## 1545 – Ars Magna

Ars Magna (The Great Art) published in 1545 by Girolamo Cardano, included techniques for solving cubic (to the third power) and quartic (to the fourth power) equations. The solution for cubic equations was developed by Scipione del Ferro, then passed on to a student who provoked Niccolo Fontana (aka Tartaglia) to also develop the solution. Tartaglia then shared it with Cardano who eventually published it.

Cardano’s student, Ludovico Ferrari, discovered a formula for solving fourth degree equations, which was also published in Ars Magna.

Cubic equations had actually been previously solved by Omar Khayyam using geometrical techniques, but it was del Ferro who first produced an algebraic formula for their solution.

PREREQUISITE:

**Timeline of Trigonometry** – general knowledge of cubic equations, provided by ancient Indians, Greeks and Egyptians

1048 – **Omar Khayyam**’s geometrical solution to cubic equations

**1501 – Cardano**

SUBSEQUENT:

1673 – **Leibniz** created the first algebraic proof of the cubic equation

1799 – **Ruffini** claimed that quintic (fifth degree) equations could not be solved algebraically and introduced the idea of groups of permutations.

1824 – **Abel** developed a proof that quintic equations could not be solved.

1831- **Galois** discovered that algebraic solutions of equations are related to groups of permutations.