Th e logical Greek versus the imaginative Oriental 285
the Indologist Edward Strachey (1813, 1818) who fi rst positively formu-
lated the thesis that Hindu algebra had infl uenced Diophantus, a conten-
tion repeated, albeit in a much more nuanced fashion, by Colebrooke. 37
Th e case of Hero of Alexandria – with his imaginative and practical
problem-solving approach without emphasis on demonstrations – was less
problematic.^38 Cantor had argued for Old Egyptian infl uence, a hypothesis
- already insinuated by Hankel 39 – that nobody took the trouble to chal-
lenge. 40 In any case, there was a certain uneasiness in interpreting Hero and
Diophantus. Th e reason for our excursus is connected with the following: if
Greek mathematics can be essentially opposed to an Oriental style, how can
it be that two important Greek authors are basically ‘oriental’ in style? Th is
observation could not really undermine the main thesis: both authors were
simply given a status of exceptions...
Excursus 2: Cantor on inductive demonstrations in Ancient Egypt
A similar pattern is discernible in Cantor’s speculations about the geo-
metrical knowledge supposedly acquired by Th ales in Ancient Egypt,
and the peculiar deductive shaping he, as a Greek, immediately conferred
on the primitive rules and demonstrations of the Egyptians. Cantor had
collaborated with Eisenlohr in his eff orts to decipher the Rhind Papyrus,
a translation of which was published in Leipzig in 1877.
In the geometrical problems of Ahmes, formulae are given as such,
without derivation. But we are dealing with a book of exercises, Cantor
says, so we should not ask for something which cannot be contained in
it, namely derivations ( Ableitungsverfahren ) of the formulae. Ahmes must
have taken these derivations from another, now lost, theoretical textbook. 41
Th is hypothetical ‘theoretical’ textbook on geometry Cantor imagines to
have contained primitive inductive demonstrations or even illustrative
demonstrations ( Beweisführung durch Anschauung ), as with the Indians. 42
But to assume strict geometrical demonstrations is not necessary in the
context of Egyptian mathematics. 43
37 C1817.
38 Günther 1908 : 217.
39 Hankel 1874 : 85. Hankel, who only had access to a summary description of the Rhind Papyrus
by Birch (1868), recognized the similarities with Hero but was not sure whether the papyrus
was older than the Alexandrian’s lifetime or not.
40 Cantor 1894 : 365–7.
41 Cantor 1894 : 53; 1907 : 91, 113.
42 Cantor 1907 : 113.
43 Cantor 1907 : 106.