The Mathematical Monthly, Volume 21860 |
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Page vi
... Arc . By PLINY EARLE CHASE . On Spherical Analysis . By GEORGE EASTWOOD . · 265 Notes on Probabilities . By SIMON NEW- COMB . · The Method of Integration by Quadra- tures . By Commander CHARLES H. DAVIS . 272 266 • · • 276 · 267 On the ...
... Arc . By PLINY EARLE CHASE . On Spherical Analysis . By GEORGE EASTWOOD . · 265 Notes on Probabilities . By SIMON NEW- COMB . · The Method of Integration by Quadra- tures . By Commander CHARLES H. DAVIS . 272 266 • · • 276 · 267 On the ...
Page 87
... arcs v and u will be negative , as before . III . " The irreducible case . " When a is negative and of such value that ? ( a ) * is greater than 1 . Make cos v = x = b 3 ( ) ; then a √ a { ( cos v + √ = 1 sin v ) + ( cos v — — 1 sin v ) ...
... arcs v and u will be negative , as before . III . " The irreducible case . " When a is negative and of such value that ? ( a ) * is greater than 1 . Make cos v = x = b 3 ( ) ; then a √ a { ( cos v + √ = 1 sin v ) + ( cos v — — 1 sin v ) ...
Page 101
... arcs . Then , by $$ 5 , 7 , and 9 , we may represent q by either of the equal arcs , a 5 , or 58 , and p by sẞ , or ẞy . Then pq is represented by a y , and qp by 8. Equations ( 4 ' ) and ( 11 ) show that Kq and q1 are equal , when q is ...
... arcs . Then , by $$ 5 , 7 , and 9 , we may represent q by either of the equal arcs , a 5 , or 58 , and p by sẞ , or ẞy . Then pq is represented by a y , and qp by 8. Equations ( 4 ' ) and ( 11 ) show that Kq and q1 are equal , when q is ...
Page 160
... arc AB = rdp . But the triangle AB M may be regarded as rectilinear , and right- S Fig . 2 . B M. = angled at B ; and if we put the angle AMB = & , we shall have A B AM sin AMB ; or rdq = ds sinɛ . Multiplying by r , we have 2dq = cdt ...
... arc AB = rdp . But the triangle AB M may be regarded as rectilinear , and right- S Fig . 2 . B M. = angled at B ; and if we put the angle AMB = & , we shall have A B AM sin AMB ; or rdq = ds sinɛ . Multiplying by r , we have 2dq = cdt ...
Page 163
... arcs of great circles of the sphere intersecting each other in the point 0 ; and let OP be the great circle whose equation is re- quired . Through any point P , pass the great circle arcs XP M , YPN , and designate ON by x , OM by y ...
... arcs of great circles of the sphere intersecting each other in the point 0 ; and let OP be the great circle whose equation is re- quired . Through any point P , pass the great circle arcs XP M , YPN , and designate ON by x , OM by y ...
Common terms and phrases
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
Popular passages
Page 113 - Multiplying or dividing both terms of a fraction by the same number does not change its value.
Page 60 - Method of correcting the apparent distance of the Moon from the Sun, or a Star, for the effects of Parallax and Refraction.
Page 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.
Page 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.
Page 285 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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...