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Documents et études > ARAGO, EULOGY ON AMPÈRE., 1872.
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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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