Involution
The term “involution”
in mathematics was coined in the late eighteenth century, a term which had gone
out of favour by the twentieth century. It is a oneword term for taking a
numerical value and multiplying it by itself several times. In other words it
is raising that numerical value to some power.
The wording
of Macdonald’s definition of involution seems to have been taken from John Bonnycastle’s Introduction
to Arithmetic while the wording of his rule to make a power calculation
seems to have been taken from Nicholas Pike’s A New and Complete System of Arithmetick.
Macdonald
solved four involution problems, one of them incorrectly. Here are the
problems:
Find 
Form of the Answer 
Answer 
35^{3} 
whole number 

(0.029)^{5} 
decimal fraction 

(¾)^{3} 
fraction 

(3 ⅔)^{3} 
fraction 

(3 ⅔)^{3} 
decimal fraction
(3 decimal places) 

Macdonald’s
error may have been a copying error. He found (¾)^{4} rather than (¾)^{3}.