The Oxford, Cambridge, and Dublin Messenger of Mathematics, Volume 4Macmillan, 1868 |
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a₁ acceleration acnode algebraical anapole asymptotic axes axis B₁ B₂ blank lots C₁ centre of gravity coefficient coincide cone confocal conic section constant coordinates cose curvature curve denote determine double points dx dx ellipse ellipsoid equal equation expression f+gh finite fraction function g+hf geometrical given h+fg Hence horizontal hyperbola hyperbolic paraboloid hyperboloid infinity initial integral intersect limit line joining locus meet moment of inertia motion multiplying nine-point circle obtained orthotomic parabola parallel parcels perpendicular plane point of contact position ratio respectively right angle sides Similarly singular solution straight line surface tangent tension THEOREM things tion triangle ABC trilinear trilinear coordinates unity vanish vertex vertical x₁ Y₁ zero
Populaire passages
Pagina 99 - 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.
Pagina 79 - Mp*, where p is the perpendicular from the centre on the tangent plane Ix + my + nz = p (3), of the ellipsoid (2) ; that is, if we draw a plane perpendicular to the given axis to touch the ellipsoid (2), then p is the central perpendicular on this plane. It is also known* that the moment of inertia about any axis whatever, is equal to the moment about a parallel axis through the centre of gravity, together with the moment which the whole mass, if collected at the centre of gravity, would have about...
Pagina 6 - An elliptic lamina is supported, with its plane vertical and transverse axis horizontal, by two weightless pins passing through its foci. If one of the pins be released, determine the eccentricity of the ellipse in order that the pressure on the other may be initially unaltered.
Pagina 79 - Ix + my + nz=}) (3), of the ellipsoid (2) ; that is, if we draw a plane perpendicular to the given axis to touch the ellipsoid (2), then p is the central perpendicular on this plane. It is also known + that the moment of inertia about any * [From The Oxford, Cambridge and Dublin Messenger of Mathematics, Vol.
Pagina 232 - And consequently : if we take any two finite straight lines not in the same plane, and divide each into the same number of equal parts...
Pagina 20 - P. (ii) 00 bisects PT. (iii) FP, FT are equally inclined to OF. A particular case of § (i) is : If the common tangents of an ellipse and its circle of curvature at P be...
Pagina 76 - Possibly when p is equal to m{ or m2 or n, an interesting special case would present itself. THEOREM LXVI. Let lines be drawn from the angles of a triangle through any two points and terminating in the opposite sides; by joining the extremities of each set of lines so drawn, two other triangles will be formed. The three lines joining the intersections of corresponding sides of these two triangles with the corresponding angle of the original triangle meet in a point. If the co-ordinates of the two...
Pagina 14 - O'K' be perpendiculars on either of the tangents drawn from P to an interior confocal, then . b For PK=PO cos0 = -^.P£ = ^ (fig. 9). Similarly PK' = PG' cos 0 = ~ . PG' = ^ . COR. (i). If a circle has double contact with a fixed ellipse, the length of its chord drawn from either point of contact, so as to touch a fixed confocal, is constant. The centre must evidently lie on one of the axes. Hence if P be one point of contact the centre will be either G or G', according as the points of contact lie...
Pagina 195 - In general, the equation above gives the number of ways in which N things can be arranged in groups, the numbers Ni, N2, etc., representing the number in each group. In the Maxwell-Boltzmann statistics the "things" to be arranged are the phase points, the number of "groups" equals the number of cells in phase space, and the number of ways of arranging the "things...
Pagina 81 - In a manner precisely similar, it may be shewn that if we draw through P an hyperboloid of two sheets confocal to the ellipsoid of gyration, the value of X for its tangent plane at P is a minimum; and therefore that the normal to this surface at P is the principal axis of greatest moment at P. This being so, we know that the remaining principal axis is perpendicular to these two, and is therefore normal to the confocal hyperboloid of one sheet which passes through P. We have proved then that the...