There are actually two things called a "rule of thirds". One of them divides the canvas into thirds and guides layout, visual masses may be placed inside thirds. "one third land, two-thirds sky, or vice versa" has been a maxim of landscape painting since the eighteenth century, at least. This is really mostly about proportion and balance, and it's been around for a while. The "put the subject ON the line, or the intersection of lines" (which is arguably the exact opposite of of the older rule, note) is the modern one.
Nineteenth century composition in two lines or less?
First, let me recommend Henry Peach Robinson's "Pictorial effect in photography" available for free from books.google.com. It was my first, and it's directly aimed at translating ideas from painting for photographers (albeit b&w glass plate photographers using very very slow orthochromatic emulsions). Google up the paintings he refers to as you read. You'll find fascinating and amusing references to "these damned fauxtographers and their easy to use dry plates are ruining portraiture" as well.
Second, a few hints and samples. A prominent line sloping in one direction should be opposed and balanced by another line sloping in the opposing direction, approximating a triangular shape. This creates a sense of visual stability (always assuming you want it, which maybe you don't). A dark mass may be balanced by a light mass; large may be contrasted and balanced by small; straight by curved. Unity can be aided by connecting contrasting elements with a common one: connect a dark mass to a light one by placing a small spot of light within it, and vice versa. Unity can be created by repeated/echoed shapes, colors, and lines. Unity is desirable but not to the extent of being boring, it must be salted with variety, to taste, to be interesting.
That's some rough ideas, anyways. It makes a lot more sense when you're looking at examples.