The nineteenth meeting was held October 5-6, 2007, at Northern Kentucky University. This was the second meeting in celebration of the Leonhard Euler tricentennial. We read from Euler's Introductio in analysin infinitorum (Introduction to the analysis of the infinite), translated by John D. Blanton (Springer-Verlag, 1988). The selections from Book One: Chapter I. On Functions in General; Chapter VI. On Exponentials and Logarithms; Chapter VII. Exponentials and Logarithms Expressed through Series; Chapter VIII. On Transcendental Quantities Which Arise from the Circle; Chapter XVII. On using recurrent series to find roots of equations; and Chapter XVIII On continued fractions; and from Book Two: Chapters I and II.