In the first volume of Gergonne's Annales de Mathématiques (1810–11), there is a paper by Lhuilier, in which he gives properties of the right-angled spherical triangle, analogous to the following properties of the right-angled plane triangle:

1. The square on the hypotenuse is equal to the sum of the squares on the other two sides;

2. If a perpendicular be drawn from the right angle to the hypotenuse, the square on each side is equal to the rectangle contained by the hypotenuse and the adjacent segment of the hypotenuse;

3. The squares on the sides are to one another as the adjacent segments of the hypotenuse;

4. The square on the perpendicular is equal to the rectangle contained by the segments of the hypotenuse;

5. The hypotenuse, the sides, and the perpendicular are in proportion.