## The Quarterly Journal of Pure and Applied Mathematics, Volume 6James Joseph Sylvester, James Whitbread Lee Glaisher J.W. Parker, 1864 - Mathematics |

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### Common terms and phrases

a₁ acnode Algebra angle axes axis b₁ C₁ centre of gravity circle coefficients condition cone conic conjugate points coordinates cosec covariant crunodal curvature curve D₁ denote determine differential dv dv dx dy ellipsoid equal equation expression formula frustum function given line H₁ Hence hyperbola inflexions integral intersection logt maxima and minima multiple Nine-Point Circle obtained P₁ P₂ parabola parallel perpendicular plane point of contact Prohessian quadric quadrilateral quantities quartic quartic function quintic equation Representative Notation roots S₁ sides sinx straight line substituting suppose surface tangent ternary cubic theorem tion triangle Trilinear Coordinates values vanish vector whence WILLIAM WALTON zero

### Popular passages

Page 36 - A contribution to the history of the problem of the reduction of the general equation of the fifth degree to a trinomial form,

Page 293 - TrWl=e ........ (10), the equation to the new surface, which is evidently a central surface of the second order, and therefore, of course, an ellipsoid (Cauchy — Exercises, vol. ii.).

Page 294 - If the small displacement of each point of a medium is in the direction of, and proportional to, the attraction exerted at that point by any system of material masses, the displacement is effected without rotation. For if Fp= C be the potential surface, we have Sadp a complete differential ; ie in Cartesian coordinates is a differential of three independent variables.

Page 285 - In the case of a rigid body moving about a fixed point let vr, p, a denote the vectors of any three points of the body; the fixed point being origin. Then or", p*, o-* are constant, and so are S&p, Spa, and Sanr.

Page 317 - OB=-)-m, we find the areas PAOY and QOBY both positive and infinite, which agrees with all our notions derived from the theory of curves. Again, if we attempt to find the area PYQB by summing PAOY and YOQB, we find an infinite and positive result, which still is strictly intelligible. But if we want to find the area by integrating at once from P to Q, we find, as above, - (2 : m), a negative result for the sum of two positive infinite quantities.

Page 293 - V.&<r represents twice the vector axis of rotation of the same group of points. Similarly or is equivalent to total differentiation in virtue of our having passed from one end to the other of the vector <r.

Page 128 - ... the intersection of the lines bisecting the middle points of pairs of opposite sides (say 0) the mid-centre (which, it may be observed, is the centre of gravity of the four angles viewed as equal weights) ; then the centre of gravity is in the line joining these two centres produced past the latter (the mid-centre), and at a distance from it equal to one-third of the distance between the two centres ; in a word, if G be the centre of gravity of the quadrilateral, QOG will be in a right line,...

Page 106 - Prohessian ia considered, but not in much detail, in Dr. Salmon's Geometry of Three Dimensions, (1862), pp. 338 and 426 : the theorem given in the latter place is almost all that is known on the subject. I call to mind that the tangent plane along a generating line of the developable meets the developable in this line taken 2 times, and in a curve of the order...

Page 43 - CONSENT. AMPLISS. FACULT. PHILOS. IN REGIA ACADEMIA CAROLINA PRAESIDE D. ERLAND SAM. BRING, HIST. PROFESS. REG. & ORD. PUBLICO ERUDITORUM EXAMINI MODESTE SUBJICIT SVEN GUSTAF SOMMELIUS STIPENDIARIUS REGIUS & PALMCREUTZIANUS LUNDENSIS. DIE XIV DECKMB.