Consider the following three theorem from Synthetic Geometry:

1  Pappus' Theorem. The double ratio of four lines of a flat pencil is equal to the corresponding double ratio of four points which are sections of the above mentioned four lines with a transversal not incident with the base of the pencil.

2  Pascal's Theorem. If a hexagon is inscribed in a conic, the three pairs of opposite sides meet in collinear points.

3  Pascal - Pappus Theorem. If the six vertices of a hexagon lie alternately on two straight lines, the three pairs of opposite sides meet in collinear points.

This last theorem (number 3) is sometimes called the Theorem of Pappus. Since we already have one Theorem of Pappus (number 1), then to avoid confusion we shall call this one (number 3) Pascal-Pappus Theorem.

We normally write the names in alphabetical order, unless there is some very strong reason to do otherwise. Here the reason is that Pascal's Theorem is more general, while Pappus' Theorem is only a special case of Pascal's Theorem, although historically Pappus discovered his theorem centuries before Pascal discovered the more general theorem.

In Germany, Hermann Hankel (1839-1873) proclaimed the Principle of Permanency in Mathematics which involves the principle of retaining the same formal laws of algebra. This principle states that when expanding mathematical concepts one should strive to retain, if at all possible, the same laws of algebra as in the previous system. In Continental Europe this has been known as Hankel's Principle of Permanency in Mathematics and served as a powerful guideline ever since.

Several years earlier in England, George Peacock (1791-1858) called the justification of the extension of the rules of arithmetic algebra to symbolic algebra The Principle Of The Permanence Of Equivalent Forms. This is basically the same principle as Hankel's Principle of Permanency in Mathematics, only said in a different way.

The Principle of the Permanence of Equivalent Forms never achieved the same fame which Hankel's Principle of Permanency in Mathematics enjoyed among the mathematicians of Continental Europe. Nevertheless, it was regarded in its day as a powerful guideline in mathematics, and it played a historical role in such matters as the early development of the arithmetic of complex numbers.

Here we are justified in writing their names in alphabetical order as Hankel-Peacock Principle of Permanency in Mathematics.

Boyle-Mariotte's Law follows alphabetical order. However, in English speaking countries it is known as Boyle's Law. It is not clear why. Is it called Mariotte's Law in French speaking countries?
 
 

Friday,  12 d  03 me  2004 a,   18 h  32 min  21 s   GMT