"The Pythagoreans originated the subject of equivalent areas, the transformation of an area of one form into another of different form and, in particular, the whole method of the application of areas, constituting a geometrical algebra, whereby they affected the equivalent of the algebraic processes of addition, subtraction, multiplication, division, squaring, extraction of the square root, and finally the complete solution of the mixed quadratic equation x^2 \pm px \pm q = 0, so far as its roots are real. Expressed in terms of Euclid, this means the whole content of Book I. 35-48 and Book II. The method of application of areas is one of the most fundamental in the whole of later Greek geometry; its takes place by the side of the powerful method of proportions; moreover, it is the starting point of Apollonius's theory of conics, and the three fundamental terms, parabole, ellipsis, and hyperbole used to describe the three separate problems in 'application' were actually employed by Apollonius to denote the three conics... Nor was the use of geometrical algebra for solving numerical problems unknown to the Pythagoreans..."
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Sir Thomas Little Heath, A History of Greek Mathematics (1921) Vol. 1, From Thales to Euclid.
https://en.wikiquote.org/wiki/History_of_mathematics
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History of mathematics
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