## The Messenger of Mathematics, Volume 24 |

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becomes binomial theorem circle coefficients coeﬁicients coetﬁcient compartment congruence conic corresponding cosec cosw cubic deduce deﬁned deﬁnition denote determinant distinct solutions elliptic integrals equal equation Euler’s constant expressed in terms ﬁnally ﬁnd ﬁnite ﬁrst minors ﬁrst term ﬁve formula Gamma Functions given gives Hence I I I improper automorph inﬁnite integers J. W. L. Glaisher le Prof left-hand side linear factors log2 log3 log5 log4 logA method modulus multiple number of distinct obtained occurs parabola partial fractions permutations perpendiculaire positive integer present paper prime proper automorph putting quadratic residue quarter-squares ratio relation result right-hand side root of unity roots satisﬁed set of quantities shew shewn Similarly sin(A square substituting this value suppose tangent theorem transformed uneven numbers unity vanish veriﬁed whence write XXIV