It is well known that the six rotations of an equilateral triangle form a group; that is to say that, if an equilateral triangle ABC occupies a certain triangular space, there are six operations and six only which when performed either singly or in succession will leave the triangle still occupying the same space, but with vertices in different positions. The set of six possible orientations of the movable triangle are drawn below and numbered.

The use of Mathematics we understand as not merely utilitarian applications, such as those by which astronomy is employed in navigation, “whereby our nautical logbooks can be better kept, and water transport of all kinds has grown more commodious”; flight too can be made in the air, but also the cultivation at the same time of the intellect, to think correctly, and arrive at the right conclusion from data which are certain ; and the enlargement generally of the interest in this life.

And so our subject received its name from MA⊖HMATA, meaning disciplined exact knowledge, and formed an important branch in the old University ideal, to teach how to live a life, not merely to make a living. To keep the soul alive, body and soul together, and to cure intellectual timidity, the worst form of cowardice.

Boolean class algebra is a special case of lattice theory and it is well known that the propositional calculus is Boolean. It is also well known that there are sixteen and only sixteen truth functionally distinct relationships between two elementary propositions in the pronositional calculus.