Th e logical Greek versus the imaginative Oriental 277
knowledge of the East; and it is much to be feared that the means of removing it no
longer exist. 5
Playfair regretted the absence of demonstrations, because he mainly
expected them to illuminate the mechanisms of mathematical discovery
among ancient authors.
His interest in the innate heuristic patterns of mathematical creation
thus stands in remarkable contrast to the usual strict concern for results ,
which is characteristic of most nineteenth-century writings on history
of mathematics (however naive it might be to hope that demonstrations
would necessarily provide clues for understanding the underlying patterns
of discovery).
Concerning a particular geometrical theorem, he further remarks that it
‘is demonstrated in a very ingenious and palpable manner, not altogether
according to the rigour of the Greek geometry, but abundantly satisfactory
to those who are pleased with an argument when it is sound, though it be
not dressed in the costume of science’. 6 Another proof he sees as revealing
‘ingenious and simple’ reasoning that must stem from ‘a system of geo-
metrical demonstration that was not very refi ned, or very scrupulous about
introducing mechanical considerations’. 7 But even in those cases when dem-
onstration was wanting, Playfair nevertheless believed that there existed an
original procedure of demonstration, no longer extant. 8 In passing we must
note the belief expressed by Playfair that science, as for every other civiliza-
tional aspect of India, was ‘immoveable’ and deprived of progress.
Th ree comparative views on Greek and Oriental mathematics:
Hankel, Cantor and Zeuthen
I now come to the major part of my inquiry, in which I off er a detailed anal-
ysis of the comparative views of three eminent historians of mathematics,
Hankel, Cantor and Zeuthen, on Greek versus ‘Oriental’ (Indian, Chinese,
Islamic) mathematics.
5 Playfair 1817 : 151.
6 Playfair 1817 : 159–60.
7 Playfair 1817 : 160.
8 See on p. 159 the remarks on the theorem that in a circumscribed [this condition is not
specifi ed in the Sanskrit text] quadrilateral with sides a , b , c , d and diagonals g , h we have
ac + bd = gh , a theorem ‘by no means very easy to be demonstrated’ and which ‘argues for a very
extensive knowledge of elementary trigonometry, and such as is by no means easily acquired’.