Nicomachus (c. 60 – c. 120) was an important mathematician in the ancient world and is best known for his works
Introduction to ArithmeticIntroduction to Arithmetic was written by Nicomachus almost two thousand years ago, and contains both philosophical prose and very basic mathematical ideas. Nicomachus refers to Plato quite often, and wrote about how philosophy can only be possible if one knows enough about mathematics. This is...
(Arithmetike eisagoge) and
The Manual of Harmonics in
GreekGreek , an independent branch of the Indo-European family of languages, is the language of the Greeks. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. In its ancient form, it is the language of classical...
. He was born in Gerasa,
RomanAncient Rome was a civilization that grew out of a small agricultural community founded on the Italian Peninsula as early as the 10th century BC. Located along the Mediterranean Sea, it became one of the largest empires in the ancient world....
SyriaSyria , officially the Syrian Arab Republic , is a country in Western Asia, bordering Lebanon and the Mediterranean Sea to the west, Turkey to the north, Iraq to the east, Jordan to the south and Israel to the southwest....
(now
JerashJerash, the Gerasa of Antiquity, is the capital and largest city of Jerash Governorate , which is situated in the north of Jordan, 48 km north of the capital Amman towards Syria...
,
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), and was strongly influenced by Aristotle. He was a
PythagoreanPythagoreanism is a term used for the esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were much influenced by mathematics and probably a very inspirational source for Plato and Platonism....
.
Nothing is known about the life of Nicomachus except that he was a
PythagoreanPythagoreanism is a term used for the esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were much influenced by mathematics and probably a very inspirational source for Plato and Platonism....
and that he came from Gerasa.
Nicomachus (c. 60 – c. 120) was an important mathematician in the ancient world and is best known for his works
Introduction to ArithmeticIntroduction to Arithmetic was written by Nicomachus almost two thousand years ago, and contains both philosophical prose and very basic mathematical ideas. Nicomachus refers to Plato quite often, and wrote about how philosophy can only be possible if one knows enough about mathematics. This is...
(Arithmetike eisagoge) and
The Manual of Harmonics in
GreekGreek , an independent branch of the Indo-European family of languages, is the language of the Greeks. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. In its ancient form, it is the language of classical...
. He was born in Gerasa,
RomanAncient Rome was a civilization that grew out of a small agricultural community founded on the Italian Peninsula as early as the 10th century BC. Located along the Mediterranean Sea, it became one of the largest empires in the ancient world....
SyriaSyria , officially the Syrian Arab Republic , is a country in Western Asia, bordering Lebanon and the Mediterranean Sea to the west, Turkey to the north, Iraq to the east, Jordan to the south and Israel to the southwest....
(now
JerashJerash, the Gerasa of Antiquity, is the capital and largest city of Jerash Governorate , which is situated in the north of Jordan, 48 km north of the capital Amman towards Syria...
,
JordanJordan , officially the Hashemite Kingdom of Jordan, is a country in Western Asia spanning the southern part of the Syrian Desert down to the Gulf of Aqaba. Jordan shares borders with Syria to the north, Iraq to the northeast, Saudi Arabia to the east and south, the Gulf of Aqaba to the southwest,...
), and was strongly influenced by Aristotle. He was a
PythagoreanPythagoreanism is a term used for the esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were much influenced by mathematics and probably a very inspirational source for Plato and Platonism....
.
Life
Nothing is known about the life of Nicomachus except that he was a
PythagoreanPythagoreanism is a term used for the esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were much influenced by mathematics and probably a very inspirational source for Plato and Platonism....
and that he came from Gerasa. The age in which he lived (c. 100 AD) is only known because he mentions
ThrasyllusThrasyllus of Mendes whose full name was Tiberius Claudius Thrasyllus . Thrasyllus was an Egyptian Greek from Mendes Egypt...
in his
Manual of Harmonics, and because his
Introduction to Arithmetic was apparently translated into
LatinLatin is an Italic language originally spoken in Latium and Ancient Rome. Through the Roman conquest, Latin spread throughout the Mediterranean and a large part of Europe...
in the mid 2nd century by
ApuleiusLucius Apuleius Platonicus was a Latin prose writer remembered most for his bawdy picaresque novel, the Metamorphoses, otherwise known as The Golden Ass...
. As a Neo-Pythagorean, Nicomachus was often more interested in the mystical properties of numbers rather than their mathematical properties.
Introduction to Arithmetic
Introduction to ArithmeticIntroduction to Arithmetic was written by Nicomachus almost two thousand years ago, and contains both philosophical prose and very basic mathematical ideas. Nicomachus refers to Plato quite often, and wrote about how philosophy can only be possible if one knows enough about mathematics. This is...
, the lesser work on arithmetic. Nicomachus writes extensively on
numberA number is a mathematical object used in counting and measuring. A notational symbol which represents a number is called a numeral, but in common usage the word number is used for both the abstract object and the symbol, as well as for the word for the number...
s, especially on the significance of prime numbers and perfect numbers and argues that
arithmeticArithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations, such as addition, subtraction, multiplication and division...
is ontologically prior to the other mathematical sciences (
geometryGeometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
,
musicMusic is an art form whose medium is sound. Common elements of music are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...
