Proceedings of the Edinburgh Mathematical Society, Volumer 23-24Scottish Academic Press, 1905 |
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Resultat 1-5 av 42
Side
... Roots , 66 A Proof of Waring's Expression for a ' in terms of the Coefficients of an Equation , 71 OFFICE - BEARERS , 1 PICKEN , D. K. The Proof by Projection of the Addition Theorem in Trigonometry , 40 A direct method of obtaining the ...
... Roots , 66 A Proof of Waring's Expression for a ' in terms of the Coefficients of an Equation , 71 OFFICE - BEARERS , 1 PICKEN , D. K. The Proof by Projection of the Addition Theorem in Trigonometry , 40 A direct method of obtaining the ...
Side 43
... Roots of Cubic and Quartic Equations . By P. PINKERTON , M.A. THE CUBIC . Let a cubic function be denoted by a1 Put z = x - ≈2 + a1 ~ 22 + b1≈ + c1 . and the function takes the form x2 + 3qx + r . Consider the graph of this function ...
... Roots of Cubic and Quartic Equations . By P. PINKERTON , M.A. THE CUBIC . Let a cubic function be denoted by a1 Put z = x - ≈2 + a1 ~ 22 + b1≈ + c1 . and the function takes the form x2 + 3qx + r . Consider the graph of this function ...
Side 44
... roots . The roots will be all real and different if the roots of equation ( 5 ) are unlike in sign , i.e. , if r2 + 4q " is negative . There will be two equal roots if a value of k as determined from equation ( 5 ) is zero , i.e. , if ...
... roots . The roots will be all real and different if the roots of equation ( 5 ) are unlike in sign , i.e. , if r2 + 4q " is negative . There will be two equal roots if a value of k as determined from equation ( 5 ) is zero , i.e. , if ...
Side 45
... roots of the cubic equation may be all equal . h3 + 3gh + r = 0 ( 6 ) Since the coefficient of h2 in the equation is zero , each root is zero ; .. q = 0 and r = 0 and the equation of the graph becomes , by ( 8 ) , n = & . The graph is ...
... roots of the cubic equation may be all equal . h3 + 3gh + r = 0 ( 6 ) Since the coefficient of h2 in the equation is zero , each root is zero ; .. q = 0 and r = 0 and the equation of the graph becomes , by ( 8 ) , n = & . The graph is ...
Side 46
... roots of the equation h3 + 3gh + r = 0 . Take h equal to the real root of this equation k = 3qh2 + 3rh + 8 . Then the equation of the graph by ( 8 ) is n = §23 { ( § + 2h ) 2 + 2 ( h2 + 3q ) } . 2 ' Now h2 + 3q = = - . h ( 6 ) But the ...
... roots of the equation h3 + 3gh + r = 0 . Take h equal to the real root of this equation k = 3qh2 + 3rh + 8 . Then the equation of the graph by ( 8 ) is n = §23 { ( § + 2h ) 2 + 2 ( h2 + 3q ) } . 2 ' Now h2 + 3q = = - . h ( 6 ) But the ...
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Proceedings of the Edinburgh Mathematical Society Edinburgh Mathematical Society Uten tilgangsbegrensning - 1966 |
Proceedings of the Edinburgh Mathematical Society, Volumer 16-19 Edinburgh Mathematical Society Uten tilgangsbegrensning - 1898 |
Vanlige uttrykk og setninger
a₁ Academy Allan Glen's School angles Apollonian circles arcs axes axis of similitude B.Sc b₁ centre of similitude circle touching circonférence coefficient common tangents conic corresponding cos(a cosB cosC cose cosẞ cosy côtés cubic curve D.Sc determinant deux directrix droite Edinburgh EDINBURGH MATHEMATICAL SOCIETY égal envelope equal equation Figure formula George Heriot's School George Watson's College given circles Glasgow Hence hypocycloid inscrit intersection l'angle l'arc l'on le point M'INTOSH Mathematical Society Mathématiques method negative orthogonal P₁ parallel pédale perpendiculaires point of contact positive Professor of Mathematics proof quadratic quantities r₁ radical axis radii radius rational points rayon de courbure roots S₁ Simson Line sin(a sinb solution sommets tangent tangent circles theorem triangle équilatéral trois rebroussements valeur values x₁ Y₁ zero
Populære avsnitt
Side 86 - Sur la limite de ^~n, pour я = oo (p. 29 — 30). M1 5 b. HP NIELSEN. Om de usammensatte Kurver af fjerde Orden, som daekke sig selv ved en tredie Del af en hel Omdrejning om Begyndelsespunktet. Sur les courbes rationnelles du quatrième ordre qui se couvrent en les faisant tourner d'un angle de |тг autour de l'origine des coordonnées (p. 30 — 34). Archiv der Mathematik und Physik, 2t<= Reihe, XII (l, 2) 1893.
Side 54 - Theorem that the Arithmetic Mean of n Positive Quantities is not less than their Harmonic Mean [Title].
Side 120 - The distance from the eye at which the object must be placed to subtend the same angle, when viewed directly, that it appears to subtend when seen through the instrument is called its apparent distance.
Side 79 - RF MUIRHEAD. On the number and nature of the solutions of the Apollonian contact problem. In this paper, containing 5 tables and accompanied by 71 figures, the author classifies the various special cases according to the relative positions of the given circles (p. 135—147). [Moreover this volume contains a review of: V7, 8.
Side 7 - Dec. 19 (Sun.). — Sat up last night till 4 am, over a tempting problem, sent me from New York, " to find 3 equal rationalsided rt.-angled A'S." I found two, whose sides are 20, 21, 29; 12, 35, 37 ; but could not find three.
Side 43 - The Turning- Values of Cubic and Quartic Functions, and the Nature of the Roots of Cubic and Quartic Equations.
Side 81 - Schrbter noticed that the three-cnsped qnartic of Steiner was also the envelope of the connector of corresponding points of two auharmonically corresponding systems, one on a circle, the other on the line at infinity ; and hence he was led to interesting generalisations.
Side 82 - ... paper on this Envelope (see the Educational Times for June) may be readily deduced from the two following properties of the hypocycloid of three cusps : (I.) The chord intercepted by the inscribed circle on any tangent to the curve is trisected externally at its point of contact with the curve. (II.) The two arcs into which the inscribed circle is divided by any tangent to the curve are trisected internally at their points of contact with the corresponding branches of the curve. These may be...
Side 34 - The proof, usually given, that the path of a projectile in vacua is a parabola, assumes the equivalent of the equation to a parabola referred to a tangent and the diameter through the point of contact as axes. The following proof * requires only the theorem, PN