Transactions of the Cambridge Philosophical Society

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Page 52 - R for which the following conditions are satisfied: (i) ( + b) + c — a + (b + c) and (a . b) . c — a . (b . c) for all a, b, c, e R (associative).
Page 341 - ... Northern and Southern Heights of the Lowlands are better entitled to be so designated than any series of mountains in the Highlands. THE SOUTHERN UPLANDS. — The northern margin of this wide division having already been defined, we may now proceed to examine the distribution of its mountain-masses. Before doing so, however, it may be as well to point out that considerable tracts in Tweeddale, Teviotdale, and Liddesdale, together with the Cheviot Hills, do not properly belong to the Southern...
Page 103 - After determining the second constant he however dismisses the subject with the remark, " This - - - gives the mean radial displacement, a matter which need not detain us here.
Page 56 - Clebsch's lectures; and finally VIII. gives some notes on the geometry of the forms — though apparently any competent expression thereof requires the establishment of new geometrical ideas. IX. gives a list of memoirs on three conies. II. Explanation of the method. The method here followed for obtaining the system of concomitants of a system of ternary forms in terms of which all others can be expressed as rational integral algebraic functions is based on the remark, due to Gordan or Clebsch...
Page 275 - The opposite sides of any hexagon inscribed in a conic intersect in three points which lie on one right line.
Page 99 - ... may be generated as the locus of the points of contact of tangents from у to the bundle bx + Xcza = 0.
Page 46 - Hence, sin A sin В sin С sin a sin b sin c* Ш 78. Law of Tangents. From Art. 42, page 43, we have A 11 — cos A . . tan 2 - \ITcosA...
Page 46 - Vl — cos* a - cos" b — cos* с + 2 cos a cos b cos...
Page 365 - Ari, oft/ occurring in the fundamental curve F(x, y) = 0 mark on this ruled quadrant, or chart, the point whose coordinates are x = r, y = s. Call this point a curve point, the original points being called merely unit points. Then it is possible to form a polygon each of whose sides shall begin and end in a curve point, which shall be everywhere convex, and have all the curve points (other than those on its sides) in its interior. For example we may take the cases (i) (2) witli thtj diagrams...

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