The Mathematical Monthly, Volume 21860 |
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Page iv
... Equations of the Second Decree . 79 On the Motions of Fluids and Solids rela- tive to the Earth's Surface . By Prof. WM . FERREL Note on Equation of Payments . By PLINY EARLE CHASE . Decomposition of an Irreducible Rational Fraction ...
... Equations of the Second Decree . 79 On the Motions of Fluids and Solids rela- tive to the Earth's Surface . By Prof. WM . FERREL Note on Equation of Payments . By PLINY EARLE CHASE . Decomposition of an Irreducible Rational Fraction ...
Page vii
... Equation ( a + b2 ) 2 - = ( a3 - b2 ) 2 + ( 2 ab ) 2 . By Prof. D. WOOD . On the Logarithmic Solution of Cubic Equations . By L. W. MEECH .. On the Indeterminate Analysis . By Rev. A. D. WHEELER . • Solution of a Problem in " Curves of ...
... Equation ( a + b2 ) 2 - = ( a3 - b2 ) 2 + ( 2 ab ) 2 . By Prof. D. WOOD . On the Logarithmic Solution of Cubic Equations . By L. W. MEECH .. On the Indeterminate Analysis . By Rev. A. D. WHEELER . • Solution of a Problem in " Curves of ...
Page 39
... equation of the ellipse referred to its centre and axes is A2x2 + B2 y2 = A2 B2 ; and if x , y ' denote the coördinates of the point of tangency , the equation of the tangent line is Ayy B2 x x A2 B2 . The tangent of the angle which the ...
... equation of the ellipse referred to its centre and axes is A2x2 + B2 y2 = A2 B2 ; and if x , y ' denote the coördinates of the point of tangency , the equation of the tangent line is Ayy B2 x x A2 B2 . The tangent of the angle which the ...
Page 44
... equation of the abola is y2 = 2zx . Also , L B P F Fig . EB22 - 22 , .. AB = = AC AB + BP PC 7.2 2z = * = * + z + r ... equation = -a , and therefore y + a must exactly divide the equation y ― uyur = 0 . y + a ) y3 - uy + ur = 0 ( y2 ...
... equation of the abola is y2 = 2zx . Also , L B P F Fig . EB22 - 22 , .. AB = = AC AB + BP PC 7.2 2z = * = * + z + r ... equation = -a , and therefore y + a must exactly divide the equation y ― uyur = 0 . y + a ) y3 - uy + ur = 0 ( y2 ...
Page 55
... equation , ax — -by = c , is always possible ; and will admit of an infinite number of positive integral solutions . DEMONSTRATION . Transferring and dividing , we have x = which has already been shown to be possible . PROP . V. , Cor ...
... equation , ax — -by = c , is always possible ; and will admit of an infinite number of positive integral solutions . DEMONSTRATION . Transferring and dividing , we have x = which has already been shown to be possible . PROP . V. , Cor ...
Common terms and phrases
a₁ astronomers atmosphere axis b₁ body cells centre CHARLES HENRY DAVIS circle coefficients College computation conic section constant cos² curve denote distance divided earth's ellipse equal equation force fraction Geometry given gives Hamilton College hence hyperbola inscribed integral logarithms Marietta College Mass Mathematical Monthly maximum Mercury motion multiplied observations obtain parallel perihelion perpendicular Perry City plane polygon Prize is awarded PRIZE PROBLEMS PRIZE SOLUTION Probs Prof Prop proposition quantities quaternions quotient R₁ radius ratio regular polygon remainder result rhombs right angles roots rotation sides SIMON NEWCOMB sin² sine SOLUTION OF PROBLEM sphere spherical square 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...