MATHEMATICAL NOTES 233

MATHEMATICAL NOTE.

Several answers have been received in reply to Mr. Plunkett’s com-munication in Vol. VII, 1907, No. 1, page 59. The first reply is heregiven:

In reference to the note in SCHOOL SCIENCE AND MATHEMATICS con-cerning the correctness of the proposition that "In the same circle, orin equal circles, arcs whose extremities can be made to coincide areequal," the author of the text has probably pointed out previously thatany chord of a circle subtends two arcs and that -unless otherwisestated the lesser is intended when the word arc is used, in which casethe proposition is true.

There is, however, a more subtile objection to this proposition. Theidea of the inequality of the two arcs of any circle subtended by anychord (not a diameter) presupposes a knowledge of the conditionsunder which two arcs of a circle are equal, so that such a propositionis truly an "argument in a circle," but unfortunately of the kindwhich good logic teaches us to avoid. G. W. GREENWOOD,

Roanoke College, Salem, Va.

RESUME OF CURRENT MAGAZINES FOR TEACHERS OF

SECONDARY MATHEMATICS.

Teachers of high school mathematics will find interest and profit in

the following recently published mathematical papers: In the Bulletin

of the American Mathematical Society for January, 1907, page 166, is

a paper on "A New Approximate Construction for TT," by Mr. GeorgePierce; and on page 197 is a good review of McOormack’s translationof Dr. Ernst Mach’s "Space and Geometry in the Light of Physiological,Psychological, and Physical Inquiry."

In the November, 1906, L’Enseignment Mathematique (Paris and

Geneva), "Logarithms before Napier," by A. Aubry; "Pure Mathematicsand Approximation," by L. Kollros; "Graphical Method of Determiningthe Real Roots of the Equation a?3 + px + q == o," by E. Brand;"Demonstration of a Proposition in Linear Equations," by G. Dumas.For those who read French these papers will be of considerable interest.

In the School World (London, Macmillan) for September, 1906, isa paper on "The Curriculum of Secondary Schools," by Hon. andRev. E. Lyttleton, M.A.; another on "The Secondary School Curriculumand the Training of Teachers," by Arthur 0. Benson, M.A., and a thirdon ^The Balance of Studies in Secondary Schools," by T. E. Page, M.A.These three papers refer to the situation in English schools, but theyare illuminating to the American teacher as well.

In the American Mathematical Monthly for December, 1906, is a"Note on the Addition Theorem in Trigonometry," by Dr. G. A. Miller.