The American Mathematical Monthly: The Official Journal of the Mathematical Association of America, Volume 22Mathematical Association of America, 1915 - Mathematicians Includes articles, as well as notes and other features, about mathematics and the profession. |
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Page 14
... contains in the first seventy - five pages an excellent introduction to the classical multiplicative theory of numbers , while an additional chapter of seventeen pages gives a brief account of the meaning of some advanced topics , such ...
... contains in the first seventy - five pages an excellent introduction to the classical multiplicative theory of numbers , while an additional chapter of seventeen pages gives a brief account of the meaning of some advanced topics , such ...
Page 37
... contains a tribute to the American astronomer GEORGE WILLIAM HILL , who lectured for several years on celestial mechanics at Columbia University . A good portrait accompanies the article . A paper by Professor G. A. MILLER entitled ...
... contains a tribute to the American astronomer GEORGE WILLIAM HILL , who lectured for several years on celestial mechanics at Columbia University . A good portrait accompanies the article . A paper by Professor G. A. MILLER entitled ...
Page 53
... contain several pages of material not connected with the title . This lack is partly compensated for by a full index . Several hundred exercises for the student are included , the answers to which are not furnished . The first and ...
... contain several pages of material not connected with the title . This lack is partly compensated for by a full index . Several hundred exercises for the student are included , the answers to which are not furnished . The first and ...
Page 54
... contains the traditional treatment of many of the problems of analytic geometry , including tangents and normals , the general equa- tion of a conic , and confocal conics . The criterion given for determining the positive and negative ...
... contains the traditional treatment of many of the problems of analytic geometry , including tangents and normals , the general equa- tion of a conic , and confocal conics . The criterion given for determining the positive and negative ...
Page 74
... contains an article by PHILIP E. B. JOURDAIN entitled " The Theories of Irrational Numbers , Part I. " According to the author's own words " the aim of this his- torical and critical study is somewhat different from that of the other ...
... contains an article by PHILIP E. B. JOURDAIN entitled " The Theories of Irrational Numbers , Part I. " According to the author's own words " the aim of this his- torical and critical study is somewhat different from that of the other ...
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Common terms and phrases
A. M. HARDING Achilles algebra American Mathematical Society analytic geometry angle angular momentum applied Aristotle arithmetic C. N. SCHMALL calculus Cantor centers of similitude chapter circle circles of Apollonius circumcircle College Colorado College continuum coördinates cos² course curve differential discussion elementary equal equation finite FLORIAN CAJORI formula Georg Cantor given Hence high school indivisible infinite divisibility infinite number infinitesimal infinity integral interest L. C. KARPINSKI L. E. DICKSON limit logarithms mathe mathematicians matics meeting method motion perpendicular philosophy plane problem Proposed by C. N. quadric radius Science sin² SOLUTION solved space sphere straight line tangent teachers of mathematics teaching theorem tortoise triangle trigonometry University of Arkansas variable vector velocity W. H. BUSSEY York City Zeno Zeno's arguments
Popular passages
Page 7 - DESCRIPTIVE GEOMETRY, an Elementary Treatise on; with a Theory of Shadows and of Perspective, extracted from the French of G. MONGE. To which is added, a description of the Principles and Practice of Isometrical Projection ; the whole being intended as an introduction to the Application of Descriptive Geometry to various branches of the Arts.
Page 143 - For those ultimate ratios with which quantities vanish are not truly the ratios of ultimate quantities, but limits towards which the ratios of quantities decreasing without limit do always converge; and to which they approach nearer than by any given difference, but never go beyond, nor in effect attain to, till the quantities are diminished in infinitum.
Page 108 - ... elaborate treatises .which attempt to cover several or all aspects of a wide field. The volumes of the series will differ from the discussions generally appearing in technical journals in that they will present the complete results of an experiment or series of investigations which previously have appeared only in scattered articles, if published at all. On the other hand, they will differ from detailed treatises by confining themselves to specific problems of current interest, and in presenting...
Page 143 - QUANTITIES, AND THE RATIOS OF QUANTITIES, WHICH IN ANY FINITE TIME CONVERGE CONTINUALLY TO EQUALITY, AND BEFORE THE END OF THAT TIME APPROACH NEARER THE ONE TO THE OTHER THAN BY ANY GIVEN DIFFERENCE, BECOME ULTIMATELY EQUAL.
Page 194 - Quadrant. But he knew little out of his way, and was not a pleasing companion; as, like most great mathematicians I have met with, he expected universal precision in everything said, or was for ever denying or distinguishing upon trifles, to the disturbance of all conversation.
Page 292 - ... to occupy at least two successive positions, unless at least two moments are allowed it. At a given moment, therefore, it is at rest at a given point. Motionless in each point of its course, it is motionless during all the time that it is moving. Yes, if we suppose that the arrow can ever be in a point ^ of its course.
Page 294 - Weierstrass, by strictly banishing all infinitesimals, has at last shown that we live in an unchanging world, and that the arrow, at every moment of its flight, is truly at rest. The only point where Zeno probably erred was in inferring (if he did infer) that, because there is no change, therefore the world must be in the same state at one time as at another.
Page 91 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 113 - Je suis tellement pour l'infini actuel , qu'au lieu d'admettre que la nature l'abhorre, comme l'on dit vulgairement, je tiens qu'elle l'affecte partout, pour mieux marquer les perfections de son auteur. Ainsi je crois qu'il n'ya aucune partie de la matière qui ne soit, je ne dis pas divisible , mais actuellement divisée ; et, par conséquent , la moindre particelle doit être considérée comme un monde plein d'une infinité de créatures différentes.
Page 219 - Barbara, Celarent, Darii, Ferioque, prioris; Cesare, Camestres, Festino, Baroko, secundae; Tertia, Darapti, Disamis, Datisi, Felapton, Bokardo, Ferison, habet ; Quarta insuper addit Bramantip, Camenes, Dimaris, Fesapo, Fresison.