No Direct Link Found Between Babylonian Trapezoids, Mertonian Theorem, and Jupiter — E8 Intelligence Research

FINDING: Search returned pedagogical trapezoidal-rule content plus one arXiv paper on Babylonian trapezoid division; no source directly links Babylonian trapezoidal integration to the Mertonian mean speed theorem or to Jupiter. | MATH: Trapezoidal rule: ∫ₐᵇ f(x)dx ≈ (h/2)[f(x₀) + 2Σf(xᵢ) + f(xₙ)], h = (b−a)/n. Mertonian mean speed theorem (Oresme, ~1350): for uniform acceleration from rest, s = ½·v_max·t, i.e. distance = area of triangle = (1/2)bt. Babylonian trapezoid area: A = ½(a+b)h (attested in BM 85194, YBC 4675 etc.). | CONNECTION: The mean speed theorem is literally the trapezoidal area formula applied to a velocity–time graph: v(t) linear ⇒ s = ½(v₀+v₁)t. The factor ½ is the same 0.5 appearing in trapezoid area; no 0.618/1.618 or base-60 harmonic ratio is evidenced in these findings. Babylonian trapezoid problems do use base-60 arithmetic (sexagesimal), but the search results do not establish a base-60 derivation of the mean speed theorem. | DEPTH: 3 — the mathematical content

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com