Abstract
In this dissertation the most common methods of solution, in which
The Rule of Three is included, are presented. The Rule of Three tasks
have been considered in various manners during the centuries. This
dissertation examines how The Rule of Three, as a rhetorical method
of calculus, is presented in Swedish textbooks from the 17th century
till the beginning of the 20th century. Moreover, a comparative
analysis, of The Rule of Three tasks and their solutions, is presented.
In addition, a variety of other rules are presented and treated as
examples of rhetorical mathematics. Similar to The Rule of Three,
these rules are built on proportionality.
The tradition that Björk started in using proportionality was continued
by Celsius, Beckmarck and Forsell and later by Björling and
Zweigbergk. Zweigbergk’s textbook is excellent from a mathematical
as well as from a pedagogical point-of-view. In Zweigbergks’s
account of Regula de Tri the emphasis is on comprehension and
mechanical skills.
The results of this thesis show that the textbooks can be divided into
three groups, based on their description of The Rule of Three. Group:
1. Include the (textbook) authors who strongly emphasize
algorithms and mechanical arithmetics.
2. Include the (textbook) authors who build their descriptions of
The Rule of Three on the theory of proportion.
3. Include the (textbook) authors who solve The Rule of Three
problems through going back to the unit.