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 2
... reach the end - point , since the quantity is divided in some manner . However , this second argument has the additional con- tention , that , in a race , even the most rapid cannot overtake the slowest and the refutation must therefore ...
... reach the end - point , since the quantity is divided in some manner . However , this second argument has the additional con- tention , that , in a race , even the most rapid cannot overtake the slowest and the refutation must therefore ...
Page 40
... reach the circum- ference of the circle , even though the cutting should be continued ad infinitum : if we did , a geo- metrical principle would be set aside , which lays down that magnitudes are divisible ad infinitum . ” 4 Aristotle's ...
... reach the circum- ference of the circle , even though the cutting should be continued ad infinitum : if we did , a geo- metrical principle would be set aside , which lays down that magnitudes are divisible ad infinitum . ” 4 Aristotle's ...
Page 42
... reach its limit ? This query finds no reply in Aristotle . To be noted is also the fact that Aristotle denied the existence of actual infinity , as distinguished from potential infinity . The " Arrow " called for a sharp definition of ...
... reach its limit ? This query finds no reply in Aristotle . To be noted is also the fact that Aristotle denied the existence of actual infinity , as distinguished from potential infinity . The " Arrow " called for a sharp definition of ...
Page 63
... reach the path in front of A , and how far to reach the path again behind A ? SOLUTION BY ELIJAH SWIFT , University of Vermont . Take the origin at the place where B starts and the Y - axis through A. Then the coördinates of A at any ...
... reach the path in front of A , and how far to reach the path again behind A ? SOLUTION BY ELIJAH SWIFT , University of Vermont . Take the origin at the place where B starts and the Y - axis through A. Then the coördinates of A at any ...
Page 68
... reach between two hooks on the same hori- zontal line . A ring of weight w is placed at its middle point . Show that the ring will sink through a distance h = a √√3ew / 2 , where e is the elasticity of the string and 2a the distance ...
... reach between two hooks on the same hori- zontal line . A ring of weight w is placed at its middle point . Show that the ring will sink through a distance h = a √√3ew / 2 , where e is the elasticity of the string and 2a the distance ...
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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.