In his Principia, Book I Section 1 Lemma 5 Newton states, “In similar figures, all sorts of homologous sides, whether curvilinear or rectilinear, are proportional; and the areas are in the duplicate ratio of the homologous sides.” He gives no proof nor any comment. Of course, it is almost trivially obvious for figures such as triangles and circles, yet to assert it of all continuous figures seems worthy of at least a brief note. I find the perversity and cantankerousness of the man who would commit this omission kind of pretty.
Serena Williams’ hand reaches for the ball as she gets ready and serve to China’s Shuai Zhang, during their match at the Italian open tennis tournament in Rome, Friday, May 16, 2014. (AP Photo/Gregorio Borgia)