At the rise vs On the rise

at the rise—at the start of smth.; at an early stage in smth.:

• The book portrays American cities at the rise of industrialism.

Note: The expression does not correlate in meaning with the phrase at rise—(Theater) when the rising curtain discloses a scene:

• At rise we see an interview room with a desk and simple furnishings.

on the rise—

1. on the increase:

• The stealing of intellectual property is on the rise.

2. (of prices) going up:

• Now, with an improving economy, gas prices are on the rise.