Babylonian Mathematics/Examples

Examples of Babylonian Mathematics

A triangular field is to be divided between $6$ brothers by equidistant lines parallel to one of the sides.

the length of the marked side is $6; 30$

the area of the triangle is $11, 22; 30$.

What is the difference between the brothers' shares?

$\text {(1)}: \quad$

$\ds x y$

$=$

$\ds a$

$\text {(2)}: \quad$

$\ds \dfrac {b x^2} y + \dfrac {c y^2} x + d$

$=$

$\ds 0$

An area $A$, consisting of the sum of $2$ squares, is $1000$.

The side of one square is $10$ less than $\dfrac 2 3$ of the other square.

What are the sides of the squares?

A ladder of length $0; 30$ stands upright against a wall.

The upper end slides down a distance $0; 6$.

How far away will the lower end move out from the wall?

All lengths are expressed in Babylonian form.

Consider a Pythagorean triangle whose hypotenuse and one leg are in the ratio $1.54 : 1$.

What are the lengths of that hypotenuse and that leg?