In 1756, Borda wrote Mémoire sur le mouvement des projectiles, a product of his work as a military engineer. For that, he was elected to the Academy of Sciences in 1764.
Borda was a sailor and a scientist, spending time in the Caribbean testing out advances in chronometers. Between 1777 and 1778, he participated in the American Revolutionary War. In 1781, he was put in charge of several vessels in the French Navy. In 1782, he was captured by the English, and was returned to France shortly after. He returned as an engineer in the French navy, making improvements to waterwheels and pumps.
Borda invented a voting system known as the Borda count, which is still widely advocated by election system reformers around the world. As a contemporary of the Marquis de Condorcet, he engaged in many scholarly debates regarding the merits of their respective voting systems (Condorcet advocated a Condorcet method)