Good "history of mathematical ideas" book?

John Stillwell's Mathematics and Its History is a terrific book for precisely this purpose. See my Amazon review.

I have also written some free history of mathematics course materials myself in a similar spirit.

Try these books by Morris Kline:

• Mathematical Thought from Ancient to Modern Times

• Mathematics: A Cultural Approach

I have taught history of mathematics using the text

Mathematical Expeditions - Chronicles by the Explorers , Reinhard Laubenbacher and David Pengelley, Springer, 1999, ISBN 978-0-387-98433-9 (softcover). (http://www.springer.com/us/book/9780387984346).

Each chapter traces an idea through time with well chosen excerpts from the original literature.

You can see the philosophy (and some sample free reads) here: https://www.math.nmsu.edu/~history/