## Proceedings of the Edinburgh Mathematical Society, Volumes 18-20 |

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angle applied axes B.Sc centre circle circumscribed College common condition conic conjugate considered coordinates corresponding cosC curve decimal definition determinant difference direction Edinburgh ellipse equal equation expression figure fixed four fractions function geometrical George Gergonne point given gives Glasgow greater harmonic Hence infinity inscribed integral intersection isotomic conjugate JOHN less Limit magnitudes Mathematics means measure meet Member method Note obtained obvious pairs parallel passes plane polar pole positive problem Proceedings Professor proof proportion proved quantities ratio reference relation respect result School sides similar sinh Society solution space square straight line suppose surface tangent theorem third touches transformation triangle University vanishes vertices write zero

### Popular passages

Page 2 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 19 - And as one of the antecedents is to its consequent, so is the sum of the antecedents to the sum of the consequents; [V.

Page 25 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means.

Page 2 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Page 21 - After some analytical discussion, Prof. Sylvester adds : " My reader will now be prepared to see why it is that all the geometrical demonstrations given of this theorem are indirect, I believe I may venture to say necessarily indirect. It is because the truth of the theorem depends on the necessary non-existence of real roots (between prescribed limits) of the analytical equation expressing the conditions of the question ; and I believe that it may be safely taken as an axiom in geometrical method...

Page 23 - 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 19 - 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 57 - 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 73 - ... 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...