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algebraic angles applied axes axis becomes CAMBRIDGE centre circle coefficients condition conic consequently constant contained coordinates corresponding cubic curve denote described determine differential distance ellipsoid equal equation evident expression factor foci formula four function give given Hence identical inscribed integral intersection Journal known limiting locus manner method notation Note obtain operation parallel particular passes perpendicular plane points positive powers properties proved quadratic quantities quintic radical radius rational rational function reciprocal regard relation remark represent respect result roots satisfied sides similar solution square successive suppose surface tangents theorem theory touch triangle Trinity College values variable
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.