, and
astronomyAstronomy is the scientific study of celestial objects and phenomena that originate outside the Earth's atmosphere...
), and is their cause.
Manual of Harmonics
Manual of Harmonics . This is the first important
music theoryMusic theory is the field of study that deals with how music works. It examines the language and notation of music. It identifies patterns that govern composers' techniques. In a grand sense, music theory distills and analyzes the parameters or elements of music – rhythm, harmony , melody,...
treatise since the time of
AristoxenusAristoxenus of Tarentum was a Greek peripatetic philosopher, and writer on music and rhythm.He was taught first by his father Spintharus, a pupil of Socrates and also a musician, and later by the Pythagoreans, Lamprus of Erythrae and Xenophilus, from whom he learned the theory of music...
and
EuclidEuclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician and is often referred to as the "Father of Geometry." He was active in Hellenistic Alexandria during the reign of Ptolemy I...
. It provides the earliest surviving record of the story of
PythagorasPythagoras of Samos was an Ionian Greek philosopher and founder of the religious movement called Pythagoreanism. He is often revered as a great mathematician, mystic and scientist; however some have questioned the scope of his contributions to mathematics and natural philosophy...
's epiphany outside a
smithyA blacksmith is a person who creates objects from iron or steel by forging the metal; i.e., by using tools to hammer, bend, and cut. Blacksmiths produce things like wrought iron gates, grills, railings, light fixtures, furniture, sculpture, tools, agricultural implements, decorative and religious...
that pitch is determined by numeric ratios. Nicomachus also gives the first in depth account of the relationship between music and the ordering of the universe via the "
music of the spheresMusica universalis is an ancient philosophical concept that regards proportions in the movements of celestial bodies—the Sun, Moon, and planets—as a form of musica . This 'music' is not literally audible, but a harmonic and/or mathematical and/or religious concept...
." Nicomachus's discussion of the governance of the ear and voice in understanding music unites Aristoxenian and Pythagorean concerns, normally regarded as antitheses. In the midst of theoretical discussions, Nicomachus also describes the
instrumentsA musical instrument is an object constructed or used for the purpose of making the sounds of music. In principle, anything that produces sound can serve as a musical instrument. The history of musical instruments dates back to the beginnings of human culture...
of his time, also providing a valuable resource. In addition to the
Manual, ten extracts survive from what appear to have originally been a more substantial work on music.
Lost Works
The works which are lost are:
- Art of Arithmetic , the larger work on arithmetic, mentioned by Photius. Boethius wrote a loose paraphrase of this work , which contributed to medieval education.
- A larger work on music, promised by Nicomachus himself, and apparently referred to by Eutocius in his comment on the sphere and cylinder of Archimedes
Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity...
.
- An Introduction to Geometry, referred to by Nicomachus, although whether it was his work in unclear.
- Theology of Arithmetic , on the mystic properties of numbers in two books mentioned by Photius. There is an extant work under this name written two centuries later which contains quotations from this work of Nicomachus.
- A Life of Pythagoras, one of the main sources used by Porphyry
Porphyry of Tyre was a Neoplatonic philosopher who was born in Tyre in what is now Lebanon. He is particularly important for the history of philosophy because he edited and published the Enneads, the only collection of the work of his teacher Plotinus. He also wrote many works himself on a wide...
and Iamblichus, for their (extant) Lives of Pythagoras.
- A collection of Pythagorean dogmata, referred to by Iamblichus.
- On Egyptian festivals , is mentioned by Athenaeus
Athenaeus , of Naucratis in Egypt, Greek rhetorician and grammarian, flourished about the end of the 2nd and beginning of the 3rd century A.D. The Suda only tells us that he lived in the times of Marcus Athenaeus (Ancient Greek - Athếnaios Naukratios, Latin Athenaeus Naucratita), of Naucratis in...
, but whether by this Nicomachus is uncertain.
See also
- Monad
- Dyad
The Dyad is a title used by the Pythagoreans for the number two, representing the principle of "twoness" or "otherness".Numenius said that Pythagoras gave the name of Monad to God, and the name of Dyad to matter...
- Triad
The Triad is a Pythagorean title for the number three. According to Priya Hemenway they considered it the most beautiful number, as it is the first number to equal the sum of all the terms below it, and the only number whose sum with those below equals the product of them and itself.-See also:*...
- Pentad
The pentad was a Pythagorean term for the number five. A pentagram, symbol of the pentad, was used by the Pythagoreans as a secret sign to recognize each other.In a passage from Lucian, he refers to the pentagram as the secret sign of brotherhood between the Pythagoreans. It represents the...
- Tetrad
The tetrad or number four is the first number formed by the addition and multiplication of equals. To the Pythagoreans, this symbol and number represented justice as it is the first number that is divisible every way into equal parts.-See also:*Monad*Dyad...
- Decad
The decad was seen by the Pythagoreans as an "assembly point" and a symbol of earth and heaven. They regarded the decad as something perfect, which embraces the whole nature of number.-See also:*Monad *Dyad...
- Nicomachus's theorem
External links