# 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.

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### 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 ...
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?
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 ...
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 ...
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 $\omega + \phi + \psi = 180^\circ$): ...
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 ...
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 ...
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 ...
116 views

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### 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 ...