Chapter A.6, Problem 147AYU

To determine

To find: The word quadratic seems to imply four (quad), yet a quadratic equation is an equation that involves a polynomial of degree 2. Investigate the origin of the term quadratic as it is used in the expression quadratic equation. Write a brief essay on your findings.

Answer to Problem 147AYU

To the best of our knowledge the origin of the term “quadratic” is Latin. It is derived from quadratus which is the past participle of quadrare which means “to make square.” From this it is clear that part of the word is connected to the Latin word for “four,” though not a way which one might expect: it refers to squaring, and a square is a regular four-sided figure.

Al-Khwarizmi gives the rule for solving each type of equation, essentially the familiar quadratic formula given for a numerical example in each case, and then a proof for each example which is a geometrical completing the square.

Abraham bar Hiyya Ha–Nasi, often known by the Latin name Savasorda, is famed for his book Liber embadorum published in 1145 which is the first book published in Europe to give the complete solution of the quadratic equation.

Explanation of Solution

To the best of our knowledge the origin of the term “quadratic” is Latin. It is derived from quadratus which is the past participle of quadrare which means “to make square.” From this it is clear that part of the word is connected to the Latin word for “four,” though not a way which one might expect: it refers to squaring, and a square is a regular four-sided figure.

Al-Khwarizmi gives the rule for solving each type of equation, essentially the familiar quadratic formula given for a numerical example in each case, and then a proof for each example which is a geometrical completing the square.

Abraham bar Hiyya Ha-Nasi, often known by the Latin name Savasorda, is famed for his book Liber embadorum published in 1145 which is the first book published in Europe to give the complete solution of the quadratic equation.