1850 RARE SQUARING THE CIRCLE

ANCIENT MATHEMATICAL PUZZLE

GEOMETRICAL SOLUTIONS OF THE QUADRATURE OF THE CIRCLE. By Peter Fleming, Civil Engineer. Montreal: Printed for the Author, 1850. First Edition. Original green cloth (12.75 x 8 inches), printed paper cover label, 10 pages and 6 folding plates, pp. [viii], 10, [6(double leaves of folding plates)]. Text prints the Geometric Solutions of the Quadrature of the Circle in Lemmas, and Nine Solutions with Propositions & Theorems. The text is followed by the six numbered plates of geometric diagrams, each plate has: “Geo. Quad. of the Cir. Pub. by P. Fleming. March 1850” printed at lower right. Preface by Peter Fleming dated 1850, page [v] prints a list of Subscribers' Names and the number of copies for each subscriber- totaling 82 copies. Binding is quite worn (disbound), spine perished, both covers, some plates and text detached or partially detached, several long tears, thin chipping, etc.; text complete and sound. A genuinely rare 19th century mathematical monograph on the ancient problem of squaring the circle, which was ultimately proven impossible in 1882 as a consequence of the Lindemann–Weierstrass theorem which proves that pi (π) is a transcendental, rather than an algebraic irrational number. It had been known for decades that the construction would be impossible if π were transcendental, but π was not proven transcendental until 1882. Approximate squaring to any given non-perfect accuracy, in contrast, is possible in a finite number of steps, since there are rational numbers arbitrarily close to π. The expression "squaring the circle" is sometimes used as a metaphor for trying to do the impossible. OCLC locates only 2 institutional holdings: National Library of Scotland and University College London. Currently absent from the trade and recent auction records.

Peter Fleming, a Civil Engineer, was also the author of other books on land surveying.