The Mathematical Monthly, Volum 21860 |
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Side 10
... ratios must not exceed a certain limit of simplicity ( the limit to be determined by the areas of all the surfaces investigated in plane geometry may be exhibited to the eye by simple construction ; and quite young children may readily ...
... ratios must not exceed a certain limit of simplicity ( the limit to be determined by the areas of all the surfaces investigated in plane geometry may be exhibited to the eye by simple construction ; and quite young children may readily ...
Side 11
ability of the ear to appreciate them ) , it was stated that those ratios only were admissible which were derived from the prime numbers 2 , 3 , 5 , and 7. That the three lower primes 2 , 3 , and 5 belong to the musical system has been ...
ability of the ear to appreciate them ) , it was stated that those ratios only were admissible which were derived from the prime numbers 2 , 3 , 5 , and 7. That the three lower primes 2 , 3 , and 5 belong to the musical system has been ...
Side 12
... ratios are al- together appreciable by the common ear , and are in constant use in common music . It is this which constitutes , when added to the common chord , the concord ( falsely called the discord ) of the Seventh , and this ...
... ratios are al- together appreciable by the common ear , and are in constant use in common music . It is this which constitutes , when added to the common chord , the concord ( falsely called the discord ) of the Seventh , and this ...
Side 14
... ratios 4 : 5 : 6 : 7 : 9 . To distinguish these scales , I have called the first the Triple Diatonic , and the last the Double Diatonic . Assum- ing the tonic or the key - note , as C , with 48 vibrations , the two scales will stand as ...
... ratios 4 : 5 : 6 : 7 : 9 . To distinguish these scales , I have called the first the Triple Diatonic , and the last the Double Diatonic . Assum- ing the tonic or the key - note , as C , with 48 vibrations , the two scales will stand as ...
Side 15
... ratio . A fifth then will be " two - three , " a major - tone " eight - nine , ” a dia- tonic semitone " fifteen - sixteen , " the interval , ( unnamed ) between the third of the scale and the dominant seventh , is the " twenty twenty ...
... ratio . A fifth then will be " two - three , " a major - tone " eight - nine , ” a dia- tonic semitone " fifteen - sixteen , " the interval , ( unnamed ) between the third of the scale and the dominant seventh , is the " twenty twenty ...
Vanlige uttrykk og setninger
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
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...