Proceedings of the Edinburgh Mathematical Society, Volumes 23-24Scottish Academic Press, 1905 - Electronic journals |
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Common terms and phrases
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
Popular passages
Page 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.
Page 54 - Theorem that the Arithmetic Mean of n Positive Quantities is not less than their Harmonic Mean [Title].
Page 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.
Page 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.
Page 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.
Page 43 - The Turning- Values of Cubic and Quartic Functions, and the Nature of the Roots of Cubic and Quartic Equations.
Page 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.
Page 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...
Page 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