The Mathematical Monthly, Volume 21860 |
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Page vii
... ( supposed ) New Instru- 367 Editorial Items . 391 • Mathematical Monthly Notices . 391 No. XII . Prize Problems for Students . . Notes and Queries . 393 Second Solution . By Prof. O. Rooт .. 414 Note on Diacaustics . By Rev. THOMAS HILL ...
... ( supposed ) New Instru- 367 Editorial Items . 391 • Mathematical Monthly Notices . 391 No. XII . Prize Problems for Students . . Notes and Queries . 393 Second Solution . By Prof. O. Rooт .. 414 Note on Diacaustics . By Rev. THOMAS HILL ...
Page 10
... supposed impossibility of Just Intona- tion and the necessity of Temperament , have their origin only in the short - sightedness of the theorist , and the unskilfulness of the practitioner . Having settled upon the rule that musical ...
... supposed impossibility of Just Intona- tion and the necessity of Temperament , have their origin only in the short - sightedness of the theorist , and the unskilfulness of the practitioner . Having settled upon the rule that musical ...
Page 17
... common multiple , otherwise the supposed mul- tiple would not be divisible by this number . On the other hand , VOL . II . 3 if any common factor , raised to a higher power 17 Notes and Queries Least Common Multiple No II Notes and Queries.
... common multiple , otherwise the supposed mul- tiple would not be divisible by this number . On the other hand , VOL . II . 3 if any common factor , raised to a higher power 17 Notes and Queries Least Common Multiple No II Notes and Queries.
Page 22
... supposed d to be contained n times in S , and n ' times in A , then will it obviously be contained -n times in B ; and this must be an integer according to Axiom 2 . n In the same way may the truth of the proposition be shown , whatever ...
... supposed d to be contained n times in S , and n ' times in A , then will it obviously be contained -n times in B ; and this must be an integer according to Axiom 2 . n In the same way may the truth of the proposition be shown , whatever ...
Page 30
... supposed to be the case . II . QUATERNIONS . 5. The abstract operation of so changing the length and direc- tion of one line as to make it coincide in length and direction with another line , is considered as the quotient of the second ...
... supposed to be the case . II . QUATERNIONS . 5. The abstract operation of so changing the length and direc- tion of one line as to make it coincide in length and direction with another line , is considered as the quotient of the second ...
Common terms and phrases
A₁ Algebra astronomers atmosphere axis b₁ body centre CHAUNCEY WRIGHT circle coefficients College computation conic section constant cosē curve denote distance divide earth's ellipse equal equation factor force fraction geometry given gives Hence hyperbola inscribed integral logarithms Marietta College Mass Mathematical Monthly Mathematics maxima and minima maximum motion multiplied obtain oxen parabola parallel perihelion perpendicular Perry City plane polygon Prize is awarded PRIZE PROBLEMS PRIZE SOLUTION Probs Prop proposition quantities quaternions quotient R₁ radius ratio rectangle regular polygon remainder result rhombs right angles roots sides SIMON NEWCOMB sinē SOLUTION OF PROBLEM spherical square straight line supposed surface tangent Theorem tion triangle TRUMAN HENRY SAFFORD vector velocity whole number
Popular passages
Page 113 - Multiplying or dividing both terms of a fraction by the same number does not change its value.
Page 60 - Method of correcting the apparent distance of the Moon from the Sun, or a Star, for the effects of Parallax and Refraction.
Page 224 - Physical Optics, Part II. The Corpuscular Theory of Light discussed Mathematically. By RICHARD POTTER, MA Late Fellow of Queens' College, Cambridge, Professor of Natural Philosophy and Astronomy in University College, London.
Page 326 - PUCKLE.— An Elementary Treatise on Conic Sections and Algebraic Geometry. With a numerous collection of Easy Examples progressively arranged, especially designed for the use of Schools and Beginners. By G. HALE PUCKLE, MA, Principal of Windermere College.
Page 285 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 305 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 326 - AN ELEMENTARY TREATISE ON THE LUNAR THEORY, with a Brief Sketch of the Problem up to the time of Newton. Second Edition, revised. Crown 8vo. cloth. 5*. 6d. Hemming. — AN ELEMENTARY TREATISE ON THE DIFFERENTIAL AND INTEGRAL CALCULUS, for the Use; of Colleges and Schools.
Page 360 - URIAH A. BOYDEN, ESQ., of Boston, Mass., has deposited with THE FRANKLIN INSTITUTE the sum of one thousand dollars, to be awarded as a premium to "Any resident of North America who shall determine by experiment whether all rays of light,* and other physical rays, are or are not transmitted with the same velocity.
Page 358 - Calculus — a connection which in some instances involves far more than a merely formal analogy. The work is in some measure designed as a sequel to Professor Boole's Treatise on Differential Equations.
Page 321 - First, that the maximum of polygons formed of given sides may be inscribed in a circle ; secondly, that the maximum of isoperimetrical polygons having a given number of sides has its sides equal ; and thirdly, that such a regular polygon is of smaller area than a circle isoperimetrical with it. 134. Theorem. The area of a triangle is found by multiplying the base by half the altitude. This theorem has been already proved (Art. 111). 135. We shall need the Pythagorean proposition, which implies all...