On his return to London in 1818 he applied himself assiduously to the art of engraving, in which he acquired a skill that in after years became a most valuable assistant to his literary labours, and enabled him to illustrate his various humours and fancies by a profusion of quaint devices, which not only repeated to the eye the impressions of the text, but, by suggesting amusing analogies and contrasts, added considerably to the sense and effect of the work.
"Napier's analogies" are the four formulae - tan (A +B) cos = cos l(a - b) cotzC, tan2(A - B) - sin(a - b)cot2C; a (a+b) sine (a+b) tan a(a +b) = cos(A - B) tan1c, tan2(a - b) = s in(A - B) tan2c.
Only one of the four analogies is actually given by Napier, the other three being added by Briggs in the remarks which are appended to Napier's results.
They are, however, so simply deducible from the results he has.given that all the four analogies may be properly called by his name.
- Although the legal basis for the final stage is found in the legislation of the time of Moses (latter part of the second millennium B.C.), it is in reality scarcely earlier than the 5th century B.C., and the Jewish theory finds analogies when developments of the Levitical service are referred to David (I Chron.