608 PROFESSOR D'ARCY WENTWORTH THOMPSON ON 



2. The contractions appended to the symbol in the inflected cases correspond with 



the declension of the noun. 



3. As we commonly find for Swa/nts and kv{3os not merely the initial letter, but rather 



<5 U , k v , so we find, instead of our ?', at times ? '. I do not know how far, in 

 the age and domicile of Diophantus, we might or might not reasonably 

 expect to find a confusion in manuscript between o and w ; but in this 

 particular instance the relation between o-wp6$ and aopos may atone for any 

 palseographic difficulty. 



4. The ordinary meaning of o-wpog is in a fair degree akin to the sense required. 



5. The same symbol ?' occurs several times in MSS. of the Arenarius of Archimedes 



(vide Heiberg, Archimedis Opera Omnia, vol. ii. p. 268), where it has 

 hitherto been rendered by upiB/xog, and it seems to me that there also we 

 derive advantage by a substitution of the new reading. 



If we be induced by these considerations to accept the rendering a-wpo?, we are next 

 led on to a point of very great interest, and of much value in authenticating the 

 hypothesis. For we learn that to the Egyptian mathematician Ahmes, the symbol and 

 name for the unknown quantity was hau, a heap, 2000 years before Diophantus ; and 

 we may place this coincidence alongside the information that is growing in our hands 

 as to the connection of the arithmetic or algebra of Diophantus with Egyptian sources. 

 Certain it is, as Bonnycastle * long ago remarked, "that Diophantus was not the 

 inventor of algebra, as has been generally imagined . . . since he nowhere treats of 

 the first principles and leading rules of the science, as a writer in the infancy of the art 

 would have done ; but proceeds, at once, to the resolution of a particular class of 

 indeterminate problems . . . which even at present are generally considered as forming 

 one of the most difficult branches of pure analysis." 



Dr Gow and others have surmised that Heron was an Egyptian, just as a generation 

 ago De Morgan suspected that Diophantus was not a Greek. " Such evidence as this," 

 says Dr Gow,t after a compendious comparison of the methods of Heron and of Ahmes, 

 " goes a long way to confirm the suspicions not only that Heron was an Egyptian, but 

 also that algebra was an Egyptian art, and that the symbolism of Diophantus was of 

 Egyptian origin." 



And, in regard to the Egyptian sources of his knowledge, not very long ago, in the 

 Wissensch. Beilage d. Leipzig er Zeitung, April 27, 1895, Dr Hultsch said briefly, but 

 explicitly, "Nur beiliiufig konnte darauf hingewiesen werden, dass die Diophantischen 

 Aufgaben nichts Anderes als eine, allerdings vervollkommnete Nachbildung agyptischer 

 Aufgaben der verhaltnissmcissigen Theilung sind. Charakteristisch fiir die agyptische 

 Logistik ist die vollstandige Beherrschung und geschickteste Verwendung der Einheits- 

 schlusses." And Hultsch further remarks, in a letter communicated to me by Dr Gow, 



* Treatise on Algebra, London, 8vo, 2 vols., 1820; vol. i. pt. i. p. 225. This writer's interesting 

 and sympathetic account of the Diophantine analysis is not alluded to by Heath. 

 t Hist, of Math., p. 286. 



