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accurate algebraical prime factor angle approximation complete quotient congruence convergent corresponding cos'a cosh cosV cot'a cotr ft criterion cubic residue cycles deduced denote determinant discriminant displacements elliptic functions elliptic integral equal equianharmonic exact differential expression follows formula fractions geodesic given gives group of degree Hence Hessian hypersphere inclusive invariant of degree irreducible invariant Jacobi latitude linear negative non-residue number of interchanges numerical multiple obtained octavic character pairs paper plane primitive root proved quadratic form quadratic function quadratic residue quadric quantities quartic quintic rational integral reciprocal factor reduced reduced latitude respectively result rows and columns satisfy sectorial point sextic sin'a sina0 sinh sinV sphere spheroid square subgroup of order substitution suppose synodic periods tana tangents terms free theorem transform tres ft triangle values vanish variables write zero zonal point
Page 50 - ... the three angles of a triangle are together equal to two right angles, although it is not known to all.
Page 72 - Q 1. W. BURNSIDE. On two theorems in elementary kinematics. 1. Successive translations along the sides AB, BC, CA of any finite triangle, represented by AB , BC, CA in magnitude , are equivalent to a rotation round A, through an angle equal to the difference between the sum of the angles of the triangle and two right angles. 2. Successive translations along the sides AB , BC , CA of any finite triangle , represented by 2AB , 2BC , 2CA in magnitude , are equivalent to no displacement at all. For...
Page 58 - ... 0. The author confines himself to a generalization of the ordinary properties of the triangle (p. 49—59). B 1 a. M. JENKINS. On a shortened rule for ascertaining the sign of a given term of a determinant ; and on some problems in which the application of the rule occurs (p. 60—68). I 2 b. G. OSBORN. On a property of prime numbers. If...
Page 63 - Journ., vol. 55 and 56), but there is a slight increase of generality, as in his papers the possibility of a function occurring in the subject of integration without its derivatives is not considered. Three cases are considered, the first being the ordinary one with one dependent and one independent variable, the second that with several dependent variables and one independent, the third that of a multiple integral with several dependent variables (p. 65
Page 55 - On a System of Triple Algebra and its application to the Geometry of three dimensions. — * JA de Morgan , Trigonometry and double Algebra. London. 1849. 8°. 9S) Over de theorie der „Triplets
Page 100 - ... or both divergent, where a is any positive integer not less than 2. There is a clear reason why a cannot be un'ty, for then 2д'|Дя") = 2/(l), which is alwa>s infinite. It is proved in Chrysial's
Page 55 - C 1 f . EJ NANSON. Conditions that a quadric may be one-signed. In a former paper (Rev. sem. IV 2, p. 97) the conditions that a quadric may be one-signed for all values of the variables which satisfy given linear homogeneous equations, were deduced from the well-known conditions of Dr. Williamson for the case in which all variables are independent The object of this paper is to give a direct investigation of the general problem (p. 57 — 62). L2 17 d. EJ NANSON. The content of the common selfconjugate...
Page 183 - ... account. 2. There is no effusion of lymph or creation of fresh surface during the operation. If there is any foundation for the growing feeling among surgeons that there lurks a possible danger in these operations of accidental re-implantation of cancer cells, this is a matter of prime importance. It is, perhaps, not superfluous -to call attention to the fact that according to such a conception the ordinary asepsis against bacterial invasion constitutes no barrier to cancerous re-infection, but...
Page 38 - He considered (349-60) their residues modulo p", and proved (pp. 361-6) that if (n)r denotes the number of combinations of n things r at a time...