Proceedings of the Edinburgh Mathematical Society, Volumes 23-24

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Scottish Academic Press, 1905 - Electronic journals
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Page 84 - 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 52 - Theorem that the Arithmetic Mean of n Positive Quantities is not less than their Harmonic Mean [Title].
Page 116 - 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 77 - 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 3 - 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 41 - The Turning- Values of Cubic and Quartic Functions, and the Nature of the Roots of Cubic and Quartic Equations.
Page 79 - 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 80 - ... 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 30 - 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

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