upturning the principles of science. I must acknowledge I was not a little astonished not to find
him struggling with the quadrature of the circle. This inexplicable hiatus, in the youth of our
associate, has just been filled. A manuscript note from the secretary of the Academy of Lyons
apprises me that, on the 8th of July, 1788, Ampère, then thirteen years of age, addressed to that
learned body a paper relating to the celebrated problem just mentioned. Later during the same year
he submitted to the examination of his compatriots an analogous memoir, entitled “The
rectification of any arc of a circle less than the semi-circumference.” These memoirs have
not reached us. If the manuscript note sent to me can be relied upon, young Ampère, not only did
not think the problem insoluble, but flattered himself he had almost solved it. Scruples, respected
by me without being shared, demanded the sacrifice of this anecdote. It certainly would have been a
very small sacrifice, but I did not consider it consistent with my duty to make it. The scientific
weaknesses of men of a very high order of intellect are lessons quite as useful and profitable as
their successes, and the biographer has no right to cover them with a vail. Is it quite certain,
too, that there is anything here to excuse or conceal; that a geometer need blush for efforts made
in his childhood, or even at a riper age, to square the circle geometrically? To sustain, however,
such a proposition, we have only to recall the fact that antiquity presents to us, as deeply engaged
in this problem, Anaxagoras, Meton, Hippocrates, Archimedes, and Apollonius; and to these we may add
the modern names of Snellius, Huygens, Gregory, Wallis and Newton; and, finally, that amongst those
whose sagacity the quadrature of the circle has set at defiance — I mean who have been involved by
it in palpable errors there are many who have, in other respects, rendered genuine service to
science; for example J. B. Porta, the inventor of the camera-obscura; then Grégoire de Saint
Vincent, the Jesuit, to whom we owe the discovery of the wonderful properties of hyperbolic spaces
terminated by asymptotes; Longomontanus, the astronomer, &c., &c.
If your mind is engrossed with the idea that, in order to justify their efforts to square the
circle, others will cite hereafter, to their advantage, the attempts of a child of thirteen, I reply
unhesitatingly — for my academic duties bring me frequently in and personal relations with the
squarers of the circle — that authorities have absolutely no weight in their eyes; that they have
long since entirely separated themselves from everything that bears or has borne the name of
geometer; that Euclid himself, in his principal theorems — for example, that of the square of the
hypotenuse — seems to them scarcely worthy of trust. If a mania — I was on the point of saying a
furor which manifests itself especially in spring, as proved by experience — could ever be
amenable to logic, it would be necessary, in order to battle it successfully, to distinguish more
carefully than has ever yet been done the various aspects under which the problem of the quadrature
of the circle ought to be considered. An example
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