382

MISCELLANEOUS

TRACT 58.

editor arrived at the question above referred to, he copiedmy solution, and very inconsistently ascribed it to Mr.Hawncy before mentioned, though it was manifest to everygeometrician that no two constructions could be more unlikeone another, as the one employed seven different circles,and as many separate constructions, in effecting what theother accomplished by only one single circle and construc-tion. Prom the many gross errors, and the numerousomissions and absurdities in that ‘ Repository of Errors,’as it was commonly called, it soon fell under the necessityof coming to a sudden and premature end.

With respect to the other curious and kindred problem,that of dividing a given circle into any number of parts, thatmay be all mutually equal, both in area and perimeter, someaccount of its rise has been already given in the first volumeof these tracts, at pa. 254. It was first anonymously pro-posed in the year 1774, as a curious paradoxical problem,but unaccompanied by the least hint or intimation of anymode of solution whatever. It was indeed announced b} 5-the proposer expressly as a seeming paradox, but accom-panied with the declaration that it nevertheless was capableof a strict geometrical solution. The problem remainedhowever some time unanswered, being given up by all per-sons as a matter quite hopeless, and by most deemed in fact aslittle to be expected as the quadrature of the circle itself, towhich it was thought to be nearly allied, and indeed depen-dent on it; for no person could imagine any other possibleway of a circle being divided, even in idea, into any numberof such parts, that might be equal both in area and perime-ter, than by radii drawn from the centre to the points ofequal divisions in the circumference. This was, in effect,reducing the problem to this other, of dividing the circum-ference in any proposed number of equal parts, which wasdeemed on all hands a thing impossible to be effected. Aftersome time no person thought any more of the matter, but asa thing never to be accomplished; and so I believe it mighthave remained to this day, but for the occurrence of some