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 5
... Hence , √x2 + y2 + x = a , x + y = b . Eliminating y gives x = - — ( ab ) ± √2a ( a - b ) ; rejecting the negative sign before the radical as giving a negative value to x , we have x = - - ( ab ) + √2a ( a - b ) and y = b — x . To ...
... Hence , √x2 + y2 + x = a , x + y = b . Eliminating y gives x = - — ( ab ) ± √2a ( a - b ) ; rejecting the negative sign before the radical as giving a negative value to x , we have x = - - ( ab ) + √2a ( a - b ) and y = b — x . To ...
Side 6
... Hence , if from any point of the line . P'A tangents be drawn to the two given circles , they will be equal . * P'A is there- fore the radical axis of the two circles , and will bisect the common tangents . PRIZE SOLUTION OF PROBLEM IV ...
... Hence , if from any point of the line . P'A tangents be drawn to the two given circles , they will be equal . * P'A is there- fore the radical axis of the two circles , and will bisect the common tangents . PRIZE SOLUTION OF PROBLEM IV ...
Side 7
... Hence the two lines P'P ' and PP , having two points in common ( P ' and A ) , coincide throughout their whole ex- tent , and form one and the same straight line . In a precisely similar manner , by drawing the line P Q " and Q'Q " and ...
... Hence the two lines P'P ' and PP , having two points in common ( P ' and A ) , coincide throughout their whole ex- tent , and form one and the same straight line . In a precisely similar manner , by drawing the line P Q " and Q'Q " and ...
Side 11
... for historical reference the most respectable au- thorities of this day against Just Intonation , and to prove that the views I put forth have such opponents , and hence need to be told . The interval 4 : 7 derived from the prime seventh ...
... for historical reference the most respectable au- thorities of this day against Just Intonation , and to prove that the views I put forth have such opponents , and hence need to be told . The interval 4 : 7 derived from the prime seventh ...
Side 21
... Hence the rule . If the derivative , the first that does not vanish for a given value of the variable , be positive , and of an even order , the func- tion is at a minimum value ; if this derivative , be negative and even , the function ...
... Hence the rule . If the derivative , the first that does not vanish for a given value of the variable , be positive , and of an even order , the func- tion is at a minimum value ; if this derivative , be negative and even , the function ...
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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.