In [1] Euler derived the formula . He claimed that his formula was better for calculation than the Leibniz–Gregory formula , since for , the factor in the series has values , which are simpler to calculate with. He illustrated this with the formula . He calculated eight terms of the sum for each of the arc tangents on the right to 27 decimal places each and concluded that . On the next page he calculated terms 9–16 of the first part and terms 9–10 of the second part and concluded that . To eighteen places, . To 30 places, .