Gabriel Mouton obtained his doctorate in theology in Lyon. However he spent much of his spare time studying mathematics and astronomy. He took holy orders and spent his whole career in St Paul's Church in Lyon.
His most famous work Observationes diametrorum solis et lunae apparentium published in 1670 studied interpolation and a standard of measurement based on the pendulum. His methods of interpolation were similar to those used by Briggs in the construction of his logarithm tables.
Mouton also produced 10 place tables of logarithmic sines and cosines and an astronomical pendulum of remarkable precision.
Mouton was the first to propose the decimal system. He also suggested (1670) a standard linear measurement based on the length of the arc of one minute of longitude on the Earth's surface and divided decimally.
As an astronomical observer he made accurate observations of the apparent diameter of the sun.