Knowledge & Memory
The Sector as a Proportional Geometry Engine
- Period and origin
- Several late-sixteenth-century contexts; documented by Galileo’s manual of 1606
- What it was built to do
- To carry out arithmetic, geometric, stereometric and military calculations by converting numerical ratios into distances on rays from a common hinge.
- How the mechanism works
- Two jointed legs form an adjustable angle. Corresponding marks at equal distances from the hinge lie on similar triangles when spanned by dividers, so a length taken at one radius reappears scaled at another. Engraved lines choose the numerical encoding.
- Input
- A length set with dividers, and an opening angle.
- Transformation
- Similar triangles: the ratio of the two radii scales the transferred length.
- Output
- A length transferred back off the instrument, read against the chosen scale.
- What is evidenced
- Established: the artefact or the documentary record carries this directly.
- What it demonstrates
- Analog function encoding on a reusable interface - one instrument, many computations, because the scales and not the geometry carry the meaning.
Relationship to other mechanisms
- Next in the series
- The Slide Rule as a Logarithmic Arithmetic EngineNext in the canonical series.
Related article
Sources
- Owner monograph: 09_sector_mathematical_monograph.md
Local copies of third-party material are records, not pages: what is published here is the citation and a paraphrase, never the document.