## Proceedings of the Edinburgh Mathematical Society, Volumes 19-20 |

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Academy anallagmatic angle applied axes axis B.Sc b₁ becomes centre circle circumscribed College common condition conic connected consider constant coordinates corresponding curve D.Sc decimal denote determinant differences direction drawn Edinburgh ellipse equal equation expression figure fixed florins four function geometrical George given gives Glasgow greater Hence integral intersection inversion JOHN latter Limit LL.D Mathematics means meet method obtained obvious opposite original parallel pass path perspective plane point of contact polar pole positive problem Proceedings Professor of Mathematics proof properties proved quantities reference relation represents respect result root School sides similar Society solution straight line Suppose surface tangent theorem touch transformation triangle units University vertices written

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Page 21 - Oakland, Feb. 15, 1874. SIR, — In a Number of the London, Edinburgh, and Dublin Philosophical Magazine for the year 1852 or 1862, is a discussion of a simple geometrical problem by JJ Sylvester, in which this gentleman attempts to illustrate a conjectured principle in the Theory of Geometrical Method. The problem appears to have been given out at Cambridge many years before, and to have excited the attention of some of the first mathematicians of Europe for a number of years. A direct solution...

Page 17 - When two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the third side in that triangle which has the greater angle, is greater than in the other.

Page 55 - Now we saw above that, when multiplying by the units figure, the decimal positions of the figures of the product are the same as those of the multiplicand from which they are derived.

Page 71 - ... direction — 0,. There is, of course, *Theory of Sound, Vol. II, p. 141. considerable difficulty in performing the indicated operations, but this does not diminish the theoretical value of the solution, as the difficulties belong only to the Integral Calculus. The three-dimensional problem in which the edge of the plane is not perpendicular to the direction of the waves has also been treated by Dr. Carslaw.* The next problem in order is that of waves issuing from a point-source against the infinite...

Page 73 - K 8 d, f, L1 1 b. RF MUIRHEAD. Geometry of the Isosceles Trapezium and the Contraparallelogram , with applications to the geometry of the Ellipse. Consideration of the linkage formed by the Contraparallelogram ABCD (AB = CD, BC = DA), AB being fixed (p. 70—72). R 7 b. W.

Page 62 - Investigation about the locus of the centre of a conic, circumscribed about a given triangle , when one of the asymptotes passes through a fixed point P; the locus is a cubic, with a double point in P (p.

Page 56 - ... carry the decimal point all through the working. In fact as, in the method suggested, the units figures are always in a vertical column, the position of the units needs to be indicated only once. The methods of contraction for addition, subtraction, and multiplication call for no remark except that " much time should not be spent in ensuring accuracy in the last figure. Give and take should be permitted to save time.

Page 27 - J o = - n2 f(x') sinnx' dx'. Jo Hence the terms of the series we obtain by term to term differentiation of (2) are equal in magnitude and opposite in sign to those of the uniformly convergent series for f"(x), and these series represent the differential coefficients of the function.

Page 66 - Three foci of a bicircular quartic being given it is shown how the fourth focus may be found and also the relations subsisting between any three focal distances (p.