Visual & Euclidean Glossary

Technical Vocabulary of Pointer-Free Visual Notation & Classical Geometry

Alternando (ἐναλλάξ) (Alternate Proportion · Book V, Prop. 16)

The proportional inference from : ∷ : to : ∷ : for four magnitudes of the same kind.

Apodeixis (ἀπόδειξις) (Deductive Demonstration)

Fifth of Proclus's six parts of a proposition; formatted by Byrne as a vertical sequence of symbolic equations (=, +, ∴, ∵) with marginal :just: citations.

Congruence-Twin Coloring (Symmetric Register Sharing)

Byrne’s intentional assignment of the identical color/stroke token to two distinct symmetric magnitudes that are given or proved equal—for example, both equal legs () and both produced extensions () in I.5.

Ekthesis (ἔκθεσις) (Setting-Out / Given Block)

Second Proclean division of a proposition, exhibiting the concrete colored geometric datum on which the construction and proof operate.

Extreme and Mean Ratio (ἄκρος καὶ μέσος λόγος) (Golden Section · φ)

Division of a finite straight line so that the whole line is to the greater segment as the greater segment is to the lesser ($\phi = \frac{1 + \sqrt{5}}{2}$)—constructed by colored area subtraction in II.11 and by Book VI application of areas in VI.30.

Gnomon (γνώμων) (L-Shaped Parallelogram Complement · Book II, Def. 2)

In any parallelogram, either of the two parallelograms about the diameter together with the two complements—colored by Byrne in II.5–II.8 as an explicit composite region.

Pointer-Free Visual Notation (Pass-by-Value Geometric Grammar)

Byrne’s 1847 elimination of alphabetic vertex labels (A, B, C) in favor of inline colored vector tokens whose visual form and pigment directly denote the corresponding part of the diagram.

Chromatic Register Pressure (Four-Color Disambiguation Limit)

The threshold encountered whenever a configuration contains more than four primitives of the same geometric sort (such as the five sides of a regular pentagon in IV.11), solved by Byrne via dashed, dotted, and solid-dotted stroke modulation.