CHAPTER 419 THE GEOMETRY OF THREE DIMENSIONS Bonaventura Cavalieri (1598–1647) was a follower of Galileo and a mathematician best known for his work on areas and volumes. In this aspect, he proved to be a forerunner of the development of integral cal- culus. His name is associated with Cavalieri’s Principle which is a fundamental principle for the determination of the volume of a solid. Cavalieri’s Principle can be stated as follows: Given two geometric solids and a plane, if every plane parallel to the given plane that intersects both solids intersects them in surfaces of equal areas, then the volumes of the two solids are equal. This means that two solids have equal volume when their corresponding cross-sections are in all cases equal. 11 CHAPTER T ABLE OF CONTENTS 11-1 Points, Lines, and Planes 11-2 Perpendicular Lines and Planes 11-3 Parallel Lines and Planes 11-4 Surface Area of a Prism 11-5 Volume of a Prism 11-6 Pyramids 11-7 Cylinders 11-8 Cones 11-9 Spheres Chapter Summary Vocabulary Review Exercises Cumulative Review
