1640 in science

Botany

• John Parkinson publishes Theatrum Botanicum:The Theater of Plants, or, An Herbal of a Large Extent.

  Mathematics

• 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 : an odd prime p is expressible as the sum of two squares.

  Technology

• 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.

  Births

• April 1 – Georg Mohr, Danish mathematician
• December 13 – Robert Plot, English naturalist and chemist
• Elias Tillandz, Swedish physician and botanist in Finland

  Deaths

• December 22 – Jean de Beaugrand, French mathematician