276 François charette
demonstrations: ‘look at the fi gure’ he says, allowing nothing but illustrative
demon strations [ Anschauungsbeweise ], whereas he could not have any feeling for
the impressive but oft en awkward eff orts of a Euclid or an Archimedes to really
impose on reluctant [readers] the conviction of the validity of a theorem. 3
Günther’s judgement is obviously more respectful and nuanced than that of
Biot. I shall analyse the genealogy of the ideas expressed by Günther in the
second half of this chapter.
First it is necessary to proceed towards the source of Europe’s knowledge
of Indian mathematics. Th e eff orts of Strachey (1813) and Taylor (1816)
for making Bhāskara’s mathematical works available in English translation
were very soon rendered obsolete by Colebrooke’s authoritative anno-
tated translation of the mathematical parts of the works of Bhāskara and
Brahmagupta in 1817. Th e same year, the Scottish mathematician John
Playfair (1748–1819), who had been noted for his interest in the history
of Indian astronomy, contributed an essay–review of Colebrooke to the
Edinburgh Review. Playfair noted the absence of demonstrations in the
Lilavati and the Bīja-Gan. ita , but acknowledged that Bhāskara’s fi ft eenth-
and sixteenth-century commentators, such as Ganeśa, supplied demonstra-
tions of the rules in several instances. He had to concede, however, that
those occasional demonstrations were ‘oft en obscure, from the want of
reference to a fi gure; for, though the fi gure be constructed on the margin,
there is no reference to it by letters’. 4 A ft er having presented a survey of the
most important results achieved by Bhāskara, Playfair made the following
observation:
But in the midst of these curious results, there is a subject of regret that almost
continually presents itself. When such rules are laid down as the preceding, they are
usually given without any analysis whatever, and even without any synthetic dem-
onstration, so that the means by which the knowledge was obtained, remains quite
unknown... In consequence of this, a mystery still hangs over the mathematical3 ‘Und doch ist diese Mathematik von so auszeichnender Eigenart, daß die Beschäft igung mit
ihr den höchsten Reiz gewähren muß. Insonderheit fesselt den Beschauer der grundsätzliche
Gegensatz zwischen indischer und griechischer Denk- und Betrachtungsweise. Der Grieche
ist – und die wenigen Ausnahmen bestätigen nur die Regel – strenger Synthetiker, der auf
rigorose Beweisführung das größte Gewicht legt und so durchaus in räumlichen Vorstellungen
lebt, daß er selbst arithmetische Dinge fast ausschließlich in ein geometrisches Gewand zu
kleiden bestrebt ist. Umgekehrt liegt dem für alles Rechnerische ausnehmend befähigten
Inder sehr wenig an der Demonstration; “siehe die Figur” sagt er und läßt keine anderen
als Anschauungsbeweise zu, während er für die imponierenden, aber oft unbehilfl ichen
Anstrengungen eines Euclides und Archimedes, die Überzeugung von der Richtigkeit eines
Satzes förmlich einem Widerstrebenden aufzuzwingen, gar keinen Sinn haben konnte.’
Günther 1908 : 178.
4 Playfair 1817 : 158.