The American Mathematical Monthly: The Official Journal of the Mathematical Association of America, Volumes 9-10

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Mathematical Association of America, 1902 - Mathematicians
Registers of officers and members were issued as supplements to some vols.


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Page 125 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Page 84 - One of these, the proof that all pure mathematics deals exclusively with concepts definable in terms of a very small number of fundamental logical concepts, and that all its propositions are deducible from a very small number of fundamental logical principles, is undertaken in Parts II.
Page 87 - Rnnkle found his highest usefulness and most congenial vocation, — a vocation to be happily continued for not less than twenty-one years. His teaching was characterized by stimulating, luminous, unconventional exposition, by quick, incisive questioning, by warm personal interest in his students, and by a constant substratum of uplifting earnestness and dignity. None of his students could fail to acquire admiring affection ; very few could withstand the incentive to work.
Page 32 - Two triangles are equal when the three sides of the one are equal respectively to the three sides of the other. B B' О In the triangles AB С and A' B' C', let AB = A' B', AC = A'C', BC = B' C'. We are to prove AAB С = A A' B' C". Place A A' B' C
Page 126 - Elementary Theorems Relating to the Geometry of a Space of Three Dimensions and of Uniform Positive Curvature in the Fourth Dimension," published in Borchardt's Journal, Bd.
Page 125 - Most would indeed let that pass as an axiom; I not; it might well be possible, that, how far apart soever one took the three vertices of the triangle in space, yet the content was always under a given limit. I have more such theorems, but in none do I find anything satisfying." From this letter we clearly see that in 1799 Gauss was still trying to prove that Euclid's is the only non-contradictory system of geometry, and that it is the system regnant in the external space of our physical experience....
Page 171 - Euclid, has been discussed in numerous excellent memoirs to be found in the mathematical literature.* This problem is tantamount to the logical analysis of our intuition of space. The following investigation is a new attempt to choose for geometry a simple and complete set of independent axioms and to deduce from these the most important geometrical theorems in such a manner as to bring out as clearly as possible the significance of the different groups of axioms and the scope of the conclusions...
Page 115 - Q are related by р/с' = constant, where y is the ratio of specific heat at constant pressure to specific heat at constant volume, for compressible fluids.
Page 72 - An International Illustrated Monthly Magazine. Edited by Dr. Albert Shaw. Price, $2.50 per year in advance. Single number, 25 cents. The Review of Reviews Co..
Page 24 - To find three whole numbers such, that if to the square of each the product of the other two be added, the three sums shall be all squares. Ans. 9, 73, and 328.

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