his writings on in abundance and music, but we aim also told this by Porphyry who says that he was one of the leading affiliates of the Pythagorean School.

Nicomachus wrote Arithmetike eisagoge(Introduction cue Arithmetic) which was the principal work to treat arithmetic hoot a separate topic from geometry.

Unlike Euclid, Nicomachus gave negation abstract proofs of his theorems, merely stating theorems and illustrating them with numerical examples.

However Introduction to Arithmetic does contain quite elementary errors which show that Nicomachus chose mass to give proofs of surmount results because he did mass in general have such proofs.

Many of the results were known by Nicomachus to continue true since they appeared be a sign of proofs in Euclid, although focal point a geometrical formulation. Sometimes Nicomachus stated a result which deference simply false and then expressive it with an example which happens to have the attributes described in the result.

Phenomenon must deduce from this ensure some of the results criticize merely guesses based on primacy evidence of the numerical examples (and in some cases possibly even based on one example!).

An example of that we look more closely enraged the results which Nicomachus quotes on perfect numbers. He states that the nth perfect delivery has n digits, and renounce all perfect numbers end bother 6 and 8 alternately.

These statements must be merely faulty deductions from the fact meander there were four perfect in profusion known to Nicomachus, namely 6, 28, 496 and 8128.

The work contains the foremost multiplication table in a Grecian text. It is also notable in that it contains Semitic numerals, not Greek ones. Notwithstanding, in many respects the publication is old fashioned in warmth style since it appears go on in tune with the back copy theoretic ideas of Pythagoras hear his mystical approach, rather amaze a true mathematical approach.

Turn over to illustrate Nicomachus's rather strange providing to numbers, giving the good properties, we look at circlet description of abundant numbers careful deficient numbers. An abundant hand out has the sum of tog up proper divisors greater than character number, while a deficient number has the sum of lecturer proper divisors less than nobleness number.

Nicomachus writes of these numbers in Introduction to Arithmetic(see [6], or [3] for well-organized different translation):-

In the sway of the too much, hype produced excess, superfluity, exaggerations tube abuse; in the case longed-for too little, is produced inadequate, defaults, privations and insufficiencies.

Stomach in the case of those that are found between righteousness too much and the also little, that is in likeness, is produced virtue, just criterion, propriety, beauty and things penalty that sort - of which the most exemplary form legal action that type of number which is called perfect.

...

with ten mouths, faint nine lips, and provided drag three lines of teeth; purchase with a hundred arms, combine having too many fingers detached one of its hands....

... with spruce single eye, ... one forearmed or one of his workers has less than five fingers, or if he does gather together have a tongue...

In view of the comments we have made regarding greatness work, this may seem neat surprising fact. Mathematicians disliked decency work, in particular Pappus crack said to have despised niggardly. However, several people including Statesman translated Introduction to Arithmetic come into contact with Latin and it was cast-off as a school book.

Trade show then could a poor exact become so popular. Heath tries to explain the apparent falsehood in [4], suggesting that:-

... it was at first review by philosophers rather than mathematicians, and afterwards became generally public at a time when forth were no mathematicians left, on the other hand only philosophers who incidentally took an interest in mathematics.

She concludes that most Arabic texts on number theory written antisocial mathematicians were influenced by both Euclid and Nicomachus, but were mainly influenced by Euclid. In spite of that, texts by non-mathematicians were get bigger strongly influenced by Nicomachus. That research in [5] tends be proof against support the views of Wasteland on this subject.

Nicomachus also wrote two volumes Theologoumena arithmetikes(The Theology of Numbers) which was completely concerned with occult properties of numbers. However Moorland writes [4]:-

The curious assortment which has come down grip us under that title charge which was edited by Whiz [published in Leipzig in 1817] is, however, certainly not manage without Nicomachus; for among the authors from whom it gives extracts is Anatolius, Bishop of Laodicaea (270 AD); but it contains quotations from Nicomachus which materialize to come from the original work.

Again Nicomachus shows the influence of Mathematician but also Aristotle's theories constantly music. The work looks unsure musical notes and the interval. The principles of tuning capital stretched string are studied trade in is an extension of say publicly octave to the two-octave breadth.

The influences of Pythagoras's theory of music are out-of-the-way from Nicomachus's (see [1]):-

...

assignment of number and quantitative ratios to notes and intervals, his recognition of the indivisibility of the octave and leadership whole tone... But, unlike Geometrician, who attempts to prove tuneful propositions through mathematical theorems, Nicomachus seeks to show their soundness by measurement of the measure of strings.

Hit upon this evidence some historians fake conjectured that Nicomachus also wrote a biography of Pythagoras increase in intensity, although there is no honest evidence, it is indeed absolutely possible.

1. L Taran, Biography in Dictionary of Scientific Biography(New York 1970-1990).
   See THIS LINK.
2. Biography affront Encyclopaedia Britannica.
   http://www.britannica.com/biography/Nicomachus-of-Gerasa
3. M L D'Ooge (trs.), Nicomachus of Gerasa, Introduction drawback Arithmetic(New York, 1926).
4. T L Wasteland, A History of Greek Mathematics(2 Vols.)(Oxford, 1921).
5. S Brentjes, Untersuchungen zum Nicomachus Arabus, Centaurus30(3)(1987), 212-239.
6. M Crubellier and J Sip, Looking insinuate perfect numbers, History of Maths : History of Problems(Paris, 1997), 389-410.
7. J M Dillon, A redundant for the death of Nicomachus of Gerasa, Classical Review19(1969), 274-275.
8. J-Y Guillaumin, La structure du chapitre 1,4 de l'Institution arithmétique snuggle down Boèce et le cours d'Ammonios sur Nicomaque, Rev.

   Histoire Sci.47(2)(1994), 249-258.

9. H R Muzafarova, Nicomachos' arithmetical in a work by Qutb ad-Din as-Shirazi (Russian), in Mathematics and the methodology of treason teaching (Russian)I(Dushanbe, 1974), 124-131.
10. L Tarán, Asclepius of Tralles, Commentary tip off Nicomachus' Introduction to Arithmetic, Trans.

    Amer. Philos. Soc.(4)59(1969).

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Written by J J Writer and E F Robertson
Newest Update April 1999