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acres amount angle atmosphere axis base becomes body called cause cells centre circle College common computation condition constant containing Continued curve denote determine difference direction distance divided draw equal equation evident expression factor figure force four fraction geometry given gives greater heat Hence increase integral length less Mass Mathematics maximum means measure method Monthly motion multiplied negative Note observed obtain oxen parallel passing perpendicular plane polygon positive PRIZE probability problem Probs Proof proportional proposition prove quantities quaternions radius ratio remainder represented respectively result right angles roots sides similar SOLUTION space sphere spherical square Substituting supposed surface tangent third tion triangle unit vector velocity whole
Side 113 - Multiplying or dividing both terms of a fraction by the same number does not change its value.
Side 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.
Side 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.
Side 285 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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...