Discourses and Mathematical Demonstrations Relating to Two New Sciences
TL;DR
Surface area scales as length squared, volume as length cubed
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First articulation of the square-cube law and its implications for animal scaling. Galileo demonstrated that giant animals couldn't simply be scaled-up versions of small animals - their bones would shatter under their own weight. This fundamental geometric insight underlies all modern scaling theory.
Key Findings from Galilei (1638)
- Surface area scales as length squared, volume as length cubed
- Structural strength (proportional to cross-section) can't keep pace with weight (proportional to volume)
- Large animals require fundamentally different body plans than small animals