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a₁ ab² abelian ac² algebraic angles anharmonic ratio axes B₁ biquadratic C₁ CAMBRIDGE centre circle circumscribed coefficients conic conic section conjugate conjugate line constant coordinates corresponding cose cosy covariant cubic curve degree denote differential ellipsoid equal equation expression factor foci following theorem formula geodesic geometrical given Hence inscribed intersection Intrinsic Equation JAMES COCKLE Journal Lemma line of curvature locus notation obtained P₁ perpendicular point of contact polar properties proved quadratic quantities quintic radical axis radius rational function reciprocal represent respect result roots sides solution theory triangle trilinear coordinates Trinity College V₁ values variable velocity WILLIAM WALTON x₁ Y₁
Σελίδα 267 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base, equal to one another, and likewise those which are terminated in the other extremity.
Σελίδα 275 - THE foci of a conic are the points of intersection of the tangents through the circular points at infinity ; the pair of tangents through each of the circular points at infinity is a conic through the four foci ; and we have thus two conies P = 0, Q = 0 passing through the four foci ; the equation of any other conic through the four foci is of course P + \Q = 0 ; and in particular if X.
Σελίδα 16 - On the Argument of Abel, respecting the Impossibility of expressing a Root of any General Equation above the Fourth Degree by any finite Combination of Radicals and Rational Functions".
Σελίδα 117 - ... in all directions. For those having lower degrees of symmetry, the following proposition is true. THEOREM I. In an elastic substance which is homogeneous and symmetrical with respect to molecular action, there are three directions...
Σελίδα 368 - The locus of the foot of the perpendicular from the focus on a moving tangent is the circle on the major axis as diameter. 3. The locus of the point of intersection of perpendicular tangents is a circle with radius Va>
Σελίδα 381 - June). [Note on the value of certain determinants, the terms of which are the squared distances of points in a plane or in space.
Σελίδα 369 - Thus from the theorem that the locus of the foot of the perpendicular from the focus on the tangent of a conic is a circle, we deduce (as Mr.