The same equation may be written more compactly using the mathematical notation for summation:
This identity is sometimes called Nicomachus's theorem.
History
Many early mathematicians have studied and provided proofs of Nicomachus's theorem. Stroeker (1995) claims that "every student of number theory surely must have marveled at this miraculous fact". Pengelley (2002) finds references to the identity not only in the works of Nicomachus in what is now Jordan in the first century CE, but also in those of Aryabhata in India in the fifth century, and in those of Al-Karaji circa 1000 in Persia. Bressoud (2004) mentions several additional early mathematical works on this formula, by Alchabitius (tenth century Arabia), Gersonides (circa 1300 France), and Nilakantha Somayaji (circa 1500 India); he reproduces Nilakantha's visual proof.
Numeric values; geometric and probabilistic interpretation
Little is known about the life of Nicomachus except that he was a Pythagorean who came from Gerasa. Historians consider him a Neopythagorean based on his tendency to view the numbers having mystical properties. The age in which he lived (c. 100 CE) is only known because he mentions Thrasyllus in his Manual of Harmonics, and because his Introduction to Arithmetic was apparently translated into Latin in the mid 2nd century by Apuleius. His Manual of Harmonics was addressed to a lady of noble birth, at whose request Nicomachus wrote the book, which suggests that he was a respected scholar of some status. He mentions his intent to write a more advanced work, and how the journeys he frequently undertakes leave him short of time.
Nicomachus (Greek:Νικόμαχος; fl. c. 325 BC), was the son of Aristotle.
Biographical details
The Suda — a massive 10th-century Byzantine encyclopedia of the ancient Mediterranean world — states that Nicomachus was from Stageira, was a philosopher, a pupil of Theophrastus, and, according to Aristippus, his lover. He may have written a commentary on his father's lectures in physics. Nicomachus was born to the slave Herpyllis, and his father's will commended his care as a boy to several tutors, then to his adopted son, Nicanor. Historians think the Nicomachean Ethics, a compilation of Aristotle's lecture notes, was probably named after or dedicated to Aristotle's son. Several ancient authorities may have conflated Aristotle's ethical works with the commentaries that Nicomachus wrote on them. Ancient sources indicate that Nicomachus died in battle while still a "lad".
Aristotle was the master of virtues.
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“Aristotle was born around 384 BC in the ancient Greek kingdom of Macedonia, where his father was the royal doctor. He grew up to be arguably the most influential philosopher ever, with modest nicknames like ‘the master’, and simply ‘the philosopher’. One of his big jobs was tutoring Alexander the Great, who soon after went out and conquered the known world...”
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published: 29 Oct 2014
Unknown Most Interesting Facts About Aristotle || Pastimers
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The Greek philosopher has made significant discoveries in almost every walk of life. From sciences to subjects like poetry, music, theater, logic, metaphysics, rhetoric, ethics and politics, Aristotle aced it all.
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published: 20 Mar 2018
Aristotle Biography For Kids - Greek philosopher
Here in this video I have described about Aristotle biography for kids Video. I hope you will really like this Aristotle biography for kids Video. He was Born at 384 BC in Stagira, Greece. He is Best known for Student of Plato and teacher of Alexander the Great. Aristotle was an ancient Greek philosopher and scientist born in the city of Stagira, Chalkidiki, Greece. Along with Plato, he is considered the "Father of Western Philosophy". He Died at 322 BC in Euboea, Greece.
Please watch full video for this Aristotle biography for kids Video.
Aristotle: Biography of a Great Thinker Aristotle - Greek Philosopher | Mini Bio | Biography Aristotle Biography in English | Greek philosopher Aristotle: History's Most Influential Thinker The Truth About Aristotle Aristotle Biography in English Arist...
published: 30 Apr 2018
ARISTOTLE: The Nicomachean Ethics - FULL AudioBook | Greatest AudioBooks
ARISTOTLE: The Nicomachean Ethics - FULL AudioBook | Greatest AudioBooks
The work consists of ten books, originally separate scrolls, and is understood to be based on notes said to be from his lectures at the Lyceum which were either edited by or dedicated to Aristotle's son, Nicomachus. In many ways this work parallels the similar Eudemian Ethics, which has only eight books, and the two works can be fruitfully compared. Books V, VI, and VII of the Nicomachean Ethics are identical to Books IV, V, and VI of the Eudemian Ethics. Opinions about the relationship between the two works, for example which was written first, and which originally contained the three common books, is divided. Aristotle describes his ethical work as being different from his other kinds of study, because it is not jus...
