Questions tagged [elementary-algebra]

Elementary algebra, also called algebra precalculus, is the mathematical field studying basic properties of linear, exponential, logarithmic, polynomial, rational, and trigonometric functions, graphs, and the solving of equations and systems of equations.

Filter by
Sorted by
Tagged with
1
vote
0answers
58 views

Were ancients really so bad at computations before Arab numerals?

It is often said that Romans (see below) had a terrible number system, which made a computations a mess. I do believe this, but I'm really suspicious of the claim that nobody had better ways to do ...
2
votes
1answer
227 views

How did Ruffini discover his method of polynomial division?

How did Ruffini discover his method of polynomial division? At that time was it known that polynomial division works similar to integer division?
3
votes
1answer
114 views

When were polynomial equations first factored?

The question pretty much says it all, though I have a specific example in mind. In the mid-1500s while working on his Ars Magna Cardano asked Tartaglia to solve the cubic $x^3=9x+10$. Using ...
6
votes
1answer
184 views

Etymology of Some Terms Used in Ratio and Proportion in Old Algebra Textbooks

In older algebra textbooks for high school (mainly 19th century) four properties of ratio and proportions were used. The properties were Invertendo, Alternendo, Componendo, and Dividendo. This ...
4
votes
1answer
198 views

Do these trigonometric identities belong to Antonio Cagnoli?

I'm new to this stack community, please bear with me as I try to explain my question properly. Recently I came across with these trigonometric identities (where $ \omega + \phi + \psi = 180^\circ $): ...
1
vote
0answers
61 views

How was invented quadratic equation? [duplicate]

How actually people invented the quadratic equation? What practical problem did they solve? There are some info about this exist in internet, but it is very abstract - I cant find the concrete task ...
8
votes
2answers
661 views

How was the sum of squares formula discovered by Archimedes?

AFAIK, Archimedes is credited with discovering the following formula for computing the sum of squares: $1^2 + 2^2 + 3^2+...+n^2 = \frac{n(n+1)(2n+1)}{6}$ This seems to have come up in his quest for ...
3
votes
1answer
87 views

Where can I find the list of problems from the (Chinese) “Nine Chapters on Mathematical Art”?

For the sake of curiosity, I'm interested in the "list of problems" that were laid out in the ancient Chinese text on Math. However, I haven't found a "list" in English anywhere. Only a few excerpts ...
3
votes
1answer
116 views

When was the idea of exponents generalized from “repeated multiplication”?

Recently I became curious about when the following ideas came about, and I couldn't really find information about them with some google searches. $a^0 = 1$ $a^{\frac pq} = \sqrt [q] {2^p}$ $a^{-x} =...
1
vote
2answers
139 views

Why $x_a$ (or $x_o$) and not $a_x$? (conventions for algebraic quantities)

It's my understanding that the convention of using letters from the end of the alphabet ($x$, $y$, $z$) to represent $variables$, and letters from the start of the alphabet ($a$, $b$, $c$) to ...
4
votes
1answer
263 views

Who first introduced the longhand square-rooting method into European mathematics?

A previous question credits François Viète with introducing the well-known longhand method for the computation of square roots in digit-by-digit manner. This method is related to the binomial theorem. ...
1
vote
1answer
615 views

History of elementary proof of Fermat's last theorem for $x^3 + y^3 = z^3 $ [closed]

What was the historical back ground that probably Fermat’s could had known about a much simpler proof than the first (Euler’s elementary proof of Fermat’s last theorem for $n = 3$), at least for the ...
1
vote
1answer
403 views

Who was the first to show that this quintic equation has five radical roots?

Despite it being a very trivial question, I would like to know who was the first (with reference evidence) to show that the following quintic equation has five radical roots: $$x^5 + x + 1 = 0$$
11
votes
1answer
1k views

The origin of quadratic equation in actual practice

I read that in ancient times the quadratic equation of this kind $$x^2+10x=39$$ had been solved long ago. I read that this kind of equation originated in the geometric question of "Given an area of 39,...
2
votes
3answers
145 views

Exploring problems about quadratic function (in one variable) across the ages

I'm looking for problems about quadratic function across the ages. For example, in the Babylonian civilization, there are problems which are related with quadratic equation. Besides that, the concept ...
5
votes
0answers
95 views

How were the phenomena relating to symmetric polynomials discovered?

The "fundamental theorem of symmetric polynomials" states that any symmetric polynomial can be expressed as a polynomial in the elementary symmetric polynomials. This, or at least variants on it or ...
16
votes
2answers
782 views

Was 18th century algebra more symbolic/formal than the modern conception?

I've found Lagrange's Sur la résolution des équations algébriques to be a very confusing and difficult read, and I think I'm starting to see why: it seems that Lagrange thinks of algebra in a much ...
11
votes
1answer
2k views

Does anyone know about Ramanujan's method of solving the quartic?

I have read (probably) in Kanigel's book The Man Who Knew Infinity that S. Ramanujan devised his own method of solving the Quartic Equation after he learnt to solve the Cubic Equation. Does anyone ...
4
votes
2answers
225 views

Why does the “Principle Of Permanence” have two different definitions?

This question is a sub-question of previous question on MSE. I feel that on this website I have better chances of knowing more things. For quite some time now, I have been searching about the "...
12
votes
1answer
879 views

Was the “polynomial remainder theorem” known before polynomial long division was discovered?

Nowadays we can easily prove the following fact using polynomial long division: If $a$ is a root of the polynomial $f$, then there exists a polynomial $g$ such that $f(x) = (x - a)g(x)$. I can't ...
12
votes
1answer
402 views

What does Lagrange mean in this passage from Reflexions sur la résolution?

I'm having difficulty with section 6 of Lagrange's Réfléxions sur la résolution algébrique des équations. That's page 11 of the paper, 215 of his Oeuvres. Annoyingly, this is one of the most critical ...
16
votes
1answer
772 views

When was the method of getting square roots (invented by Viète in 1610 and developed by Harriot in 1631) first taught to school children?

François Viète's On the Numerical Resolution of Powers by Exegetics published in 1610 (Viete, 2006, pp. 311-370) introduced one way of numerically solving polynomial equations, a special case of which ...
20
votes
3answers
1k views

What mathematical developments/discoveries caused imaginary numbers to gain acceptance at the time (18th century) they did?

In a Wiki article on imaginary numbers it was asserted that "the use of imaginary numbers was not widely accepted until the work of Leonhard Euler (1707–1783) and Carl Friedrich Gauss (1777–1855)." ...