Born in 1760:

• Japanese artist Katsushika Hokusai.
• Italian composer Luigi Cheribuni.
• Bohemian composer Jan Ladislav Dussek.
• Japanese physician Hanaoka Seishu, inventor of general anesthesia.¹
• Claude Joseph Rouget de Lisle, comopser of La Marseillaise.

Died in 1760:

• King George II of Great Britain. His 18-year-old son succeeds him as George III.
• Prolific German hymn writer Nicolaus Ludwig von Zinzendorf.

Events of 1760:

• French and Indian War/Seven Years' War:
• (May) The French attempt to re-take Quebec but fail.
• (September) Generals Amherst and Johnson move on Montreal:  Governor Vaudreuil surrenders it, along with the rest of new France.
• (September) The last French fort, Fort Detroit, falls soon after. This is the end of the conflict in America.
• The Russians sack Berlin while Frederick the Great is out defeating the Austrians.  Brandenburg landowners refuse to pay any more for Frederick's campaigning.

¹Thanks to mauler for this suggestion.

1759 - 1760 - 1761