The Mathematical Monthly, Band 21860 |
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Seite 23
... become an integer , and in no two cases shall we have the same 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 ) ...
... become an integer , and in no two cases shall we have the same 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 ) ...
Seite 24
... becomes remainder . = bm , leaving no a bma + b 2. If we make y = ma + 1 , ma + 2 , & c . , we shall have bma + 2b a 9 α & c . , equal to ; from which we shall obviously obtain by ; the same remainders as when we give to y the ...
... becomes remainder . = bm , leaving no a bma + b 2. If we make y = ma + 1 , ma + 2 , & c . , we shall have bma + 2b a 9 α & c . , equal to ; from which we shall obviously obtain by ; the same remainders as when we give to y the ...
Seite 25
... becomes c ± by ma ' multiple of either m or a ' , and y becomes a multiple of the other , the period of remainders , upon performing the division , will begin to return after a terms , when b is a multiple of m , and after m terms ...
... becomes c ± by ma ' multiple of either m or a ' , and y becomes a multiple of the other , the period of remainders , upon performing the division , will begin to return after a terms , when b is a multiple of m , and after m terms ...
Seite 32
... become the publishers of the MATHEMATICAL MONTHLY . We are satisfied that their energy and large business facilities not only guarantees the permanency of the MONTHLY , but a wider usefulness and a larger measure of success . In advance ...
... become the publishers of the MATHEMATICAL MONTHLY . We are satisfied that their energy and large business facilities not only guarantees the permanency of the MONTHLY , but a wider usefulness and a larger measure of success . In advance ...
Seite 36
... becomes ( 6 ) B'C ' × PA = DE × LF . But in the triangles ABC and DEF , the angle APB = FLE ; ( 7 ) .. ABC : DEFAP X BC : FLX DE ; or , denoting the area of the triangle ABC by t , and by ( 6 ) , t : DEF = AP × BC : B'C ' × AP , .. DEF ...
... becomes ( 6 ) B'C ' × PA = DE × LF . But in the triangles ABC and DEF , the angle APB = FLE ; ( 7 ) .. ABC : DEFAP X BC : FLX DE ; or , denoting the area of the triangle ABC by t , and by ( 6 ) , t : DEF = AP × BC : B'C ' × AP , .. DEF ...
Häufige Begriffe und Wortgruppen
a₁ astronomers atmosphere axis b₁ body cells centre CHARLES HENRY DAVIS circle coefficients College computation conic section constant cos² curve denote distance divided earth's ellipse equal equation force fraction Geometry given gives Hamilton College hence hyperbola inscribed integral logarithms Marietta College Mass Mathematical Monthly maximum Mercury motion multiplied observations obtain parallel perihelion perpendicular Perry City plane polygon Prize is awarded PRIZE PROBLEMS PRIZE SOLUTION Probs Prof Prop proposition quantities quaternions quotient R₁ radius ratio regular polygon remainder result rhombs right angles roots rotation sides SIMON NEWCOMB sin² sine SOLUTION OF PROBLEM sphere spherical square supposed surface tangent Theorem tion triangle TRUMAN HENRY SAFFORD vector velocity whole number
Beliebte Passagen
Seite 113 - Multiplying or dividing both terms of a fraction by the same number does not change its value.
Seite 60 - Method of correcting the apparent distance of the Moon from the Sun, or a Star, for the effects of Parallax and Refraction.
Seite 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.
Seite 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.
Seite 285 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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...