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 102
... proof will obviously answer for the other rectangle and its square . 69. Now if we know , or can prove , that the area of a rectan- gle is measured by the product of its sides , we shall have to prove that A EX A B ' or AEX AB is ...
... proof will obviously answer for the other rectangle and its square . 69. Now if we know , or can prove , that the area of a rectan- gle is measured by the product of its sides , we shall have to prove that A EX A B ' or AEX AB is ...
Side 103
... Proof of the Pythagorean Proposition . 76. Definition . The comparative size of two quantities is called their ratio ; thus if one is twice as large as the other , they are said to be in the same ratio as that of 2 to 1 ; or to be in ...
... Proof of the Pythagorean Proposition . 76. Definition . The comparative size of two quantities is called their ratio ; thus if one is twice as large as the other , they are said to be in the same ratio as that of 2 to 1 ; or to be in ...
Side 104
... Proof . For as the straight line has but one direc- tion , and each of the parallel lines may always be considered as going in the same direction as the other , the difference of that direction from the direction of the third straight ...
... Proof . For as the straight line has but one direc- tion , and each of the parallel lines may always be considered as going in the same direction as the other , the difference of that direction from the direction of the third straight ...
Side 114
... PROOF . Let us assume the general equation , 1 - x2 + Ax2 · ± Bxn - 2 ± Ñï3¬ ' + 1 ± V = 0 . ..... A superior limit of the roots of an equation must produce a posi- tive result when substituted for ; that is , the sum of all the ...
... PROOF . Let us assume the general equation , 1 - x2 + Ax2 · ± Bxn - 2 ± Ñï3¬ ' + 1 ± V = 0 . ..... A superior limit of the roots of an equation must produce a posi- tive result when substituted for ; that is , the sum of all the ...
Side 140
... Proof . Let us sup- A B C D E pose that , in the triangles A B C and DEF , we have the side A B equal to the side DE , the angle at A equal to the angle D , and that at B equal to that at E. Let us imagine the triangle DEF to be laid ...
... Proof . Let us sup- A B C D E pose that , in the triangles A B C and DEF , we have the side A B equal to the side DE , the angle at A equal to the angle D , and that at B equal to that at E. Let us imagine the triangle DEF to be laid ...
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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.