Multiplication via similar triangles.
- Reinhard Schmidt
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.