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Any two ranges {ABC...} and {A^'B^'C^'...} which are situated on the same or different lines are said to be homographic when the cross ratio of any four points on one range ...

In a chain complex of modules ...->C_(i+1)->^(d_(i+1))C_i->^(d_i)C_(i-1)->... the module Z_i of i-cycles is the kernel of d_i, which is a submodule of C_i.

A quantity which rigorously assumes the value of zero is said to be identically zero. The "identically" is used for emphasis when simply stating that a quantity is (or ...

Three concurrent homologous lines pass respectively through three fixed points on the similitude circle which are known as the invariable points.

An involutive algebra is an algebra A together with a map a|->a^* of A into A (a so-called involution), satisfying the following properties: 1. (a^*)^*=a. 2. (ab)^*=b^*a^*. ...

Given a general second tensor rank tensor A_(ij) and a metric g_(ij), define theta = A_(ij)g^(ij)=A_i^i (1) omega^i = epsilon^(ijk)A_(jk) (2) sigma_(ij) = ...

Using Clebsch-Aronhold notation, an algebraic curve satisfies xi_1^na_y^n+xi_1^(n-1)xi_2a_y^(n-1)a_x+1/2n(n-1)xi_1^(n-2)xi_2^2a_y^(n-2)a_x^2+... ...

The exterior of a knot K is the complement of an open solid torus knotted like K. The removed open solid torus is called a tubular neighborhood (Adams 1994, p. 258).

The latus rectum of a conic section is the chord through a focus parallel to the conic section directrix (Coxeter 1969). "Latus rectum" is a compound of the Latin latus, ...

The inverse curve of the logarithmic spiral r=e^(atheta) with inversion center at the origin and inversion radius k is the logarithmic spiral r=ke^(-atheta).