Consistent interpretation of Euclid’s comparisons of angles and groups of angles

Establish a consistent formal interpretation of Euclid’s Elements that precisely specifies the objects being compared (such as single angles versus finite collections of angles) and the admissible operations (including equality, addition, and ordering), so that Euclid’s arguments involving comparisons of angles and collections of angles can be read without ambiguity.

Background

The paper argues that standard commentaries often provide historical context but do not directly resolve how to read Euclid’s comparisons of angles—especially when he avoids explicit summation of angles and does not allow straight or reflex angles—within a coherent formal framework.

A consistent interpretation would clarify what “things” are being compared under the common notions and how Euclid’s proofs are meant to proceed when he refers to relations such as being ‘less than two right angles’ without formal angle addition.