1640 in science
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- John Parkinson publishes Theatrum Botanicum:The Theater of Plants, or, An Herbal of a Large Extent.
- The Cape Verde Island of Sal is discovered, originally named "Llana" (meaning "flat").
- The 16-year-old Blaise Pascal demonstrates the properties of the hexagrammum mysticum in his Essai pour les coniques which he sends to Mersenne.
- October 18 – Fermat states his "little theorem" in a letter to Frénicle de Bessy: if p is a prime number, then for any integer a, a p − a will be divisible by p.
- December 25 – Fermat claims a proof of the theorem on sums of two squares in a letter to Mersenne ("Fermat's Christmas Theorem"): an odd prime p is expressible as the sum of two squares.
- The micrometer is developed.
- A form of bayonet is invented; in later years it will gradually replace the pike.
- The reticle telescope is developed and initiates the birth of sharpshooting.
- April 1 – Georg Mohr, Danish mathematician (died 1697)
- December 13 (bapt.) – Robert Plot, English naturalist and chemist (died 1696)
- Elias Tillandz, Swedish physician and botanist in Finland (died 1693)
- Tran, Linh. "Theatrum Botanicum: The Theater of Plants, or, An Herbal of a Large Extent". Texas A&M University Bioinformatics Working Group. Archived from the original on November 5, 2008. Retrieved 2011-04-01.