# ^^Geometrical algebra di Euclide.

Il libro2 di Euclide, dai commentatori viene titolato (dato che Euclide non
da' titolo ai libri)

- Fundamentals of Geometric Algebra (Richard Fitzpatrick)
- Geometric algebra (David E.
Joyce)
- Geometrical algebra (Heath)

Def2 gnomone

pag379 def2 Book2

## Intro

the Pythagoreans and later Greek mathematicians exhibited different kinds of
numbers as forming different geometrical figures.

Thus, says Theon of Smyrna (p. 36, 6—11), "plane numbers, triangular, square
and solid numbers, and the rest, are not so called independently but in virtue
of their similarity to the areas which they measure;

- 4, since it measures a square area, is called square by adaptation from
it
- 6 is called oblong for the same reason."
- "plane number" is similarly described as a number obtained by
multiplying two numbers together, which two numbers are sometimes spoken of
as "sides," sometimes as the "length" and "breadth" respectively, of the
number which is their product.

The product of two numbers was thus represented geometrically by the
rectangle contained by the straight lines representing the two numbers
respectively.

It only needed the discovery of incommensurable or irrational straight lines
in order to represent geometrically by a rectangle the product of any two
quantities whatever, rational or irrational; and it was possible to advance from
a geometrical arithmetic to a geometrical algebra, which indeed by Euclid's time
(and probably long before) had reached such a stage of development that it could
solve the same problems as our algebra so far as they do not involve the
manipulation of expressions of a degree higher than the second.

pag381 Heath vol1

## Links

- Numeri figurati;
triangolari, rettangolari, quadrati. Storia.
- Numeri greci.