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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... MICHIGAN , MINNESOTA , MISSOURI , NEBRASKA ; NORTH- WESTERN AND WASHINGTON UNIVERSITIES , COLORADO COLLEGE AND OBERLIN COLLEGE C. H. ASHTON R. P. BAKER W. C. BRENKE W. H. BUSSEY W. DEW . CAIRNS CONTROLLED AND EDITED BY FLORIAN CAJORI ...
... MICHIGAN , MINNESOTA , MISSOURI , NEBRASKA ; NORTH- WESTERN AND WASHINGTON UNIVERSITIES , COLORADO COLLEGE AND OBERLIN COLLEGE C. H. ASHTON R. P. BAKER W. C. BRENKE W. H. BUSSEY W. DEW . CAIRNS CONTROLLED AND EDITED BY FLORIAN CAJORI ...
Page 36
... Michigan State Teachers ' Association met at Kalamazoo , October 29 , 30 , 31. Mr. L. P. JOCELYN , of the Ann Arbor High School , presented a paper before the High School section devoted to the terminology of mathematics . Pro- fessor ...
... Michigan State Teachers ' Association met at Kalamazoo , October 29 , 30 , 31. Mr. L. P. JOCELYN , of the Ann Arbor High School , presented a paper before the High School section devoted to the terminology of mathematics . Pro- fessor ...
Page 72
... Michigan . The given equation may be written yy ' ' + ay'2 + by ' + cy + d = 0 . ( 1 ) Consider the equation yy " + ay'2 + by ' + cy = 0 . ( 2 ) This is equivalent to [ ayy ' + by ] ' + y [ ( 1 - a ) y ' + cx ] ' = 0 . ( 3 ) Hence ( 3 ) ...
... Michigan . The given equation may be written yy ' ' + ay'2 + by ' + cy + d = 0 . ( 1 ) Consider the equation yy " + ay'2 + by ' + cy = 0 . ( 2 ) This is equivalent to [ ayy ' + by ] ' + y [ ( 1 - a ) y ' + cx ] ' = 0 . ( 3 ) Hence ( 3 ) ...
Page 82
... Michigan . The object of this paper is to derive a formula for the valuation of a very general type of securities . The security is redeemed in r equal installments at intervals of t years , the first redemption being made after ƒ years ...
... Michigan . The object of this paper is to derive a formula for the valuation of a very general type of securities . The security is redeemed in r equal installments at intervals of t years , the first redemption being made after ƒ years ...
Page 103
... . BAKER , assistant in mathematics at the University of Michigan , died December 6 , following an operation for appendicitis . 1 Volume XXI , page 157 , May , 1914 . Professor L. C. KARPINSKI has been promoted to a junior NOTES AND NEWS ...
... . BAKER , assistant in mathematics at the University of Michigan , died December 6 , following an operation for appendicitis . 1 Volume XXI , page 157 , May , 1914 . Professor L. C. KARPINSKI has been promoted to a junior NOTES AND NEWS ...
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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.