Archimedes, most noted for his theory regarding the displacement of a liquid by a solid, was not only a prominent physicist but also mathematician. One if the disciplines he explored was geometry. He presented his findings differently from Euclid, showing the methodology he used to derive his theorems. His contributions include results on areas and volumes.

The Islamic mathematicians also worked on geometry. The earliest Arabic geometry is the work of al-Khwarizmi. He had realised the formulas for computation of area and circumference of circles, and had approximated p to be 22/7. Later Islamic authors were influenced by the Greeks. Ibn al-Haytham attempted to reformulate Euclid's theory of parallel. The parallel postulate problem was attempted without success.

Euclid's Elements also reached Europe and made an impact there. Abraham bar Hiyya gave geometric proofs of algebraic methods. He also proved the relationship A = Cd / 4 (refer the first article), using infinitesimals. Trigonometry was introduced into geometric calculations. Leonardo of Pisa, noted for his Fibionacci sequence, also contributed to the abovementioned developments; among which was the calculation of areas of segments and sectors of a circle.

Further work on geometry was done in the eighteenth century. By this time, geometry has been connected to algebra and calculus (further explanation of this point will be in our next section, Analytic Geometry). Alexis Clairant believed that measurement of fields was the beginning of geometry, and was thus able to define geometric terms. He expanded on the ideas in Euclid's work and tried to cover up the loopholes. Other mathematicians also worked on the parallel postulate problem.