Theoretic Arithmetic, in Three Books; Containing the Substance of All That Has Been Written on This Subject by Theo of Smyrna, Nicomachus, Iamblichus

Theoretic Arithmetic, in Three Books; Containing the Substance of All That Has Been Written on This Subject by Theo of Smyrna, Nicomachus, Iamblichus
Author: Anonymous
Publisher: Theclassics.Us
Total Pages: 80
Release: 2013-09
Genre:
ISBN: 9781230334950

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1816 edition. Excerpt: ... CHAPTER IV. On the duad. TtfE duad was called by the Pythagoreans, as we learn from? Nicomachus, " audacity, matter, the cause of dissimilitude, and the interval between multitude and the monad. This alone produces equality from composition and mixture, on which account also it is equal. But it is likewise unequal, defect, and abundance, and is alone unfigured, indefinite, and infinite- It is also alone the principle and cause of the even; yet is neither evenly-even, nor unevenly-even, nor evenly-odd* But many of these things are proximate to the physical peculiarity of the duad* It is likewise the fountain of all symphony, and among the Muses is Erato. It is also harmony, patience, and a root, though not in a certain respect in energy. It is power too, the feet of Ida abounding with fountains, a summit and Phases. It is also Justice, and Isis, Nature and Rhea, the mother of Jupiter, and the fountain of distribution. It was likewise called by them Phrygia, Lydia, Dindymene, Ceres, and Eleu* sinia, Diana and Cupid, Dictynua, Aeria, Asteria, Disamos, and Esto. Also Venus, Dione, Mychaea, Cytherei, ignorance DEGREES ignobility, falsehood, difference, indistihction, strife, dissension, Fate and Death." Prior, however, to a developerftent of these appellations, it will be requisite to observe concerning the duad, that the Pythagoreans, before they evinced that multitude subsists iu intelligibles, necessarily investigated the cause of the multitude which is there, and found that among the genera of being it is difference) which subsists according to non-being; but that in causes most eminently the first, it is the indefinite duad, which, -r-v- 1 says Syrianus, Pythagoras m the Sacred Discourse calls Chaos, and which he associates with intellect; for...

Number Theory

Number Theory
Author: George E. Andrews
Publisher: Courier Corporation
Total Pages: 292
Release: 2012-04-30
Genre: Mathematics
ISBN: 0486135101

Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.

Excursions in Number Theory

Excursions in Number Theory
Author: Charles Stanley Ogilvy
Publisher: Courier Corporation
Total Pages: 196
Release: 1988-01-01
Genre: Mathematics
ISBN: 9780486257785

Challenging, accessible mathematical adventures involving prime numbers, number patterns, irrationals and iterations, calculating prodigies, and more. No special training is needed, just high school mathematics and an inquisitive mind. "A splendidly written, well selected and presented collection. I recommend the book unreservedly to all readers." — Martin Gardner.

Theoretic Arithmetic

Theoretic Arithmetic
Author: Thomas Taylor
Publisher:
Total Pages: 286
Release: 2015-10-12
Genre:
ISBN: 9781517773014

Theoretic arithmetic, in three books: containing the substance of all that has been written on this subject by Theo of Smyrna, Nicomachus, Iamblichus, and Boetius, together with some remarkable particulars respecting perfect, amicable, and other numbers, which are not to be found in the writings of any ancient or modern mathematicians. Likewise, a specimen of the manner in which the Pythagoreans philosophized about numbers, and a development of their mystical and theological arithmetic.

Graph Theoretic Methods in Multiagent Networks

Graph Theoretic Methods in Multiagent Networks
Author: Mehran Mesbahi
Publisher: Princeton University Press
Total Pages: 424
Release: 2010-07-01
Genre: Mathematics
ISBN: 1400835356

This accessible book provides an introduction to the analysis and design of dynamic multiagent networks. Such networks are of great interest in a wide range of areas in science and engineering, including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum networks, networked economics, biological synchronization, and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, the book presents a powerful new formalism and set of tools for networked systems. The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications. The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications. This book has been adopted as a textbook at the following universities: ? University of Stuttgart, Germany Royal Institute of Technology, Sweden Johannes Kepler University, Austria Georgia Tech, USA University of Washington, USA Ohio University, USA