Leibniz's concept of vis visa (literally translated as living force) was a precursor to our modern concept of kinetic energy. His formula for it was close to the modern non-relativistic one: $mv^2$, but not including factor $\tfrac{1}{2}$.

Vis viva became a bone of contention between the Newtonians and the Cartesians in the 18th century; historians call this the vis viva debates. The debate mixed technical, philosophical, and even theological issues in a manner that seems very strange to modern sensibilities. However, this kind of argument was characteristic of the time.

Can someone provide a summary?

Note: the modern concept of energy (including conservation) only emerged fully in the 19th century, thanks to the work of Helmholtz, Meyer, Joule, William Thomson, Clausius, and others. However, that is a topic for another question (maybe this one).

Leibniz's concept of vis visa (literally translated as living force) was a precursor to our modern concept of kinetic energy. His formula for it was close to the modern non-relativistic one: $mv^2$, but not including factor $\tfrac{1}{2}$.

Vis viva became a bone of contention between the Newtonians and the Cartesians in the 18th century; historians call this the vis viva debates. The debate mixed technical, philosophical, and even theological issues in a manner that seems very strange to modern sensibilities. However, this kind of argument was characteristic of the time.

Can someone provide a summary?

Note: the modern concept of energy (including conservation) only emerged fully in the 19th century, thanks to the work of Helmholtz, Meyer, Joule, William Thomson, Clausius, and others. However, that is a topic for another question (maybe this one).