"Practical, scientific, philosophical & artistic problems have caused men to investigate mathematics. But there is one other motive which is as strong as any of these-the search for beauty. Mathematics is an art, & as such affords the pleasures which all the arts afford."--The Author
Preface
Why mathematics?
A historical orientation
Logic & mathematics
Number: the fundamental concept
Algebra, the higher arithmetic
The nature & uses of Euclidean geometry
Charting the earth & the heavens
The mathematical order of nature
The awakening of Europe
Mathematics & painting in the Renaissance
Projective geometry
Coordinate geometry
The simplest formulas in action
Parametric equations & curvilinear motion
The application of formulas to gravitation
The differential calculus
The integral calculus
Trigonometric functions & oscillatory motion
The trigonometric analysis of musical sounds
Non-Euclidean geometries & their significance
Arithmetics & their algebras
The statistical approach to the social & biological sciences
The theory of probability
The nature & values of mathematics
Table of Trigonometic Ratios
Answers to Selected & Review Exercises
Additional Answers & Solutions
Index