published: 08 Feb 2013
The Nicomachean Ethics - Book VIII - (FULL Audio Book)
The Nicomachean Ethics (FULL Audio Book)
by Aristotle (384 BCE - 322 BCE)
Translated by Thomas Taylor (1758-1835)
The work consists of ten books, originally separate scrolls, and is understood to be based on notes said to be from his lectures at the Lyceum which were either edited by or dedicated to Aristotle's son, Nicomachus. In many ways this work parallels the similar Eudemian Ethics, which has only eight books, and the two works can be fruitfully compared. Books V, VI, and VII of the Nicomachean Ethics are identical to Books IV, V, and VI of the Eudemian Ethics. Opinions about the relationship between the two works, for example which was written first, and which originally contained the three common books, is divided. Aristotle describes his ethical work as being different from his ...
Aristotle was the master of virtues.
Enjoying our Youtube videos? Get full access to all our audio content, videos, and thousands of thought-provoking article...
Aristotle was the master of virtues.
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FURTHER READING
“Aristotle was born around 384 BC in the ancient Greek kingdom of Macedonia, where his father was the royal doctor. He grew up to be arguably the most influential philosopher ever, with modest nicknames like ‘the master’, and simply ‘the philosopher’. One of his big jobs was tutoring Alexander the Great, who soon after went out and conquered the known world...”
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Aristotle was the master of virtues.
Enjoying our Youtube videos? Get full access to all our audio content, videos, and thousands of thought-provoking articles, conversation cards and more with The School of Life Subscription: https://t.ly/D71Sz
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FURTHER READING
“Aristotle was born around 384 BC in the ancient Greek kingdom of Macedonia, where his father was the royal doctor. He grew up to be arguably the most influential philosopher ever, with modest nicknames like ‘the master’, and simply ‘the philosopher’. One of his big jobs was tutoring Alexander the Great, who soon after went out and conquered the known world...”
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Watch more films on PHILOSOPHY in our playlist:
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http://www.madadamfilms.co.uk #TheSchoolOfLife
Source : http://bit.ly/2GPDVzr
The Greek philosopher has made significant discoveries in almost every walk of life. From sciences to subjects like poetry, musi...
Source : http://bit.ly/2GPDVzr
The Greek philosopher has made significant discoveries in almost every walk of life. From sciences to subjects like poetry, music, theater, logic, metaphysics, rhetoric, ethics and politics, Aristotle aced it all.
☛ Visit our website : http://Wirally.com
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Source : http://bit.ly/2GPDVzr
The Greek philosopher has made significant discoveries in almost every walk of life. From sciences to subjects like poetry, music, theater, logic, metaphysics, rhetoric, ethics and politics, Aristotle aced it all.
☛ Visit our website : http://Wirally.com
☛ For More Videos Subscribe Our Channel : http://goo.gl/CnuhTj
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Here in this video I have described about Aristotle biography for kids Video. I hope you will really like this Aristotle biography for kids Video. He was Born a...
Here in this video I have described about Aristotle biography for kids Video. I hope you will really like this Aristotle biography for kids Video. He was Born at 384 BC in Stagira, Greece. He is Best known for Student of Plato and teacher of Alexander the Great. Aristotle was an ancient Greek philosopher and scientist born in the city of Stagira, Chalkidiki, Greece. Along with Plato, he is considered the "Father of Western Philosophy". He Died at 322 BC in Euboea, Greece.
Please watch full video for this Aristotle biography for kids Video.
