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Tinseau wrote on the theory of surfaces, working out the equation of a tangent plane at a point of a surface. He continued Monge's study of curves of double curvature and ruled surfaces. Two papers were published in 1772, one on infinitesimal geometry and one on astronomy. He only published one further paper but continued to correspond with Monge on mathematical topics.
Tinseau campaigned against the French Revolution. He tried to organise uprisings and tried to help the Allied powers against the French armies. He gave the strategic plans of the French armies to the Allies in 1813. He was exiled to England and did not return to France until 1816.
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