Prospectus -- The railway transition curve / W.H. Echols -- The beginnings of mathematics / W.B. Richards -- Tallow clays / W.H. Seamon -- On the continuous construction of the ellipse / W.H. Echols -- On the establishment of the true meridian by means of observations on the sun with the engineer's solar instrument / George R. Dean -- Exercises for solution, 1-6 -- Errata.

Imaginaires in analytical geometry / William B. Smith -- Our belief in axioms and the new spaces / George Bruce Halsted -- The volume of the prismoid and cylindroid / W.H. Echols -- The beginning of mathematics, II. Geometry -- W.B. Richards -- A new elementary demonstration of the pythagorean theorem / William B. Smith -- Solution of Exercises, 1, 3, 5, 6 -- Exercises 7-20.

The science of absolute space : independent of the truth or falsity of Euclid's Axiom XI (which never can be established a priori), followed by the geometric quadrature of the circle in the case of the falsity of Axiom XI / John Bolyai ; translated into English by George Bruce Halsted ; [includes Appendix I. Remarks on the preceding memoir, by Wolfgang Bolyai ; Appendix II. Some points in John Bolyai's appendix compared with Lobatschewsky, by Wolfgang Bolyai ; Appendix III. Light from Non-Euclidean spaces on the teaching of elementary geometry, by G.B. Halsted -- Note on the transition curve / W.H. Echols -- Number, discrete and continous / George Bruce Halsted -- Geometric inversion / Annie L. MacKinnon -- The pneumatic-hydraulic sand-lift / W.H. Echols -- Editorial note -- Solution of exercises 21, 23 -- Exercises 28-37.,"It has been decided to discontinue the publication of this Journal and its issue ceases with this number, which closes the first volume."--Page 328.

Geometrical researches on the theory of parallel lines / Nicolaus Lobatscheusky ; translated by George Bruce Halsted -- An elementary expansion of the sine and cosine in terms of circular measure / W.H. Echols -- The two-term prismoidal formula / George Bruce Halsted -- Copy multiplication table / Levi W. Meech -- The transit of mercury across the sun's disk on May 9th, 1891 / H.C. Williiams -- Note on stadia measuring / W.H. Echols -- Historical note on "A new elementary demonstration of the Pythagorean Proposition" / Artemas Martin -- Solutions of Exercises 4, 7, 8, la, II, 12, 13, 14, 15 -- Exercises 21-27.