Introduction to the
Notebook

John
A. Macdonald’s mathematics school notebook was written by him in 1827 when he
was 12. The notebook is in the genre of cyphering books that have been analyzed
by Nerida F. Ellerton and
M.A. (Ken) Clements in two monographs: *Rewriting
the History of School Mathematics in North America 1607 – 1861: The Central
Role of Cyphering Books* and *Abraham
Lincoln’s Cyphering Book and Ten other Extraordinary Cyphering Books*.
Typically, at this time all students aged 10 or more across Europe and North
America prepared these cyphering books as a method of learning their
mathematics.

The
general format for a cyphering book would be to have a set of sequenced topics
in which each topic has a set of rules followed by cases, model examples, and
exercises. The most common type of cyphering book deals with commercial
arithmetic beginning with basic arithmetical manipulations. John A’s notebook
does not contain any commercial arithmetic. His cyphering book begins with
general properties of numbers and then proceeds to deal with the arithmetic of
vulgar fractions. It culminates with topics in square and cube roots with
applications of Pythagoras’s Theorem to calculating the side of a right-angled
triangle. Macdonald must have learned basic arithmetic prior to writing his
notebook.

There
was a general procedure that was followed to produce a cyphering book; and
Macdonald’s notebook is probably no exception. The teacher would cover a topic
in class. The student would memorize the rule described in class and
demonstrate knowledge by reciting the rule. Then the student would solve set
problems either on a slate or on scraps of paper. Once corrected, the student
was then expected to write out the topic, rules and problems in a fine hand in
the notebook. The fine copy was shown to the teacher at which time the student
progressed to the next topic.

John
A’s notebook indicates a bit of lack of interest setting in in this particular
set of mathematical exercises. He makes a few minor arithmetical and copying
errors deep in the notebook. He also quits the notebook mid topic. The final
topic is cube roots. Macdonald defines a cube root and then has a heading for
the next topic “Application and use of the cube root”. What follows has nothing
to do with cube roots and it was written at least three years after the
mathematical entries in the notebook were completed. The material that replaces
what should be cube root calculations is actually part of a ghost story. The
excerpt from the story that John A copied is a political description of King
Charles XI of Sweden including how the king “changed the entire constitution of
his country,” a foreshadowing of what Macdonald did himself 30 to 40 years
later. Macdonald was apparently just using handy empty pages of his old
notebook. In a later entry in the notebook, Macdonald has copied the words to
the song “Go Where Glory Waits Thee” by the Irish poet Thomas Moore,
best known for the lyrics to “The Minstrel Boy” and “The Last Rose of Summer”.