Smith, David Eugene, 1860-1944 · Boston, New York [etc.] Ginn and Company · leaf 340
Marcel-lus carried out the wishes of Archimedes with respect tothe figures on his tomb. The volume of a sphere can also be very elegantlyfound by means of a proposition known as CavalierisTheorem. This asserts that if two solids lie betweenparallel planes, and are such that the two sections madeby… … are equal sections made by a plane parallel to MN,then the solids have the same volume. The proof is sim-ple, since prismsof the same alti-tude, say --> and non the basest and Sf are equivalent, and the sums of n such prisms are the given solids; m and as n increases, the sums of the prisms…
Geometry
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