He entered the École Royale du Génie at Mézières in 1769 and graduated as a military engineer in 1771. At Mézières he was a student of Monge who encouraged him to undertake mathematical research. It seems highly unlikely that Tinseau would have become a mathematician but for the inspiring teaching and encouragement of Monge. For twenty years, from 1771 to 1791, Tinseau was an officer in the engineering corps. It was during this period that he was active as a mathematician and we shall examine his contributions below. First, however, let us continue to look at his life through the extremely difficult times of the French Revolution and the Napoleonic era.
Certainly given his noble birth, one would expect Tinseau to be a supporter of the French monarchy and this was indeed the case; he was a passionate supporter of the Bourbons despite the problems that they were encountering. In 1788 the monarchy was in serious difficulties and there was a breakdown in law and order with officials unable to collect taxes. Tinseau joined in the efforts to support the doomed Bourbon monarchy but by this time the situation was out of control. On the fall of the Bastille in 1789, Louis-Joseph, Duc de Bourbon and Prince of Condé was one of the first princes to emigrate and he established himself at Worms in 1791. There he led a collection of émigrés including Tinseau. They raised the émigré "army of Condé" with the aim of opposing the Revolution by military means. Their campaigns of 1792-96 proved ineffective.
Charles-Philippe, Comte D'artois (later Charles X) was the fifth son of the dauphin Louis and Maria Josepha of Saxony. Ordered by his brother Louis XVI to leave France soon after the fall of the Bastille, he went first to the Austrian Netherlands and then to Turin in Piedmont. He was joined by his brother the Comte de Provence (later Louis XVIII) in 1791. Charles-Philippe travelled to Austria, Prussia, Russia, and England. Tinseau also lived in exile and conducted a vigorous campaign in support of the Bourbons and against the Revolution. He published a series of anti-Revolution writings from 1792 onwards and tried to organise uprisings in France, as did Charles-Philippe who made an unsuccessful attempt to land in the Vendée to lead a royalist rising there. Both men had a military career and Tinseau, with the rank of brigadier general, acted as aide de camp to Charles-Philippe. In fact Tinseau supported the Allied powers against France and used his military knowledge to pass on information of strategic importance to the Allies.
Napoleon became First Consul in 1799 and then emperor of the French in 1804. Tinseau was as opposed to Napoleon and all he stood for as he had been to the earlier years of the Revolution. He continued to publish anti-Napoleonic writings but Napoleon tried to offer him an amnesty. This was vigorously rejected by Tinseau who continued to be a devoted supporter of the Bourbons. Tinseau, like Charles-Philippe, lived in exile in England and was offered British nationality by the government. This too was far from what he wanted, striving desperately to be a Frenchman in a France under a restored Bourbon monarchy. After military defeat, Napoleon resigned in March 1814 and the Bourbons were restored to the French throne. Charles-Philippe returned to France after the fall of Napoleon but Tinseau did not return until 1816. By this time he was 68 years old and immediately retired.
Tinseau wrote on the theory of surfaces, working out the equation of a tangent plane at a point on a surface, and he generalised Pythagoras's theorem proving that the square of a plane area is equal to the sum of the squares of the projections of the area onto mutually perpendicular planes. He continued Monge's study of curves of double curvature and ruled surfaces, being in a sense Monge's first follower. Taton writes in  that Tinseau's works:-
... deal with topics in the theory of surfaces and curves of double curvature: planes tangent to a surface, contact curves of circumscribed cones or cylinders, various surfaces attached to a space curve, the determination of the osculatory plane at a point of a space curve, problems of quadrature and cubature involving ruler surfaces, the study of properties of certain special ruled surfaces (particularly conoids), and various results in the analytic geometry of space.Two papers were published in 1772 on infinitesimal geometry Solution de quelques problèmes relatifs à la théorie des surfaces courbes et des lignes à double courbure Ⓣ and Sur quelques proptiétés des solides renfermés par des surfaces composées des lignes droites Ⓣ. He also wrote Solution de quelques questions d'astronomie Ⓣ on astronomy but it was never published. He did publish further political writings, as we mentioned above, but other than continuing to correspond with Monge on mathematical topics, he took no further part in mathematics.
Article by: J J O'Connor and E F Robertson