# Multiplication via similar triangles.

- Author:
- Reinhard Schmidt

- Topic:
- Multiplication, Similar Triangles, Triangles

It is well known that the 17th Century mathematician, Rene Descartes, modified Euclid's 12th proposition from Book VI of Elements by assigning a unit to be one of four proportional lines. Before this, the unit was not considered a number as Euclid had defined number as a multitude of units. (Euc. VII Def. 1)
Yet what is almost unknown, is how the 13th Century mathematician, Campanus of Novara, presented a difference construction and proof for (Euc. VI Prop. 12).
Had Descartes seen the construction of Campanus, he might have produced a diagram to explain the multiplication of two line segments (alongside unity) that produce a line segment as the fourth proportional.

**Task 1)**Drag the multiplier upwards to increase it and you will see the product change.

**Task 2)**Drag the multiplicand leftwards to increase it and you will see the product change.

**Task 3)**Drag the multiplier downwards to decrease it and you will see the product change. If you drag the multiplier below where an x axis would be, you can see how a negative multiplier multiplied by a negative multiplicand produces a 'positive' product.