[and] + [be] -- lines and circles
Geometry is based on straight lines and circles. All other shapes are derived from these two building blocks. They are so fundamental that Euclid includes them in three of his five postulates.
Postulate 1: To draw a straight line from any point to any point.
Postulate 2: To produce a finite straight line continuously in a straight line.
Postulate 3: To describe a circle with any center and radius.
Euclid and other ancient Greek mathematicians thought about arithmetic geometrically. Addition is defined as the result of joining two parallel lines together.
__ + ___ = _____
Multiplication is defined as the area between two perpendicular lines.
__ x ___ = |___|
Subtraction and division, as inverse operations, follow naturally from the definitions of addition and multiplication. Thus, all elementary arithmetic can be derived from straight lines.
The uniform curve of circles makes them unsuitable for modeling addition and multiplication. Instead, they form the prototype of all cyclical phenomena, like modular arithmetic and permutations.
However, in Elements II.14 Euclid shows that combining straight lines and circles solves an arithmetic problem of a higher order: finding square roots.