Histoire des recherches sur la quadrature du cercle ... avec une
addition concernant les problemes de la duplication du cube et de la
trisection de l'angle. Paris, 1754, 12mo. [By Montucla.]
This is _the_ history of the subject.[346] It was a little episode to the
great history of mathematics by Montucla, of which the first edition
appeared in 1758. There was much addition at the end of the fourth volume
of the second edition; this is clearly by Montucla, though the bulk of the
volume is put together, with help from Montucla's papers, by Lalande.[347]
There is also a second edition of the history of the quadrature, Paris,
1831, 8vo, edited, I think, by Lacroix; of which it is the great fault that
it makes hardly any use of the additional matter just mentioned.
Montucla is an admirable historian when he is writing from his own direct
knowledge: it is a sad pity that he did not tell us when he was depending
on others. We are not to trust a quarter of his book, and we must read many
other books to know which quarter. The fault is common enough, but
Montucla's good three-quarters is so good that the fault is greater in him
than in most others: I mean the fault of not acknowledging; for an
historian cannot read everything. But it must be said that mankind give
little encouragement to candor on this point. Hallam, in his {160} _History
of Literature_, states with his own usual instinct of honesty every case in
which he depends upon others: Montucla does not. And what is the
consequence?--Montucla is trusted, and believed in, and cried up in the
bulk; while the smallest talker can lament that Hallam should be so unequal
and apt to depend on others, without remembering to mention that Hallam
himself gives the information. As to a universal history of any great
subject being written entirely upon primary knowledge, it is a thing of
which the possibility is not yet proved by an example. Delambre attempted
it with astronomy, and was removed by death before it was finished,[348] to
say nothing of the gaps he left.
Montucla was nothing of a bibliographer, and his descriptions of books in
the first edition were insufficient. The Abbe Rive[349] fell foul of him,
and as the phrase is, gave it him. Montucla took it with great good humor,
tried to mend, and, in his second edition, wished his critic had lived to
see the _vernis de bibliographe_ which he had given himself.
I have seen Montucla set down as an _esprit fort_, more than once: wrongly,
I think. When he mentions Barrow's[350] address to the Almighty, he adds,
"On voit, au reste, par la, que Barrow etoit un pauvre philosophe; car il
croyait en l'immortalite de l'ame, et en une Divinite autre que la nature
{161} universelle."[351] This is irony, not an expression of opinion. In
the book of mathematical recreations which Montucla constructed upon that
of Ozanam,[352] and Ozanam upon that of Van Etten,[353] now best known in
England by Hutton's similar treatment of Montucla, there is an amusing
chapter on the quadrators. Montucla refers to his own anonymous book of
1754 as a curious book published by Jombert.[354] He seems to have been a
little ashamed of writing about circle-squarers: what a slap on the face
for an unborn Budgeteer!
Montucla says, speaking of France, that he finds three notions prevalent
among the cyclometers: (1) that there is a large reward offered for
success; (2) that the longitude problem depends on that success; (3) that
the solution is the great end and object of geometry. The same three {162}
notions are equally prevalent among the same class in England. No reward
has ever been offered by the government of either country. The longitude
problem in no way depends upon perfect solution; existing approximations
are sufficient to a point of accuracy far beyond what can be wanted.[355]
And geometry, content with what exists, has long passed on to other
matters. Sometimes a cyclometer persuades a skipper who has made land in
the wrong place that the astronomers are in fault, for using a wrong
measure of the circle; and the skipper thinks it a very comfortable
solution! And this is the utmost that the problem ever has to do with
longitude.