Aristotle: Biography of a Great Thinker Aristotle - Greek Philosopher | Mini Bio | Biography Aristotle Biography in English | Greek philosopher Aristotle: History's Most Influential Thinker The Truth About Aristotle Aristotle Biography in English Aristotle Biography Aristotle Part 1: Introduction (For Political Science Optional in English and English) Aristotle Biography Of a Great Thinker in English
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Abraham Lincoln Biography : https://youtu.be/EO6AXx6fXFo #biography, #biographies, #bio, #facts, #famouspeople, #lifestyle, #lifestory, #unknownfacts
Here in this video I have described about Aristotle biography for kids Video. I hope you will really like this Aristotle biography for kids Video. He was Born at 384 BC in Stagira, Greece. He is Best known for Student of Plato and teacher of Alexander the Great. Aristotle was an ancient Greek philosopher and scientist born in the city of Stagira, Chalkidiki, Greece. Along with Plato, he is considered the "Father of Western Philosophy". He Died at 322 BC in Euboea, Greece.
Please watch full video for this Aristotle biography for kids Video.
Aristotle: Biography of a Great Thinker Aristotle - Greek Philosopher | Mini Bio | Biography Aristotle Biography in English | Greek philosopher Aristotle: History's Most Influential Thinker The Truth About Aristotle Aristotle Biography in English Aristotle Biography Aristotle Part 1: Introduction (For Political Science Optional in English and English) Aristotle Biography Of a Great Thinker in English
*DON'T FORGET TO WATCH THESE BIOGRAPHIES
Plato Biography : https://youtu.be/HWJ51s_oQ0Q
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Mother Teresa Biography : https://youtu.be/UBMSESVo88k
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Margaret Thatcher Biography : https://youtu.be/o1CxP-WDcwQ
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Louis Pasteur Biography : https://youtu.be/t_Oedb-z7OQ
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Jawaharlal Nehru Biography : https://youtu.be/SYS_SgfO7Lo
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Isaac Newton Biography : https://youtu.be/X09rtF7WMjI
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ARISTOTLE: The Nicomachean Ethics - FULL AudioBook | Greatest AudioBooks
The work consists of ten books, originally separate scrolls, and is understood to be ba...
The Nicomachean Ethics (FULL Audio Book)
by Aristotle (384 BCE - 322 BCE)
Translated by Thomas Taylor (1758-1835)
The work consists of ten books, originally s...
The Nicomachean Ethics (FULL Audio Book)
by Aristotle (384 BCE - 322 BCE)
Translated by Thomas Taylor (1758-1835)
The work consists of ten books, originally separate scrolls, and is understood to be based on notes said to be from his lectures at the Lyceum which were either edited by or dedicated to Aristotle's son, Nicomachus. In many ways this work parallels the similar Eudemian Ethics, which has only eight books, and the two works can be fruitfully compared. Books V, VI, and VII of the Nicomachean Ethics are identical to Books IV, V, and VI of the Eudemian Ethics. Opinions about the relationship between the two works, for example which was written first, and which originally contained the three common books, is divided. Aristotle describes his ethical work as being different from his other kinds of study, because it is not just for the sake of contemplating what things are, but rather to actually become good ourselves. It is therefore practical rather than theoretical in the original Aristotelian senses of these terms. (Summary from Wikipedia)
The Nicomachean Ethics (FULL Audio Book)
by Aristotle (384 BCE - 322 BCE)
Translated by Thomas Taylor (1758-1835)
The work consists of ten books, originally separate scrolls, and is understood to be based on notes said to be from his lectures at the Lyceum which were either edited by or dedicated to Aristotle's son, Nicomachus. In many ways this work parallels the similar Eudemian Ethics, which has only eight books, and the two works can be fruitfully compared. Books V, VI, and VII of the Nicomachean Ethics are identical to Books IV, V, and VI of the Eudemian Ethics. Opinions about the relationship between the two works, for example which was written first, and which originally contained the three common books, is divided. Aristotle describes his ethical work as being different from his other kinds of study, because it is not just for the sake of contemplating what things are, but rather to actually become good ourselves. It is therefore practical rather than theoretical in the original Aristotelian senses of these terms. (Summary from Wikipedia)
Aristotle was the master of virtues.
Enjoying our Youtube videos? Get full access to all our audio content, videos, and thousands of thought-provoking articles, conversation cards and more with The School of Life Subscription: https://t.ly/D71Sz
Be more mindful, present and inspired. Get the best of The School of Life delivered straight to your inbox: https://t.ly/EMeNO
FURTHER READING
“Aristotle was born around 384 BC in the ancient Greek kingdom of Macedonia, where his father was the royal doctor. He grew up to be arguably the most influential philosopher ever, with modest nicknames like ‘the master’, and simply ‘the philosopher’. One of his big jobs was tutoring Alexander the Great, who soon after went out and conquered the known world...”
