Analogous is based on the Latin root word "leg".
leg, in its origin, means “to collect or gather” (particularly using words) as in to "log" or "catalog" and "logos".
an means “on”,
However, ana means “upon”, as in consecutive order. For example, you may put a brick on the ground and then you may put another brick upon it because they are similar shapes and sizes.
So,analogous means to identify things by corresponding similarities. For example, each color in the rainbow sits upon the next one in analogous order.