578 POPULAR LECTURES AND ADDRESSES. 



proceeds to apply what he calls his own superior 

 human intelligence to investigation of useless 

 knowledge, and gives results in his Book V., 

 which consists of fifty-five theorems and fifty- 

 seven propositions on the areas of various plane 

 figures having equal circumferences. In this 

 Book, written originally in Greek, we find 

 (Theorem IX. Proposition X.) the expression 

 " isoperimetrical figures," which is, so far as I 

 know, the first use of the adjective " isoperi- 

 metrical " in geometry ; and we may, I believe, 

 justly regard Pappus as the originator, for 

 mathematics, of isoperhnetrical problems, the 

 designation technically given in the nineteenth 

 century L to that large province of mathematical 

 and engineering science in which different figures 

 having equal circumferences, or different paths 

 between two given points, or between some two 

 points on two given curves, or on one given 

 curve, are compared in connection with definite 

 questions of greatest efficiency and smallest cost. 



, Woodhouse's Isopfrimetrical / y n>l>/iniy, Cambridge, 



