The Mathematical Monthly, Band 21860 |
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Seite 1
... inscribed in a given circle to determine its sides geometrically , when the diag- onals intersect each other at right angles . IV . Given ( 1 ) xw + yz = ab , ( 2 ) x y + z wad ( 3 ) xz + yw = bd , ( 4 ) x2 + w2 = y2 + z2 ; to find the ...
... inscribed in a given circle to determine its sides geometrically , when the diag- onals intersect each other at right angles . IV . Given ( 1 ) xw + yz = ab , ( 2 ) x y + z wad ( 3 ) xz + yw = bd , ( 4 ) x2 + w2 = y2 + z2 ; to find the ...
Seite 2
of the circumscribed and inscribed circles , and d the distance be- tween the centres of these circles ; then in the plane triangle * sin A + sin B + sin C 4 cos A cos B cos C and in the spherical triangle sin A + sin B + sin C4 cos A ...
of the circumscribed and inscribed circles , and d the distance be- tween the centres of these circles ; then in the plane triangle * sin A + sin B + sin C 4 cos A cos B cos C and in the spherical triangle sin A + sin B + sin C4 cos A ...
Seite 32
... radii of the circumscribed and inscribed ygg " , " , the radii of the circles touching exteriorly a , b , c respectively ; by d ' , d " , " " , the distances of th VOL . II . 5 Muir Dardelit THE MATHEMATICAL MONTHLY . Vol . II ...
... radii of the circumscribed and inscribed ygg " , " , the radii of the circles touching exteriorly a , b , c respectively ; by d ' , d " , " " , the distances of th VOL . II . 5 Muir Dardelit THE MATHEMATICAL MONTHLY . Vol . II ...
Seite 33
... inscribed circles ; by g ' , g " , " " , the radii of the circles touching exteriorly the sides a , b , c respectively ; by d , d " , " " , the distances of the centres of VOL . II . 5 these circles from the centre of the circle ...
... inscribed circles ; by g ' , g " , " " , the radii of the circles touching exteriorly the sides a , b , c respectively ; by d , d " , " " , the distances of the centres of VOL . II . 5 these circles from the centre of the circle ...
Seite 35
... inscribed in the triangle DEF and the other circumscribed about it ; prove that the area of DEF will be a mean proportional between the areas of ABC and A'B'C ' . " Let DEF be any triangle , ABC an inscribed , and A'B'C ' a similar ...
... inscribed in the triangle DEF and the other circumscribed about it ; prove that the area of DEF will be a mean proportional between the areas of ABC and A'B'C ' . " Let DEF be any triangle , ABC an inscribed , and A'B'C ' a similar ...
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...