Page:Scientific Monthly, volume 14.djvu/304

 our obstruse problem. Seldom has a subtle abstract question found such striking concrete illustration. In the fore-ground are three bearded men in old-time garb. One of them with staff in hand has just drawn upon the ground, a circle and an equivalent triangle. On the right, the sphere and the cube suggest among other things the accomplished cubature of the sphere. As if these two drawings were not sufficient reference to the solution of the great problem, there is shown also the transmutation of the square and circle into each other by the solar beam of light passing through the square opening in a board and forming upon the ground below, a circular illuminated area. Mutat quadrata rotundis. One of the cherubs indicates by a pair of compasses that the figure is a circle. Another gives vivid evidence of surprise and delight. We omit descriptions of the twisted and fluted columns and other details, and only point out the challenge which this engraving makes to modern pedagogues, to equal or surpass, if they can, this powerful appeal to the eye.

Recently the present writer experienced a surprise by the discovery that this same title-page (with only very slight changes in unimportant details) was appropriated sixty years later in an edition of the collected works of another noted Jesuit mathematician, Andreas Tacquet. This edition appeared at Antwerp in 1707, some years after the death of Tacquet. Hence this "bor rowing" was done by the editors and publishers. Evidently the novelty and impressiveness of the picture appealed to them so strongly that they used it in Tacquet's works even though this mathematician is not associated with the problem of squaring the circle. Tacquet is known chiefly as a teacher and as the editor of an edition of Euclid which was translated into English and used in Great Britain as a school book for the larger part of a century. The title-page of the 1707 publication represents therefore the transfer of a fanciful portal originally opening into the mystic realm of transcendental mathematics, to a well-trodden avenue leading to elementary schools.