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In a letter to Stirling, dated July 27, 1738, Euler mentions having happened on the infinite product, “satis notatu dignam,” the numerators being the odd primes in their natural order, the denominators the multiples of 4 nearest to those primes. He says he can prove that the limit of this product is His proof was probably as follows:
Let O be the centre of the circumscribing circle of ΔABC, A1 the middle point of BC, and EA1OF the diameter at right angles to BC. Draw AX perpendicular to BC and produce it to meet the circle in K. Let H be the orthocentre of ΔABC; join OH and bisect it in N, the centre of the nine-point circle.