^^Euclide. Book1 map.



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.


credits:  A Concept Map for Book 1 of Euclid's Elements >>>

Alexander Boxer and Justace Clutter
Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture (2015)


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.



Book1 propositions.