1759 in science

Astronomy

• Halley's Comet returns; a team of three mathematicians, Alexis Clairaut, Jérome Lalande and Nicole Reine Lepaute, have – for the first time – predicted the date.

Biology

• Caspar Friedrich Wolff's dissertation at the University of Halle Theoria Generationis supports the theory of epigenesis.

Botany

• Kew Gardens established in England by Augusta of Saxe-Coburg, the mother of George III.

Geology

• Giovanni Arduino proposes dividing the geological history of Earth into four periods: Primitive, Secondary, Tertiary and Volcanic, or Quaternary.

Medicine

• June 15 – The first vascular surgery in history is performed by a Dr. Hallowell at Newcastle upon Tyne in England, who uses suture repair rather than a tying off with a ligature to repair an aneurysm on a patient's brachial artery. The new procedure of reconstructing a damaged artery replaces the practice of ligation that had risked the amputation of a limb or organ failure.
• Angélique du Coudray publishes Abrégé de l'art des accouchements.

Physics

• Posthumous publication of Émilie du Châtelet's French translation and commentary on Newton's Principia, Principes mathématiques de la philosophie naturelle.

Technology

• English clockmaker John Harrison produces his "No. 1 sea watch", the first successful marine chronometer.

Transport

• James Brindley is engaged by the Duke of Bridgewater to construct a canal to transport coal to Manchester from the duke's mines at Worsley, in North West England.
• October 16 – Smeaton's Tower, John Smeaton's Eddystone Lighthouse off the coast of South West England, is first illuminated.

Awards

• Copley Medal: John Smeaton

Births

• January 29 – Louis Augustin Guillaume Bosc, French botanist
• July 19 – Jacques Anselme Dorthès, French physician, entomologist and naturalist
• August 12 – Thomas Andrew Knight, English horticulturalist
• September 19 – William Kirby, English entomologist
• December 2 – James Edward Smith, English botanist
• Date unknown – Maria Petraccini, Italian anatomist and physician

Deaths

• February 16 – Bartholomew Mosse, Irish surgeon
• April 6 – Johann Gottfried Zinn, German anatomist and botanist
• July 27 – Pierre Louis Maupertuis, French mathematician
• September 10 – Ferdinand Konščak, Croatian explorer
• November 29 – Nicolaus I Bernoulli, Swiss mathematician