(III.) Again in (I.) transposing a x (bc) to the other side and squaring, we obtain 2(ac) (bc)axbx = (bc) 2 a'+(ac) 2 bx- (ab) 2 c1.
Dinostratus, a Greek geometer and disciple of Plato, discussed the curve, and showed how it effected a mechanical solution of squaring the circle.
It became known as the "Delian problem" or the "problem of the duplication of the cube," and ranks in historical importance with the problems of "trisecting an angle" and "squaring the circle."
The Pythagorean discovery of "squaring a square," i.e.
The history of these attempts, together with modern contributions to our knowledge of the value and nature of the number 7r, is given below (Squaring of the Circle).
(C. E.*) Squaring of the Circle.
The problem of finding a square equal in area to a given circle, like all problems, may be increased in difficulty by the imposition of restrictions; consequently under the designation there may be embraced quite a variety of geometrical problems. It has to be noted, however, that, when the " squaring " of the circle is especially spoken of, it is almost always tacitly assumed that the restrictions are those of the Euclidean geometry.
In a small commonplace book, bearing on the seventh page the date of January 1663/1664, there are several articles on angular sections, and the squaring of curves and " crooked lines that may be squared," several calculations about musical notes, geometrical propositions from Francis Vieta and Frans van Schooten, annotations out of Wallis's Arithmetic of Infinities, together with observations on refraction, on the grinding of " spherical optic glasses," on the errors of lenses and the method of rectifying them, and on the extraction of all kinds of roots, particularly those " in affected powers."