An interesting idea for a book, but it doesn't quite come off. The author, a professor of mathematics at the University of Minnesota, has assembled a series of chapters on some ""greats""--e.g., Durer, Leonardo, Vitruvius--concentrating on what they did or did not know about geometric constructions and how they applied their knowledge in their work. He discusses how laws of perspective were developed in the Renaissance and provides an exegesis on Euclid (the Optics as well as the Elements of Geometry). In the latter half of the book are more technical chapters on analytic and projective geometry, on curves (including some of the more aesthetically pleasing spirals, hypocycloids, and the like), on solids, and on the nature of space. The style is earnest and texty, more in the English tradition (the author was born in London) of a lecture than an entertainment. Reader is invited to do the exercises at the end of each chapter--proofs or constructions--as well as to follow the many rigorous geometric proofs given throughout the book. Students of art or architecture might find it of interest to skim the sections on aesthetics and traditions as exemplified in historical writings, but it is unlikely that any but the most dedicated math students will sit still to follow the demonstrations in the text much less get out their rulers and compasses to do the problems.