No one ever squared the circle with so much genius, or, excepting his principal object, with so much success.
Attributed to Montucla in Augustus De Morgan, A Budget of Paradoxes, (London, 1872), p. 96; Cited in: Robert Edouard Moritz. Memorabilia mathematica; or, The philomath's quotation-book, (1914) p. 366
About Gregory St. Vincent, described by De Morgan as "the greatest of circle-squarers, and his investigations led him into many truths: he found the property of the arc of the hyperbola which led to Napier's logarithms being called hyperbolic."
Preface to Recreations in Mathematics and Natural Philosophy. (1803)
Mathematics and philosophy are cultivated by two different classes of men: some make them an object of pursuit, either in consequence of their situation, or through a desire to render themselves illustrious, by extending their limits; while others pursue them for mere amusement, or by a natural taste which inclines them to that branch of knowledge. It is for the latter class of mathematicians and philosophers that this work is chiefly intended j and yet, at the same time, we entertain a hope that some parts of it will prove interesting to the former. In a word, it may serve to stimulate the ardour of those who begin to study these sciences; and it is for this reason that in most elementary books the authors endeavour to simplify the questions designed for exercising beginners, by proposing them in a less abstract manner than is employed in the pure mathematics, and so as to interest and excite the reader's curiosity. Thus, for example, if it were proposed simply to divide a triangle into three, four, or five equal parts, by lines drawn from a determinate point within it, in this form the problem could be interesting to none but those really possessed of a taste for geometry. But if, instead of proposing it in this abstract manner, we should say: "A father on his death-bed bequeathed to his three sons a triangular field, to be equally divided among them: and as there is a well in the field, which must be common to the three co-heirs, and from which the lines of division must necessarily proceed, how is the field to be divided so as to fulfill the intention of the testator?" This way of stating it will, no doubt, create a desire in most minds to discover the method of solving the problem; and however little taste people may possess for real science, they will be tempted to try iheir ingenuity in finding the answer to such a question at this.
There is reason, however, to think that the author would have rendered it much more interesting, and have carried it to si higher degree of perfection, had he lived in an age more enlightened and better informed in regard to the mathematics and natural philosophy. Since the death of that mathematician, indeed, the arts and sciences have been so much improved, that what in his time might have been entitled to the character of mediocrity, would not at present be supportable. How many new discoveries in every part of philosophy? How many new phenomena observed, some of which have even given birth to the most fertile branches of the sciences? We shall mention only electricity, an inexhaustible source of profound reflection, and of experiments highly amusing. Chemistry also is a science, the most common and slightest principles of which were quite unknown to Ozanam. In short, we need not hesitate to pronounce that Ozanam's work contains a multitude of subjects treated of with an air of credulity, and so much prolixity, that it appears as if the author, or rather his continuators, had no other object in view than that of multiplying the volumes.
To render this work, then, more worthy of the enlightened agt in which we live, it was necessary to make numerous corrections and considerable additions. A task which we have endeavoured to discharge with all diligence
John Stephen Montucla, member of the National Institute, and of the academy of Berlin, censor royal for mathematical books, and author of this new-modelled and enlarged edition of the Mathematical Recreations of Ozanam, was born at Lyons, the 5th of September 1725. His father was a banker, by whom he was intended for the same profession; but the science of calculations, to which he was early introduced, soon produced a discovery of the natural bent of his mind. In the Jesuits college at Lyons he laid a good foundation in the ancient languages, as well as in the mathematical sciences, which enabled him afterwards easily to acquire a competent acquaintance with the Italian, the German, die Dutch, and the English, .which he not only read, but also spoke very well.
In the qualities of his heart too Montucla was truly estimable: remarkably modest in his manner and deportment; benevolent far beyond the means of his small fortune: of a very respectable personal appearance; he spoke with ease and precision, but unassuming and with simplicity; related anecdotes and stories in a pleasant and playful manner; and breathing, in all his conduct and deportment the sweetness of virtue, and the delicacy of a fine taste.
Montucla says, speaking of France, that he finds three notions prevalent among 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 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 hi no way depends upon perfect solution; existing approximations are sufficient to a point of accuracy far beyond what can be wanted. 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 at 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 has to do with longitude.