Goal: plane and solid geometry on points, lines and circles #2151

Once points (#2149), maps (#2150), a conjugate (#2145) and facts about symbols (#2148) exist, the rest of Modenov's Problems in Geometry (#2131) is a vocabulary over them. It needs no further change to the architecture. In the book's own terms, each item below is one formula from its Chapter V.

• Objects: line, ray, segment, circle, plane, sphere; a pencil of circles.
• Constructions:
  • the foot of a perpendicular, a reflection in a line, the second intersection with a circle;
  • a tangent, a circle through three points, a pole and polar;
  • the compass-only constructions of Mascheroni.
• Measures: oriented area and volume, directed ratio, cross-ratio, power of a point, angle between lines.
• Predicates: collinear, concurrent, concyclic, parallel, perpendicular, tangent, directly or oppositely similar.
• Named points: centroid, orthocentre, circumcentre, incentre and excentres, nine-point centre, Feuerbach point, Lemoine point, the Simson line, the orthopole, the Boutin point.
• Loci: the set a point traces as a parameter moves, as an image set.

Readers of the book counted between 14 and 58 rows for each of these themes per chapter. Their algebraic core, an identity or a determinant, is #2146 and #2147. #746 places geometry with proofs in its applied tier, on top of the polynomial layer. Under #2131's milestones that is 3.2: details within v3's architecture.