Excerpts on the Euler-Maclaurin summation formula, from

tion and exercises may be provided at this site at a later time. The only commentary that remains here summarizes some of those portions of Chapters 5 and 6 that were not translated. In excerpts from chapter 5 we see Euler derive his summation formula, analyze the nature of its Bernoulli numbers in connection with trigonometric functions, find the precise sums of infinite series of reciprocal even powers, and prove Bernoulli's sums of powers formulas. From chapter 6 we see three diverse applications of the summation formula, each revealing a fundamentally di#erent way of using it. We first see Euler approximate large partial sums of the slowly diverging harmonic series , which involves approximating the now famous "Euler constant". Then we see how in the early 1730's Euler approximated the infinite sum of reciprocal squares to great precision without knowledge of the infinite sum itself. Finally Euler goes on to use the summation formula to study sums of logarithms, from which h

M. Fabii Quintiliani Institutionis oratoriae, liber decimus.

Mode of access: Internet

Ars oratoria : selections from Cicero and Quintilian on oratory /

"The text followed has been, for Cicero, that of Klotz, collated with Orelli's; for Quintilian, Bonnell's, with a comparison of the standard edition of Spalding and Zumpt."--pref.Mode of access: Internet

De arte rhetorica libri quinque : $blectissimis veterum auctorum aetatis aurae perpetuisque exemplis illustrati

ICCU\UM1E, 004742Sign.: A-Q12Grab. calc. viñeta en port., inic,, frisos y otra ornam,A 086(2)/42