Unit I: Mathematical Morphology, Magnitude, and Rate of Growth — Summary

Analytical Synopsis — 1917 Cambridge First Edition — Prefatory Note, Epigraphs & Chapters I–IV (pp. v–vi, 1–200)

Overview of Unit I (Prefatory Note & Chapters I–IV)

Unit I establishes the philosophical, dimensional, and physiological foundations of D'Arcy Wentworth Thompson's On Growth and Form (thompson:1917), reproducing verbatim the Prefatory Note, the 1917 Scholastic-mechanical epigraphs, and Chapters I–IV:

  1. Prefatory Note & Epigraphs (pp. v–vi, xvi): Framing the treatise as “all preface,” Thompson unites Stephen Hales, St. Thomas Aquinas (De Potentia Dei, Q. 3, a. 11, aquinas:depot), and Sir Isaac Newton (Principia Preface) to argue that corporeal organic forms arise directly from physical forces acting on matter.

  2. Chapter I — Introductory (pp. 1–15): Answering Immanuel Kant's dictum that chemistry and biology become strict sciences only insofar as mathematics enters them, Thompson critiques purely historical or teleological Darwinism when divorced from physical mechanics and efficient causes.

  3. Chapter II — On Magnitude (pp. 16–49): Develops the Principle of Similitude and Galileo's Square-Cube Law (galileo:1638). Because surface areas (muscle cross-section, bone strength, gill/gut absorption, wing area, capillary surface tension) vary as $L^2$ while mass and weight vary as $L^3$, absolute spatial scale partitions the living world into distinct physical regimes—gravity-dominated vertebrates, capillarity-dominated insects and protists, and Brownian-motion-governed cocci.

  4. Chapter III — The Rate of Growth (pp. 50–155): Investigates growth velocity curves ($dL/dt$, $dW/dt$), Quetelet’s human stature curves, autocatalytic S-shaped trajectories, seasonal periodicities, and differential growth gradients—the temporal engine that drives Chapter XVII’s coordinate deformations.

  5. Chapter IV — On the Internal Form and Structure of the Cell (pp. 156–200): Models the mitotic spindle, centrosomes, and karyokinetic asters via physical lines of force (magnetic, electrostatic, osmotic, and hydrodynamic tension fields) within the protoplasmic colloid.