1764 in science
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- Lagrange publishes on the libration of the Moon, and an explanation as to why the same face is always turned to the Earth, a problem which he treats with the aid of virtual work, containing the germ of his idea of generalized equations of motion.
- Specific and latent heats are described by Joseph Black.
- The spinning jenny, a multi-spool spinning wheel, is invented by James Hargreaves in Stanhill, near Blackburn, Lancashire, England.
- Early – James Smithson, British mineralogist, chemist and benefactor (died 1829)
- April 3 – John Abernethy, English surgeon (died 1831)
- May 4 – Joseph Carpue, English surgeon (died 1846)
- September 17 – John Goodricke, English astronomer (died 1786)
- October – William Symington, Scottish mechanical engineer and steamboat pioneer (died 1831)
- November 10 – Andrés Manuel del Río, Spanish chemist (died 1849)
- Maria Medina Coeli, Italian physician (died 1846)
- Approx. date – Alexander Mackenzie, Scottish explorer (died 1820)