Bulletin of the New York Mathematical Society, Volume 2

The Society, 1892

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Pagina 24 - We measure distance, say, by a yard measure or a foot rule, anything which is short enough to make the fractions of it of no consequence (in mathematical language, by an infinitesimal element of length) ; imagine, then, the length of this rule constantly changing (as it might do by an alteration of temperature), but under the condition that its actual length shall depend only on its situation on the plane and on its direction : viz. if for a given situation and direction it has a certain length,...
Pagina 61 - ... and full of the excitement of nascent thoughts; its logic is beset with ambiguities, and its analytic processes, like Bunyan's road, have a quagmire on one side and a deep ditch on the other and branch off into innumerable by-paths that end in a wilderness.
Pagina 270 - Geometry in the Grammar Schools. An essay, together with illustrative class exercises and an outline of the work for the last three years of the grammar school.
Pagina 182 - Analytics, 1.4 : 73ft 32) proves that every isosceles triangle has the sum of its angles equal to two right angles...
Pagina 32 - The chief lesson to be obtained from all non-euclidian diversions is that the distinguishing mark of euclidian geometry is fixity of distancemeasurement, by which alone it is possible to draw the same figure upon different scales. That the same figure may be drawn upon different scales might well be laid down as the axiom necessary and sufficient to distinguish euclidian from noneuclidian geometry.
Pagina 61 - THERE is probably no other science which presents such different appearances to one who cultivates it and to one who does not, as mathematics. To this person it is ancient, venerable, and complete ; a body of dry, irrefutable, unambiguous reasoning. To the mathematician, on the other hand, his science is yet in the purple bloom of vigorous youth, everywhere stretching out after the
Pagina 62 - X = x cos a + y sin a Y = —x sin a + y...
Pagina 81 - Constructions or Strength and Elasticity of Beams, Columns, Shafts, Arches, etc., and the Principles of Hydraulics and Pneumatics with Applications. For the Use of Technical Schools.
Pagina 169 - In observations of equal precision the most probable values of the observed quantities are those that render the sum of the squares of the residual errors a minimum...
Pagina 108 - The solution of an algebraically solvable equation can always be performed by a chain of binomial equations of prime degrees whose roots are rationally expressible in terms of the roots of the given equation and of certain roots of unity.

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