Pre-Calculus – A Classical Approach

This high school text employs ideas discovered by classical mathematicians to consider topic in pre-calculus. The Real and Complex number systems are developed using the vector model and ideas originating in Descartes’ geometry. Trigonometry is considered using ideas from Ptolemy and Copernicus. The properties of the conic sections are proven using theorems from Apollonius. Tangent functions for each of the conic sections are discovered as precursors to the derivative. Archimedes’ quadrature of the parabola is studied as a precursor to the integral. Binomial expansion theorem and the various summation formulas are discovered for future work on the derivative and integral. The text includes explanations and problem sets.