Lectures on Quaternions (Google eBook)

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1853 - Quaternions - 736 pages
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Page 33 - Ba, as being in all cases constructed by the line BC. drawn to the middle point C of the line Aa: which would again agree with many modern systems. Thus Wallis seems to have possessed, in 1685, at least in germ (for I do not pretend that he fully and consciously possessed them), some elements of the modern methods of Addition and Subtraction of directed lines. But on the equally essential point of Multiplication of directed lines in one plane, it does not appear that Wallis, any more than Buee (see...
Page 30 - I thus perceived to exist, in that very general theory, deterred me from pursuing it farther at the time above referred to. |36| There was, however, a motive which induced me then to attach a special importance to the consideration of triplets, as distinguished from those more general sets, of which some account has been given. This was the desire to connect, in some new and useful (or at least interesting) way, calculation with geometry, through some undiscovered extension, to space of three dimensions,...
Page 13 - Perhaps I ought to apologize for having thus ventured here to reproduce (although only historically . . . ) a view so little supported by scientific authority. I am very willing to believe that (though not unused to calculation) I may have habitually attended too little to the symbolical character of Algebra, as a Language, or organized system of signs: and too much (in proportion) to what I have been accustomed to consider its scientific character, as a Doctrine analogous to Geometry, through the...
Page 1 - Reason," which appeared to justify the expectation that it should be possible to construct a priori a science of time as well as a science of space. The principal passage is as follows: " Time and space are two sources of knowledge from which various a priori synthetical cognitions can be derived. Of this pure mathematics gives a splendid example in the case of our cognitions of space and its various relations. As...
Page 13 - Graves. |19| After remarking that it was he who had proposed those names, of orders and ranks of logarithms, that early Essay of my own, of which a very abridged (although perhaps tedious) account has thus been given, continued and concluded as follows: But because Mr. GRAVES employed, in his reasoning, the usual principles respecting Imaginary Quantities, and was content to prove the symbolical necessity without shewing...
Page 1 - It early appeared to me that these ends might be attained by our consenting to regard algebra as being no mere art, nor language, nor primarily a science of quantity ; but rather as the science of order in progression. It was, however, a part of this conception, that the progression here spoken of was understood to be continuous and unidimensional ; extending indefinitely forward and backward, but not in any lateral direction. And although the successive states of such a progression might, no doubt,...
Page 1 - ... regard algebra as being no mere art, nor language, nor primarily a science of quantity ; but rather as the science of order in progression. It was, however, a part of this conception, that the progression here spoken of was understood to be continuous and unidimensional ; extending indefinitely forward and backward, but not in any lateral direction. And although the successive states of such a progression might, no doubt, be represented by points upon a line, yet I thought that their simple successiveness...
Page 32 - ABu} is equal to the Double of AC. So that, whereas in case of Negative Roots, we are to say, The Point B cannot be found, so as is supposed in AC Forward, but Backward from A it may in the same Line: We must here say, in case of a Negative Square, the Point B cannot be found so as was supposed, in the Line AC; but Above that Line it may in the same Plain. This I have the more largely insisted...
Page 61 - Nothwithstanding these, and perhaps some other coincidences of view, Prof. Grassmann's system and mine appear to be perfectly distinct and independent of each other, in their conceptions, methods, and results. At least, that the profound and philosophical author of the Ausdehnungslehre was not, at the time of its publication, in possession of the theory of the quaternions, which had in the preceding year (1843) been applied by me as a sort of organ or calculus for spherical trigonometry , seems clear...
Page 540 - C + sin B sin C cos a. Similarly cos B = - cos C cos A + sin C sin A cos b, and cos C = cos A cos B + sin A sin B cos c.

References from web pages

Free Books > Science > Mathematics > Applied > General > Lectures ...
Free Books > Science > Mathematics > Applied > General > Lectures On Quaternions
2020ok.com/ books/ 3/ lectures-on-quaternions-19003.htm

The Online Books Page: Lectures on Quaternions, by William Rowan ...

onlinebooks.library.upenn.edu/ webbin/ book/ lookupid?key=olbp18698

Biography of Hamilton
Picture of Hamilton. Table of Contents:. Introduction; Biography; Contributions to Mathematics; Quaternions; Bibliography ...
www.andrews.edu/ ~calkins/ math/ biograph/ biohamil.htm

Tutorial, Electric Geometry - Nabla Del Hamilton
NOTES & REFERENCES:. 1. wr Hamilton's 1843 paper - "On a new species of Imaginary Quantities connected with the Theory of Quaternions" [communicated ...
www.hypercomplex.com/ education/ intro_tutorial/ nablan1.html

Historia Matematica Mailing List Archive: Re: [HM] nabla origin
Subject: Re: [HM] nabla origin From: David Wilkins (dwilkins@maths.tcd.ie) Date: Mon Apr 10 2000 - 19:07:43 EDT. Next message: Peter Flor: "Re: [HM] ...
sunsite.utk.edu/ math_archives/ .http/ hypermail/ historia/ apr00/ 0058.html

Sir William Rowan Hamilton: Bibliography by rp Graves
List of Papers, Memoirs, Addresses, and Books published by Sir William Rowan Hamilton, and of Notices of Communications. Robert Perceval Graves ...
www.maths.tcd.ie/ pub/ HistMath/ People/ Hamilton/ GBiblio/ GBiblio.html

William Rowan Hamilton: Biography and Much More from Answers.com
Sir William Rowan Hamilton Irish mathematician (18051865) Hamilton was a child prodigy , and not just in mathematics; he also managed to learn an
www.answers.com/ topic/ william-rowan-hamilton

Topological phase in classical mechanics
Topological phase in classical mechanics. Grigorii B Malykin et al 2003 Phys.-Usp. 46 957-965 doi:10.1070/pu2003v046n09abeh001635 ...
www.iop.org/ EJ/ abstract/ 1063-7869/ 46/ 9/ A04

JSTOR: Estimate of Peirce's Linear Associative Algebra
Estimate of Peirce's Linear Associative Algebra. he Hawkes. American Journal of Mathematics, Vol. 24, No. 1, 87-95. Jan., 1902. ...
links.jstor.org/ sici?sici=0002-9327(190201)24%3A1%3C87%3AEOPLAA%3E2.0.CO%3B2-3

Quaternions - lovetoknow 1911
From lovetoknow 1911. QUATERNIONS, in mathematics. The word "quaternion " properly means " a set of four." In employing such a word to denote a new ...
www.1911encyclopedia.org/ Quaternions

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