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Page 735 - The lateral areas, or the total areas, of two similar cones of revolution are to each other as the squares of their altitudes...
Page 283 - Current educational topics, No. I. *No. 13. Influences tending to improve the work of the teacher of mathematics. 5 cts. *No. 14. Report of the American commissioners of the international commission on the teaching of mathematics.
Page 22 - Admission to its sanctuary, and to the privileges and feelings of a votary, is only to be gained by one means, — sound and sufficient knowledge of mathematics, the great instrument of all exact inquiry, without which no man can ever make such advances in this or any olher of the higher departments of science as can entitle him to form an independent opinion on any subject of discussion within their range.
Page 17 - The value of mathematical instruction as a preparation for those more difficult investigations, consists in the applicability not of its doctrines, but of its method. Mathematics will ever remain the most perfect type of the Deductive Method in general...
Page 438 - They have forgotten that a generalization is simple only in comparison with the whole mass of particular truths it comprehends — that it is more complex than any one of these truths taken singly — that only after many of these single truths have been acquired, does the generalization ease the memory and help the reason — and that to a mind not possessing these single truths it is necessarily a mystery.
Page 586 - Both members of an equation may be multiplied, or divided, by the same number, without destroying the equality.
Page 620 - OFFICERS SECTION 1. The officers of the association shall be a president, a vice-president, a secretary, a treasurer, and an executive committee composed of five members to be appointed by the president.
Page 391 - ... that the area of a rectangle is the product of the length by the altitude in terms of a unit square.
Page 736 - The lateral area of a frustum of a cone of revolution is equal to one-half the sum of the circumferences of its bases multiplied by its slant height. Hyp. S is the lateral area, C and C...
Page 452 - One of the only two articles that remain in my creed of life is that the future of our civilization depends upon the widening spread and deepening hold of the scientific habit of mind...