This problem still engages attention : and persons aro found to believe that they have attained even the arithmetical quadrature. And it is a peculiarity of this well-worn old problem, that it catches the fancy of those who have not even attended to common geometry, and frequently makes them think that the riddle is reserved for them to read. And the reason is, that they treat it as a riddle : a thing to be thought out by some sudden stroke of mother-wit. They do not know that there are thousands of problems of the same kind in every thing but notoriety. Thirty years ago, when the Penny Magazine' was young, it contained an article on this subject which might have been thought sufficient at least to establish the fact of a difficulty. A man of high rank and great wealth, who had probably never opened a book of geometry since his school days, if even then, happened to read this article, was caught, and in five minutes produced an idea which he thought so likely to be the solution of the enigma, as he would have it to be, that he forwarded it to the secretary of the Useful Knowledge Society, for transmission to the author of the article.
It has been stated in foreign newspapers within these few years that the British government does offer, and always has offered, a large reward for the solution of this problem. This, we need hardly say, is a complete mistake : the government never at any time offered one farthing for the quadrature of the circle. Some years ago, a labouring man from the country came to town with a quadrature, and addressed a letter to the Lord Chancellor, stating his claim, and desiring his lord ship to hand over forthwith 100,000G, being the sum due from govern ment for the discovery, as per proclamation : this letter we saw. The only problem for the solution of which any reward was at any time offered, was the practical mode of finding longitude : and even this offer is now retracted ; rewards having been, in fact, received by several persons. Should this article fall into the hands of any, at home or abroad, who are working at any mathematical or astronomical difficulty under the impression that our government is pledged to remunerate them in case of success, they may rest assured that their information is incorrect, and that they will find it to be so on inquiry. The only person we know of who states definitely what the reward is, and by whom offered, is Nicolas Ericitie, in a tract on the quadrature " Funda mentalis figura geometriea ....” Copenhagen, 1755. The author states, as known to all, that on the 2nd of June, 1747, the Royal Society of London publicly advertised a reward of for the quadrature of the circle and the discovery of the true nature of the magnet, over and above some previously offered sum, the amount of which is not stated.
It is needless to say that the archives of the Royal Society contain no account of any offer of the kind.
Persons who are not acquainted with the subject are puzzled by one consideration, which we admit is calculated to have weight. The quadrators appeal to great discoveries which have at last been recog nised, though their promulgators were at first treated with contempt. We pass over the last part of the assertion with the remark that Copernicus, Galileo, Tycho Brah6, Harvey, &c., were never treated with contempt : some were opposed, some were persecuted, and all were ridiculed by a section of their opponents; for ridicule is a con stituent of all opposition whatsoever, though not from every opponent.
But those with whom Copernicus, &e, came in contact, whether in person or in hook, showed amply that they knew what manner of men they had to deal with. The more important point is the following.
Invention in mechanics may have been sometimes attained—not very often—by men who were ignorant of the doings of their predecessors.
But discovery in matters of speculation—that is, conquest over old and tried difficulties—has never, that we have read Of, been reached by any one whose mind had not been trained by study of previous speculation.
All the men we have mentioned, and all of their stamp that we know of, were learned men, acquainted with the history of the subject they were destined to advance, and practised in its methods : they had all shown their power over what was known, before they presented them selves as the promulgators of what was not. The squarer of the circle, therefore, may be asked to show proof of his acquaintance with the previous history of the subject : any one who really does this would, even now, meet with some attention. But the general run of circle squarers arc as ignorant of the past as the future will be of them.
.Again, we have to meet the very plausible objection, that many difficulties have been overcome at last : why not then the quadrature of the circle ? The answer is easy. The difficulties which have been overcome at last have been overcome by the discovery of new means, and the introduction of new powers ; but our problem is to square the circle with the old allowance of means: Euclid's postulates and nothing more. We cannot remember an instance in which a question to be solved by a definite method was tried for centuries by the best heads, and answered at last, 6y that method, after thousands of complete failures.