The Geometry of the Epeira's Web 



own, is defective, will allow her. One would 

 believe her to be thoroughly versed in the laws 

 of the spiral. 



I will continue to set forth, without ex- 

 planations, some of the properties of this 

 curious curve. Picture a flexible thread wound 

 round a logarithmic spiral. If we then un- 

 wind it, keeping it taut the while, its free 

 extremity will describe a spiral similar at all 

 points to the original. The curve will merely 

 have changed places. 



Jacques Bernouilli, 1 to whom geometry 

 owes this magnificent theorem, had engraved 

 on his tomb, as one of his proudest titles to 

 fame, the generating spiral and its double, 

 begotten of the unwinding of the thread. 

 An inscription proclaimed, 'Eadem mutata 

 resurgo: I rise again like unto myself.' 

 Geometry would find it difficult to better this 

 splendid flight of fancy towards the great 

 problem of the hereafter. 



There is another geometrical epitaph no 

 less famous. Cicero, when quaestor in Sicily, 



'Jacques Bernouilli (1654-1705), professor of mathe- 

 matics at the University of Basel from 1687 to the year 

 of his death. He improved the differential calculus, 

 solved the isoperimetrical problem and discovered the 

 properties of the logarithmic spiral. Translator's Note. 



387 



