48 propositions | = 14
+ 34 |
technological constructions. logical inferences deduced from the diagrams we can construct. |
Es construction, prop1Book1
Es inference, prop5Book1
In isosceles triangles:
The blanket term “Proposition” does not come from Euclid,
in Greek
simply they appear as a numbered list without any headings.
Nevertheless, Euclid distinguish 2 classes of propositions in how their proofs are concluded
Unfortunately, in its transmission through Latin and then into modern languages, these phrases are usually contracted to the catch-all
thereby erasing this important clue about the 2 types of propositions. Some English editions of Euclid preserve the distinction by calling one type “problems” and the other type “theorems”; we prefer the terms “technological constructions” and “logical inferences” — or just “technologies” and “inferences” for short — as these terms emphasize the distinction more clearly.
Book 1 of Euclid's Elements begins with just a few simple assumptions and culminates in a profound statement about our universe — the Pythagorean Theorem. We have created a concept map of Book 1 designed to illustrate graphically this remarkable logical sequence. We hope that our effort, although preliminary, will be of interest to math teachers, devotees of the history of math, and anyone who deals with the graphical display of relational data.