1. Descent with modification: This is the idea that all living things share a common ancestor and that over time, species have changed and diversified through a process of gradual evolution. This is driven by natural selection.

2. Natural selection: This is the mechanism by which evolution occurs. It states that individuals with traits that make them better adapted to their environment are more likely to survive and reproduce, passing those advantageous traits on to their offspring. This leads to a gradual change in the characteristics of a population over time.

These two ideas were revolutionary at the time, and they continue to be the foundation of modern evolutionary biology.