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 one-word 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:



Form of the Answer



whole number



decimal fraction





(3 ⅔)3



(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.