Geometry Versus Algebra. Ancient Greek and Western Mathematics: Parallel or Intersecting Options by the Greek Scholars of the 18th Century?

Dr. Maria Terdimou
Mathematician, PhD in Philosophy

During the long - lasting scientific decline following the fall of the Byzantine empire, use of Mathematics was restricted to the daily needs only.
However, the revival of the scientific and philosophical thinking during the I8tn century, strengthened the role of Mathematics, which acquired a dominant position. Arithmetic and Euclidean Geometry, i.e. the ancient Greek mathematics, reigned supreme. The faith in the latter's ever lasting value was proclaimed in every opportunity.
The majority of the Greek Scholars belonging to this line of thought lived and taught before the so called period of Neo-Hellenic Enlightenment. Being, most of them church men were characterized by a traditional view of Science. Thus, it is to be expected for them to insist on the classical Euclidean geometry, a subject well known which offers the certainty of a solid and final knowledge; in contrast, Algebra, i.e. the more recent Mathematics, looked by its very nature, more abstract and, hence, more uncertain,
The first elements of Algebra appeared in manuscripts of the period 1750- 1775, but, Algebra was not included in the mathematics textbooks, neither in mathematics treatises. This means that the first attempts to introduce Algebra in the mathematical curriculum were not fully successful. The basic reason for this hesitancy was the difference between the algebraic and the arithmetic/ geometric way of thinking.
However, in spite of this uncertain start, the first seeds had been already planted, and, as a result, several algebraic textbooks were published in the decades to come. Thus, by the end of the 18tn century Algebra was included in the mathematics curricula on equal footing with Arithmetic and Geometry.