## A DOUBLE DISCOVERY THE SQUARE OF THE CIRCLE |

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amount ancient appearance approximate Archimedes area obtained beginning centre century circumference combined Computing contains corner crossing decimals definite demonstrated denominator DIAGRAM diameter diamond discovered discovery divide dotted lines double drawing drawn earth Egyptians equal Euclid's extending figures five five-pointed star five-square fold four four lines fraction fundamental geometry give given half important inch in area kingdom known larger largest length less lines intersect longer longest line mathematical mathematicians measurements mixed number multiply nature newly noted oblong square pertaining points present principle problem produced published recorded reduced relative representing result rounded rule searched seen sense seven short shown side smaller smallest circle solution solved space Spiritual square inch square root squares of circles squaring the circle straight lines tained taken takes thirteen tion tire triangle twice universe whole numbers

### Popular passages

Page 30 - He telleth the number of the stars; He calleth them all by their names.

Page 22 - The eye is the first circle; the horizon which it forms is the second; and throughout nature this primary figure is repeated without end. It is the highest emblem in the cipher of the world.

Page 27 - ... wheel is larger than the wheel. Whatever name is applied to the line of the circle, the mathematical principle is a line that is necessarily conceived to be a line without thickness, or an imaginary line. His result was like that of the ancients, being another one of the very near approximations in figures applied in this case, but not absolute.

Page 27 - Of other Americans who have given their attention to the problem of squaring the circle, there was one who published a book in 1851, in which it was disclosed that the side of a square being 5153, the sum of the length of the four sides is 20612 ; and the diameter of a circle being 6561, the length of the circle is...

Page 17 - It is well known that in this nineteenth century of discoveries many things have been accomplished that were formerly supposed to be impossible, and for this reason it would be generally conceded that the solution of this problem being possible, it was desirable that it should have been accomplished before the closing of the present century.