Cavalieri

Pillars of Cavalieri's Contributions

Cavalieri's Theorems

If two solids have equal altitudes, and if sections made by planes parallel to the bases and at equal distances from the bases always have a given ratio, then volumes of the solids have the same ratio to each other.

The volumes of the two prisms are the same.
If two planar pieces are included between a pair of parallel lines, and if the lengths of the two segments cut by them in any line parallel to the including lines are always in a given ratio, then the areas of the two planar pieces are also in this ratio.

Today, mathematicians accept Cavalieri's work as being a major stepping stone to the concept of infinitesimals thereby opening the door for the calculus. Galileo himself wrote , "few, if any, since Archimedes, have delved as far and as deep into the science of geometry."