VII. The application of a method of differences to the species of series whose sums are obtained by Mr. Landen, by the Help of impossible quantities

Having some years back, when reading the learned Mr. Landen's fifth Memoir, discovered the manner of applying a method of differences, to the species of series, whose sums are there obtained by the help of impossible quantities, and having since extended that application, I now venture to offer it to the consideration of others. The practice of this method, in most cases, appears to me extremely simple; and on that account, I am almost induced to imagine, that they have already been considered by mathe­maticians; indeed since the greatest part of this Paper was written, I met with Euler's Institutiones Calculi integralis ; two simple series are in that work summed by multiplications similar to those employed in the investigation of the principal theorems contained in this Paper; but whether that learned mathematician has farther pursued the method, in that or in any other work, I have not as yet been able to ascertain.