THE MATHEMATICAL REPOSITORY. CONTAINING Analytical Solutions OF NEAR Five Hundred Questions, MOSTLY SELECTED FROM SCARCE and VALUABLE AUTHORS. DESIGNED As Examples to MAC-LAURI N's and other. AND To conduct BEGINNERS to the more difficult Properties of Numbers. LONDON, Printed for J. NOURSE, in the Strand, MDCCLXXV. T is not a new cuftom for authors to de I' dicate their mathematical works, to gentlemen who are the moft illuftrious ornaments of mathematical fciences; and as the learned world have long fince thought it justice to rank You among that number, it will, I hope, fufficiently apologize for this address, which I flatter myfelf you will favourably receive, on account of the likelihood there is, that these sheets will prove beneficial to students. BESIDES the help that your celebrated works in general have afforded me, the appendix to your Mifcellanea Analytica has furnished me with the method of approximating the fums of fuch feries as are the reciprocals of the powers of arithmetical progreffions. ; this M. James Bernoulli could not fum the feries of the reciprocals of fquare numbers *; was discovered by M. John Bernoulli, who, on that occafion, expreffes a fingular fatisfaction, but confeffes his inability to fum the feries of the reciprocals of cube numbers: The fum of both thefe feries, and many others, naturally flow from an approximation you have given to fum the feries++, &c. ad infinitum; and although you well knew that the defiderata of Meffrs Bernoulli were included therein, yet you waved, not only the applica tion, but the affumption of the honour thereof. THIS, Sir, as it fufficiently fhews the mo deft opinion you have of your own excellent performances, fo it gives me this opportunity of declaring to the public, that I think myself fingularly happy in being permitted to fubfcribe myself, Sir, Your moft obliged, And most humble Servant, JAMES DODSON. See his WORKS, Vol. I. Page 398. + See bis WORKS, Vol. IV. Page 20, &c. |