Page:Carroll - Notes by an Oxford Chiel.djvu/19

Rh

The peculiarity of this process consists in its affecting all quantities alike with a negative sign.

To apply it, let H = High Church, and L= Low Church, then the geometric mean= √$\overline{HL}$: call this 'B' (Broad Church).


 * ∴ HL = B².

Also let ' and ' represent unknown quantities.

The process now requires the breaking up of U into its partial factions, and the introduction of certain combinations. Of the two principal factions thus formed, that corresponding with P presented no further difficulty, but it appeared hopeless to rationalise the other. A &apos;reductio ad absurdum&apos; was therefore attempted, and it was asked 'why should not be evaluated?' The great difficulty now was, to discover .

Several ingenious substitutions and transformations were then resorted to, with a view to simplifying the equation, and it was at one time asserted, though never actually proved,