How did William Hogarth explain beauty through the serpentine line?

In his 1753 treatise, The Analysis of Beauty, William Hogarth proposed that the "serpentine line"—often referred to as the "line of beauty"—is the essential element of aesthetic appeal.123

Hogarth argued that beauty arises from a "composed intricacy of form," which he believed "leads the eye a kind of chace," encouraging the viewer to actively engage with the work. By advocating for this sinuous, S-shaped curve, he championed the principles of variety, movement, and irregularity over rigid or static forms. For Hogarth, this line served as a shorthand symbol for the inherent expressiveness and complexity found in nature. He believed that by incorporating such dynamic elements, artists could achieve a greater level of vitality and artistic truth in their compositions.14