The Mathematical Monthly, Volum 2John Daniel Runkle John Bartlett, 1860 "A complete catalogue of the writings of Sir John Herschel": v. 3, p. 220-227. |
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Side 19
... maximum or minimum value when its rate of change , or the first derivative , vanishes , and in vanishing , changes its sign . Since a positive value in the derivative indicates an increase of the function for an increase of the variable ...
... maximum or minimum value when its rate of change , or the first derivative , vanishes , and in vanishing , changes its sign . Since a positive value in the derivative indicates an increase of the function for an increase of the variable ...
Side 20
... maximum nor a minimum . If a series of successive derivatives all vanish for a given value of the variable ; and if the following one which does not vanish , have a positive value , then the last of the vanishing derivatives is zero by ...
... maximum nor a minimum . If a series of successive derivatives all vanish for a given value of the variable ; and if the following one which does not vanish , have a positive value , then the last of the vanishing derivatives is zero by ...
Side 21
... maximum value ; but if this derivative be of an odd order , then the value of the function is neither a maximum nor a minimum . W. ON THE INDETERMINATE ANALYSIS . By Rev. A. D. WHEELER , Brunswick , Maine . DEFINITIONS . 1. THAT branch ...
... maximum value ; but if this derivative be of an odd order , then the value of the function is neither a maximum nor a minimum . W. ON THE INDETERMINATE ANALYSIS . By Rev. A. D. WHEELER , Brunswick , Maine . DEFINITIONS . 1. THAT branch ...
Side 41
... maximum , let α x = y , where the value of y , determined by the condition of 2 a x — 22 being a maximum , will show whether it is positive , zero , or negative . We now find a x — x2 = a y + 22 — y2 — ay — “ 2 = 42 — y2 , 4 - which is ...
... maximum , let α x = y , where the value of y , determined by the condition of 2 a x — 22 being a maximum , will show whether it is positive , zero , or negative . We now find a x — x2 = a y + 22 — y2 — ay — “ 2 = 42 — y2 , 4 - which is ...
Side 42
... maximum , let x2 = y2 + 22 . .. 2 2 a2 x2 — x * = a2 ( y2 + 2 ) — ( ~ 2 + — 2 ) 2 = a î2 +2 — y — a î — 4 = 4 — y . 4 which is evidently a maximum , when y = 0 , and therefore 2 = 22 , α or x = as before . B √2 ' III . To bisect a ...
... maximum , let x2 = y2 + 22 . .. 2 2 a2 x2 — x * = a2 ( y2 + 2 ) — ( ~ 2 + — 2 ) 2 = a î2 +2 — y — a î — 4 = 4 — y . 4 which is evidently a maximum , when y = 0 , and therefore 2 = 22 , α or x = as before . B √2 ' III . To bisect a ...
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A₁ Algebra astronomers atmosphere axis b₁ body c₁ centre CHAUNCEY WRIGHT circle coefficients College computation Conic Sections constant cos² cot B cot curve December 18 denote distance divided ellipse equal equation force formula fraction geometry given gives Hamilton College hence hyperbola inscribed integral logarithms Marietta College Mass Mathematical Monthly maximum Mercury motion multiplied oxen parabola perihelion perpendicular Perry City plane polygon Prize is awarded PRIZE PROBLEMS PRIZE SOLUTION probability Probs proposition quantities quaternions R₁ radii radius ratio rectangle result rhombs right angles roots sides SIMON NEWCOMB sin² SOLUTION OF PROBLEM sphere spherical square suppose surface tan² tangent Theorem tion triangle TRUMAN HENRY SAFFORD vector velocity whole number
Populære avsnitt
Side 115 - Multiplying or dividing both terms of a fraction by the same number does not change its value.
Side 60 - Method of correcting the apparent distance of the Moon from the Sun, or a Star, for the effects of Parallax and Refraction.
Side 226 - 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.
Side 328 - 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.
Side 307 - 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.
Side 61 - Published in the Monthly Anthology for December, 1807, Vol. IV. [pp. 653, 654.] 2. Review of a "Report of the Committee (of Congress,) to whom was referred, on the 25th of January, 1810, the Memorial of William Lambert, accompanied with sundry Papers relating to the Establishment of a First Meridian for the United States, at the permanent Seat of their Government.
Side 358 - Pratt. — A TREATISE ON ATTRACTIONS, LAPLACE'S FUNCTIONS, AND THE FIGURE OF THE EARTH. By JOHN H. PRATT, MA, Archdeacon of Calcutta, Author of "The Mathematical Principles of Mechanical Philosophy.
Side 362 - 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.
Side 360 - 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.
Side 328 - 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.