MORE SCHOOL OF LIFE
Watch more films on PHILOSOPHY in our playlist:
http://bit.ly/TSOLphilosophy
SOCIAL MEDIA
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CREDITS
Produced in collaboration with:
Mad Adam
http://www.madadamfilms.co.uk #TheSchoolOfLife
Source : http://bit.ly/2GPDVzr
The Greek philosopher has made significant discoveries in almost every walk of life. From sciences to subjects like poetry, music, theater, logic, metaphysics, rhetoric, ethics and politics, Aristotle aced it all.
☛ Visit our website : http://Wirally.com
☛ For More Videos Subscribe Our Channel : http://goo.gl/CnuhTj
☛ Background Music : http://www.bensound.com
Here in this video I have described about Aristotle biography for kids Video. I hope you will really like this Aristotle biography for kids Video. He was Born at 384 BC in Stagira, Greece. He is Best known for Student of Plato and teacher of Alexander the Great. Aristotle was an ancient Greek philosopher and scientist born in the city of Stagira, Chalkidiki, Greece. Along with Plato, he is considered the "Father of Western Philosophy". He Died at 322 BC in Euboea, Greece.
Please watch full video for this Aristotle biography for kids Video.
Aristotle: Biography of a Great Thinker Aristotle - Greek Philosopher | Mini Bio | Biography Aristotle Biography in English | Greek philosopher Aristotle: History's Most Influential Thinker The Truth About Aristotle Aristotle Biography in English Aristotle Biography Aristotle Part 1: Introduction (For Political Science Optional in English and English) Aristotle Biography Of a Great Thinker in English
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Jawaharlal Nehru Biography : https://youtu.be/SYS_SgfO7Lo
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Aristotle Biography : https://youtu.be/YTazZMcJU_M
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Alexander Graham Bell Biography : https://youtu.be/aAabNQxbo4U
Albert Einstein Biography : https://youtu.be/7XFZD5frKJc
Adolf Hitlar Biography : https://youtu.be/Ze-Q8Wje2MY
Abraham Lincoln Biography : https://youtu.be/EO6AXx6fXFo #biography, #biographies, #bio, #facts, #famouspeople, #lifestyle, #lifestory, #unknownfacts
The Nicomachean Ethics (FULL Audio Book)
by Aristotle (384 BCE - 322 BCE)
Translated by Thomas Taylor (1758-1835)
The work consists of ten books, originally separate scrolls, and is understood to be based on notes said to be from his lectures at the Lyceum which were either edited by or dedicated to Aristotle's son, Nicomachus. In many ways this work parallels the similar Eudemian Ethics, which has only eight books, and the two works can be fruitfully compared. Books V, VI, and VII of the Nicomachean Ethics are identical to Books IV, V, and VI of the Eudemian Ethics. Opinions about the relationship between the two works, for example which was written first, and which originally contained the three common books, is divided. Aristotle describes his ethical work as being different from his other kinds of study, because it is not just for the sake of contemplating what things are, but rather to actually become good ourselves. It is therefore practical rather than theoretical in the original Aristotelian senses of these terms. (Summary from Wikipedia)
The same equation may be written more compactly using the mathematical notation for summation:
This identity is sometimes called Nicomachus's theorem.
History
Many early mathematicians have studied and provided proofs of Nicomachus's theorem. Stroeker (1995) claims that "every student of number theory surely must have marveled at this miraculous fact". Pengelley (2002) finds references to the identity not only in the works of Nicomachus in what is now Jordan in the first century CE, but also in those of Aryabhata in India in the fifth century, and in those of Al-Karaji circa 1000 in Persia. Bressoud (2004) mentions several additional early mathematical works on this formula, by Alchabitius (tenth century Arabia), Gersonides (circa 1300 France), and Nilakantha Somayaji (circa 1500 India); he reproduces Nilakantha's visual proof.
Numeric values; geometric and probabilistic interpretation