The Mathematical Monthly, Volum 21860 |
Inni boken
Resultat 1-5 av 29
Side 17
... remainder , we shall , by following the rule , always get their least common multiple ; if we divide by any number which will divide two or more of them , and follow the rule , we shall get a common multiple , but not always the least ...
... remainder , we shall , by following the rule , always get their least common multiple ; if we divide by any number which will divide two or more of them , and follow the rule , we shall get a common multiple , but not always the least ...
Side 22
... remainder will be an integer . 3. If an integer be multiplied by an integer , the product will be an integer . 4. If an integer be divided by any of its factors , the quotient will be an integer . PROPOSITIONS . I. If a number will ...
... remainder will be an integer . 3. If an integer be multiplied by an integer , the product will be an integer . 4. If an integer be divided by any of its factors , the quotient will be an integer . PROPOSITIONS . I. If a number will ...
Side 23
... remainder . DEMONSTRATION . ( 1 ) As a is prime to b , and greater than y , it will divide neither factor , and consequently will not divide their product , Prop . IV . ( 2 ) . Suppose that any two values of y , as y ' and y " , will ...
... remainder . DEMONSTRATION . ( 1 ) As a is prime to b , and greater than y , it will divide neither factor , and consequently will not divide their product , Prop . IV . ( 2 ) . Suppose that any two values of y , as y ' and y " , will ...
Side 24
... remainder results from the division of c by a , this also will be constant ; and therefore whether we add to it or subtract from it , the unequal remainder , resulting from the division of by by a , the sums and the differences will ...
... remainder results from the division of c by a , this also will be constant ; and therefore whether we add to it or subtract from it , the unequal remainder , resulting from the division of by by a , the sums and the differences will ...
Side 25
... remainder of e divided by a . Again , suppose that b is a multiple of a ' ; then we have in the c ± by same way , α cab my c = m a ' ma ' ± by c = or ± b'y ' , which a gives the same remainder as before . All the preceding propositions ...
... remainder of e divided by a . Again , suppose that b is a multiple of a ' ; then we have in the c ± by same way , α cab my c = m a ' ma ' ± by c = or ± b'y ' , which a gives the same remainder as before . All the preceding propositions ...
Vanlige uttrykk og setninger
A₁ Algebra astronomers atmosphere axis b₁ body centre CHAUNCEY WRIGHT circle coefficients College computation conic section constant cos² curve denote distance divide earth's ellipse equal equation factor force fraction geometry given gives Hence hyperbola inscribed integral logarithms Marietta College Mass Mathematical Monthly Mathematics maxima and minima maximum motion multiplied obtain oxen parabola parallel perihelion perpendicular Perry City plane polygon Prize is awarded PRIZE PROBLEMS PRIZE SOLUTION Probs Prop proposition quantities quaternions quotient R₁ radius ratio rectangle regular polygon remainder result rhombs right angles roots sides SIMON NEWCOMB sin² SOLUTION OF PROBLEM spherical square straight line supposed surface tangent Theorem tion triangle TRUMAN HENRY SAFFORD vector velocity whole number
Populære avsnitt
Side 113 - 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 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...