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Introduction to Arithmetic by Nicomachus of Gerasa. Get A Copy. Textbook Binding , pages. Published February 1st by Johnson Reprint Corp. More Details Original Title. Other Editions 2. Friend Reviews. To see what your friends thought of this book, please sign up. To ask other readers questions about Introduction to Arithmetic , please sign up. Be the first to ask a question about Introduction to Arithmetic. Lists with This Book. Community Reviews. Showing Average rating 3. Rating details. More filters.
Sort order. Start your review of Introduction to Arithmetic. Dec 13, Roy Lotz rated it liked it Shelves: math , oldie-but-goodie. One would naturally think, judging from the title of this work, that this is a manual of addition, subtraction, multiplication, and so on. But it is nothing of the sort. Nicomachus was a Neopythagorean philosopher, influenced by both Plato and Aristotle, who considered numbers to be the basis of reality.
The result is rather strange for modern readers. Nicomachus goes through what, to us, appear to be basic and trivial aspects of number—even, odd, square, cubed, etc.
The result is uninspiring, since nowadays we are not likely to think that different sorts of ratios or number sequences have any intrinsic interest. Further, Nicomachus includes no proofs, and instead illustrates every one of his mathematical idea with a simple example, which renders the work of little value to mathematics. It is as a window into history, then, that I think the work has the most interest.
For example, the very fact that it was copied and preserved through the Middle Ages demonstrates the appeal this mathematical mysticism had for Christians. We can also see how abstract mathematical concepts could be turned into moral ones.
Even so, I think even the most generous reading of this work will find much of it to consist of uninteresting classifications of different sorts of numbers. Luckily, it is quite short. View all 3 comments. Sep 24, Evan Leach added it Shelves: , mathematics. This book is a textbook on mathematics from around the year It was not renowned for its originality - rather, the book was famous in antiquity and in the middle ages for being a useful primer covering the mathematical knowledge of its time.
I am no mathlete, and I'll admit some of the esoteric concepts and convoluted proofs that Nicomachus throws out there made my eyes glaze over. For me, the more interesting aspects of this book concerned Nicomachus' philosophy.
Nicomachus was a Neo-Pythago This book is a textbook on mathematics from around the year Nicomachus was a Neo-Pythagorean who embraced a mystical, symbolism-heavy view of numbers and mathematics. Most of his thoughts about philosophy are outside the scope of this book, but the Introduction will occasionally allude to them.
Nicomachus subscribed to the Platonic idea of eternal forms, with the wrinkle that numbers are a superior kind of form out of which the other forms are made and under which they are classified.
Numbers are the highest forms and the properties seen primarily in them are also the essential properties of things in the world, conferred upon them by number. This philosophy led its practitioners to search for all kinds of meaning in numbers. They believed that through mathematical proofs, they could uncover universal "truths" - the number seven was associated with the leader of the universe, odd numbers were considered male and even numbers female, etc.
This attitude towards mathematics persisted for centuries, at least among certain factions, but frankly it is hard for me to really grasp the rationale behind it.
To modern minds, all of the time and energy spent on "proving" these mystical numerological proofs seems pointless. This book gave me a little bit of insight into how Nicomachus and the thinkers who followed in his footsteps thought about numbers, which was interesting at times. But I have no idea who I would recommend this to, other than specialists interested in the history of mathematics and even then, this probably takes a distant backseat to Euclid.
I don't know how to even begin to rate this one, so I'm just going to give it a pass. A strange little book that opens a window onto an even stranger way of viewing the universe. View 2 comments. Mar 04, Tyler rated it it was amazing. This book was not particularly difficult, but it was just All of the different properties of numbers and even some of how they apply to music were expounded in this fine piece of Greek literature.
If you are interested even remotely in the mystical, Pythagorean properties of numbers, or even a little bit in just arithmetic in general, then this book is definitely for you. As opposed to its name 'Introduction to Arithmetic', you don't really read this if you're Fascinating. You would read this after you've read Timaeus by Plato. It's THAT kind of book. I honestly suggest you do, too, considering this book references Plato constantly.
It's also nice to be familiar with a few Euclidean definitions. Overall, beautifully done work of art. The whole book ends with four numbers perfectly exemplifying the Arithmetic, Geometric, and Harmonic ratios: 6, 8, 9, Very well done, nice work of genius right here.
May 18, JP rated it really liked it. He flourished around a. Much of the focus is on the various categories -- odd, even, perfect, superlative, deficient, prime, etc. There are quite a few orders found within a variety of series. All of this tied back to philosophy as the early mathematicians made so many connections. Perhaps not since that time has anyone thought in such away about multiple-dimensions and dualism. May 19, Michael rated it liked it.
Not at all what one might expect, but reading it one can easily see how the Ancients attributed all the mystical properties to numbers. The correspondences are amazing. How numbers are the building blocks of everything. Sort of the creation's alphabet. A difficult read, because of my own unwillingness to put in the requisite attention.
Feb 16, Claire rated it liked it Shelves: non-fiction , great-book-of-the-western-world. Surprisingly, I sort of enjoyed this book - at least some of it. Mathematics is a kind of elegant unifying idea, despite my inability to grasp it. Glad I read it! Jan 09, Arkar Kyaw rated it really liked it.
For the eye of the soul, blinded and buried by other pursuits, is rekindled and aroused again by these and these alone, and it is better that this be saved than thousands of bodily eyes, for by it alone is the truth of the universe beheld. Aug 10, Mikelis Igovens rated it it was amazing.
Great stuff. Reading for the first time, I grasped the overview of the ideas, and I very liked the philosophy. Definitely will need to read for the second time to get into details, and maybe even third and the fourth time Maths never was so exciting as for the ancient Greeks
Nicomachus of Gerasa
The work contains both philosophical prose and basic mathematical ideas. Nicomachus refers to Plato quite often, and writes that philosophy can only be possible if one knows enough about mathematics. Nicomachus also describes how natural numbers and basic mathematical ideas are eternal and unchanging, and in an abstract realm. It consists of two books, twenty-three and twenty-nine chapters, respectively. Although he was preceded by the Babylonians and the Chinese ,  Nicomachus provided one of the earliest Greco-Roman multiplication tables , whereas the oldest extant Greek multiplication table is found on a wax tablet dated to the 1st century AD now found in the British Museum. From Wikipedia, the free encyclopedia.
NICOMACHUS: Introduction to Arithmetic
View one larger picture. Biography Nicomachus of Gerasa is mentioned in a small number of sources and we can date him fairly accurately from the information given. Nicomachus himself refers to Thrasyllus who died in 36 AD so this gives lower limits on his dates. On the other hand Apuleius , the Platonic philosopher, rhetorician and author whose dates are AD to about AD, translated Nicomachus's Introduction to Arithmetic into Latin so this gives an upper limit on his dates. One of the most interesting references is by Lucian , the rhetorician, pamphleteer and satirist who was born about AD, who makes one of his characters say:- You calculate like Nicomachus.
Introduction to Arithmetic