Elements of Algebra (Google eBook)

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Longman, Orme, 1822 - Algebra - 593 pages
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MBA 502

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A genius book. This old textbook truly depicts Leonhard Euler's genius. Too bad Euler's Identity was not mentioned in here!

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Contents


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Page 153 - Three, then, is based on the principle, that the product of the extremes is equal to the product of the means...
Page 33 - Multiply the numerator of the dividend by the denominator of the divisor, and the denominator of the dividend by the numerator of the divisor ; the first product "will be the numerator of the quotient, and the second wiU be its denominator.
Page 205 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Page 139 - One hundred stones being placed on the ground in a straight line, at the distance of 2 yards from each other, how far will a person travel who shall bring them one by one to a basket, placed at 2 yards from the first stone ? Ans.
Page 205 - A privateer running at the rate of 10 miles an hour discovers a ship 18 miles off making way at the rate of 8 miles an hour : how many miles can the ship run before being overtaken ? 56.
Page 206 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take, to catch the hare?
Page 4 - The manner in which we generally calculate a person's property, is a good illustration of what has just been said. We denote what a man really possesses by positive numbers, using, or understanding the sign + ; whereas his debts are represented by negative numbers, or by using the sign — Thus, when it is said of any one that he has 100 crowns, but owes 50, this means that his property really amounts to 100 — 50 ; or, which is the same thing, + 100 — 50, that is to say 50.
Page 254 - The coefficient pt of the fourth term with its sign changed is equal to the sum of the products of the roots taken three by three ; and so on, the signs of the...
Page 223 - The general rule, therefore, which we deduce from this, in order to resolve the equation xx = — px + g, is founded on this consideration : That the unknown quantity x is equal to half the coefficient, or multiplier of x on the other side of the equation, plus or minus the square root of the square of this number, and the known quantity which forms the third term of the equation.
Page 26 - mb 90. In order therefore to reduce a given fraction to its least terms, it is required to find a number by which both the numerator and denominator may be divided. Such a number is called a common divisor, and so long as we can find a common divisor to the numerator and the denominator, it is certain that the fraction may be reduced to a lower form ; but, on the contrary, when we see that except unity no other common divisor can be found, this shews that the fraction is already in the simplest...

References from web pages

Euler's Elements of Algebra
His Elements of Algebra is one of the first books to set out algebra in the modern form we would recognize today. However, it is sufficiently different from ...
web.mat.bham.ac.uk/ C.J.Sangwin/ euler/ index.html

Elements of Algebra - Wikipedia, the free encyclopedia
Elements of Algebra is a mathematics textbook by mathematician Leonhard Euler, originally published circa 1765. His Elements of Algebra is one of the first ...
en.wikipedia.org/ wiki/ Elements_of_Algebra

First Section. Euler’s work organized chronologically by date of ...
First Section. Euler’s work organized chronologically by date of publication. 1726. E1 Constructio linearum isochronarum in medio quocunque resistente, ...
www.math.dartmouth.edu/ ~euler/ docs/ translations/ enestrom/ Enestrom_Index.pdf

A tale of two curricula: Euler's algebra text book
In particular it is about one of his books, Elements of Algebra [4 - read a review in this issue of Plus]. This mathematician was Leonhard Euler and his ...
plus.maths.org/ issue45/ features/ sangwin/ index.html

Saunderson biography
As soon as his health had recovered, he began to put in long hours working on the Elements of Algebra. In 1739, with his book close to completion, ...
www-groups.dcs.st-and.ac.uk/ ~history/ Biographies/ Saunderson.html

Elements of Algebra - shopwiki
Elements of Algebra: huge selection from the most online retailers offering the best prices, shipping to you. Reviews and product ratings.
www.shopwiki.com/ search/ Elements+of+Algebra

Euler's work in Number Theory
Euler later proved this for n=3 in his Elements of Algebra, see the attached .... Euler, Leonhard, Elements of Algebra, Dover Publications, New York, 1956. ...
www.math.rutgers.edu/ ~cherlin/ History/ Papers2000/ dunkelman.html

Convergence | Alien Encounters
Nicholas Saunderson, The Elements of Algebra (Cambridge, 1741); ... Leonhard Euler, Elements of Algebra , 1770, extract from the English (4th) edition of ...
mathdl.maa.org/ convergence/ 1/ ?pa=content& sa=viewDocument& nodeId=435& bodyId=461

JSTOR: Polygonal Roots
This article was inspired by Euler's Elements of Algebra, Section IV, Chap. 7. Note that for the sake of variety of expression here the words polygonal and ...
links.jstor.org/ sici?sici=0049-4925(197911)10%3A5%3C313%3APR%3E2.0.CO%3B2-%23

1 Background 2 Geometry
They are Elements of Algebra [2] and Introduction to .... Euler, Elements of Algebra, Springer-Verlag, Reprint of London: Longman, Ormew, ...
mathcircle.berkeley.edu/ BMC6/ ps/ Euler.pdf

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