I read the Beginnings of Western Sceince as a student at the University of Wisconsin-Madison where I had the extreme priviledge of taking two history of science courses from the author, who is also an absolutely outstanding professor. (And also one of the two or three most knowledgeable people in the world in the history of medieval science) This is by far the most comprehensive text on the history of ancient and medieval science that is out there. You might not believe it, but there aren't even a lot of other texts that cover half of what is discussed here period, let alone any that are this polished and concise. This book not only covers the development of western science from ancient times throught the Middle Ages, but it also considers the religious, and philosophical roots of this development. This book is masterfully written in that it provides a tremendous amount of detail, and yet is accessible to anyone that is an educated and interested reader. I cannot recommend this text highly enough.

Also Recommended: The Structure of Scientific Revolutions by Thomas Kuhn

In his book The Structure of Scientific Revolutions, Thomas Kuhn discusses the importance of history and its relationship to science, the changing views of how historians view past scientific achievements, the role of scientific method in science, and the nature and foundations of scientific revolutions.

I had to read this book because I'm currently taking a history of science class taught by the author at the University of Wisconsin, Madison, and I just want to say it's excellent. It is clear, concise and (best of all from a student's point of view) not boring. It teaches you so much about looking at things in context. This is a great book from a great professor.

I have read many, many histories of science, but this is far and away the best I have read.